So, the next topic is computational heat convection. So, we started with the first module computational heat conduction then we moved on to the second module computational heat advection and then we are going to the third module it is computational heat convection. Now, this is just a combination or coupling of the first and the second module. So, in the first module you had conduction heat fluxes in the second module you had enthalpy fluxes. So, here we are taking the addition of those two fluxes here again as I had. So, the way the lecture is proceeding is the same way which I had done in the previous two lectures starting with introduction moving on to finite volume method then discussing the advection scheme followed by solution methodology implementation detail and finally, discussing some example problems. So, in a convection I had mentioned that if the temperature which you feel if you are standing in between ice and fire depend upon the flow direction magnitude of the flow as well as the direction of the flow. And I had mentioned that if the flow velocity is small from the ice side you experience a temperature of 40 degree if it is more you can experience a temperature as high as 10 degree. Whereas, if it is from the fire side the flow velocity is small let us say you experience a temperature of 60 degree, but if it is high you can experience a temperature as high as 90 degree centigrade. So, here the advecting variable or the driver is velocity or which constitute the normal velocity which constitute the mass flow rate and the passenger or the advected variable is temperature. So, this I had mentioned earlier, but this is the just as I am not giving you the lecture notes. So, in my slides I tried to be as much elaborative as possible this is just an explanation of those. Now, where do you find this combination of advection and diffusion? If you look into the energy equation energy equation without volumetric heat generation and negligible viscous dissipation is basically an unsteady advection diffusion equation this is what is shown here. However, if you look into the momentum equation other than the unsteady advection and diffusion term there is another term which is called as source term in computational fluid dynamics which constitutes the pressure gradient. So, here we want to study unsteady advection diffusion or unsteady convection. Now, for that either we if you take the momentum equation we have to assume the pressure gradient which I am not doing here what I am doing is that we will I am taking the energy equation because in this energy equation there is no other term it is a pure unsteady advection diffusion. However, it consists of this flow velocity. Now, this flow velocity. So, right now in this right now the equation which I am showing you is equation for a convective heat transfer problem for force convection not for mixed on natural convection. Now, when you have a force convection situation the energy the coupling between the momentum equation and the energy equation is one way because temperature depends on the flow, but the flow does not depends on the temperature. Now, we want to develop a module for unsteady convection, but if we take this equation what we realize is that there is some velocity which is coming into this expression. Now, if we want to develop this module and if we want to test this module we have to take a test problem where velocity is prescribed a continuity satisfying velocity is prescribed. Although that problem will be hypothetical in nature, but that is a good problem as far as the objective of the our objective is just to test. So, we take a hypothetical problem where velocity is prescribed and then develop a code for this unsteady advection diffusion. So, now let us discuss the numerical procedure for the unsteady advection. Now, for this I am showing you a problem this is the animation which I show that depending upon the magnitude of the flow you the temperature which you feel. Now, the test problem which will be taking up here and actually this is the analytical solution of this problem is given in a book convective heat transfer by Bermister. So, as I said that to solve the energy equation independently without solving the flow because for to solve flow is much more difficult it involves many more things which is the last topic in this lecture and right now we want to avoid solution of flow. So, in this case flow is prescribed and we just concentrate on the solution of convection equation. Now, an analytical solution has been provided for this physical situation and the physical situation is what we call a slug flow in a plane channel. So, the fluid is entering with the velocity u is equals to u infinity and v is equals to 0 left wall is maintained that let us say ambient temperature T infinity bottom wall is hot T w and the right wall it is a fully developed boundary condition dT by dx equals to 0. Now, as far as the flow field which is prescribed is concerned this is the flow field which is prescribed. So, what we are assuming our domain is this rectangular domain where the fluid is flowing there is an inlet there is an outlet at the inlet there is a u the constant there is a velocity in the x direction which is constant and note that all over the flow field we are taking a velocity field such that u is equals to u infinity everywhere and v is equals to 0. So, this is the prescribed field for which we will solve the unsteady advection diffusion which is a convection equation and obtained a we will discuss the formulation solution algorithm implementation detail develop a program then test into this problem. This is the problem which is which you will be solving in today's lab session let us come back to the slide. So, this is the problem which will take for testing. Now, let us go to the finite volume method I will not go into too deep too much detail I will just this is just a revision of whatever has been discussed because the approximation which are involved I had already discussed in case of conduction and advection is just that I am revising it. So, unsteady term there are two level of approximation first level is volume averaging to represent temporal gradient of temperature in a control volume as the value at the centroid second level is temporal gradient of temperature at cell center is calculated by forward difference method the advection term which constitutes the rate of change of enthalpy across the control volume note that the unsteady term in the previous slide constitute rate of change of enthalpy inside note the word inside here and the across in this slide across here when we say across there is an inflow and there is an outflow here in this case enthalpy inflow and enthalpy outflow first level of approximation whenever you have inflow and outflow the first level is surface averaging to calculate the enthalpy flux at the face control volume faces. Second level of approximation is the advection scheme which I had discussed earlier and this is the total advection.  Second level is to calculate the normal gradient of temperature note that here the second level is normal gradient of temperature in previous slide is the value of temperature at face and finally we get this is the unsteady form is the rate of change of internal energy of the fluid across the inside the control volume this is the rate of change of enthalpy of the fluid across the control volume this is the total heat gained by conduction this corresponds to this this corresponds to this and this corresponds to this. So, I had quickly covered the finite volume discretization which is similar to what has been discussed earlier now let us go to the solution methodology here I will discuss study as well as study state formulation there was a question on the oscillation which will be answered in this topic. Now, let us take one dimension situation because in a one dimensional I can show you a detailed expression and convince you that why oscillation occurs. So, the objective is to demonstrate the property of finite volume method for a simple problem which has an analytical solution. So, what is the one dimensional study state advection diffusion. So, this is the advection term says it is a study state. So, you do not have a d by d t term and this is a diffusion term where rho is the density u is the velocity note that here we just we want to solve for this variable phi which can be temperature and v is this velocity is prescribed. So, u is assumed to be constant here now we are taking a problem where we will assume that at x equals to 0 which is the left boundary of the domain phi is equals to phi 0 and on the right boundary of the domain phi is equals to phi l physically what does this represent this advection if you go to the control volume and if you try to understand what does this represent. Let us say if t is temperature then you are right now you are looking into a differential equation, but can you convert this into a control volume formulation can you go back to the control volume and say that this term is coming from enthalpy flux in which phases this is coming from enthalpy flux on the vertical phases this is coming from conduction heat flux on the vertical phases. So, physically it represent a situation where let us say enthalpy transport is balanced by the conduction heat transfer in the stream wise direction the advection in stream wise direction is balanced by diffusion in the stream wise direction. I will take an example in the next slide where this is what does not happen commonly what happens commonly is advection in a stream wise direction is balanced by the diffusion in the transverse direction that is how the boundary layer grows I will show you in the next slide. I will discuss this through an animation let us come to this small window. So, here what you see is a flat plate now here I want to show you that what is the direction of advection and what is the direction of diffusion. So, we are considering free stream flow over a flat plate what is happening when the plate is stationary and the flow is passing across it. So, why action is happening because plate is stationary if plate is moving with the same velocity with which fluid is moving then there will be no action. So, what is the action in fluid mechanics when there is a difference between the velocity of a object and the fluid velocity and it what action means is that it action means velocity gradients if there is no plate there will be no velocity gradient the fluid which is coming it will keep moving with that velocity no velocity gradient no action. As soon as you have a plate which is stationary you end up with a velocity gradient and the action of flow starts. So, what we mean by action is we see a velocity variation as far as physics is concerned and we also see engineering parameter like wall shear stress. Now, let us suppose this plate is hot and the fluid is at ambient temperature then what happens then you also see a temperature gradient. So, now earlier the flow was isothermal everywhere temperature was ambient it was only fluid mechanics problem no heat transfer problem. Now it has also become heat transfer problem and what I am showing you here is what is called as ponderlai thicknesses. Here I would like to draw your attention to there was one question when Professor Puranik was teaching fluid mechanics that why there are two types of two types of viscosity. So, the question was why there are there is separate dynamic viscosity and separate kinematic viscosity. Now, before I explain the situation I would like to go back to that question and then I will come back to this slide. So, let us go to the whiteboard. So, right now I want to discuss about the physical interpretation of dynamic viscosity and kinematic viscosity. The physical interpretation of dynamic viscosity is that it represent internal fluid internal friction. So, it is a basically internal friction coefficient. So, when the fluid is moving in layers with different velocity there is a internal friction which is expressed in terms of dynamic viscosity. Now, let us try to understand kinematic viscosity denoted by mu which is mu by rho or to understand what is kinematic viscosity let us take an example. The example is let us suppose we have a tank which is infinite in this direction y tending to infinity and let us suppose we have a conveyor belt here which is moving with a constant velocity let us say u0 and let us suppose you have water here. Then what happens is that let us suppose after 5 minutes after 5 minutes let us see that the velocity or this velocity is penetrated to what depth let me denote it as delta. So, this is the penetrate this is the depth up to which this momentum is penetrated why this is happening because the depth of this tank is infinite and right now what is happening is a diffusion phenomena. The momentum of that conveyor belt is being penetrated or diffused to the bottom layers of the fluid and it takes time to penetrate. So, this kinematic this penetration depth is directly proportional to square root of kinematic viscosity. So, instead of water if you take oil it has a different kinematic viscosity. So, you can physically interpret kinematic viscosity that it has a role as far as this penetration depth is concerned. So, if a fluid has more kinematic viscosity there will be more penetration depth and a legus to kinematic viscosity there is another term which is there in heat transfer what is that term? That term is thermal diffusivity denoted by alpha which is k divided by rho Cp you can do a same experiment and you can draw the same similar physical interpretation. Let us suppose now you have a slab you have a slab which is infinite which is having a infinite depth and let us suppose this slab the slab initially it is at let us say ambient temperature and the top surface is expressed to let us say some constant temperature let us say 100 degree centigrade. So, now what will happen? Now that temperature now the temperature will be penetrating to some depth. So, let us suppose this is ambient temperature this is Tw and let me denote it as delta T. Now this delta T it is a penetration depth what penetration depth? Here it was momentum penetration depth here it is a thermal penetration depth this is directly proportional to square root of alpha. Why I taken this physical interpretation because this physical interpretation has a role in the growth of the thickness of the boundary layer? Let us come back to this slide.  Here it is different it is basically delta is the boundary layer thickness velocity boundary layer thickness this delta T is the thermal boundary layer thickness and the point I want to emphasize here is if you see the momentum exchange the momentum change if you say the along the x momentum is changing along the x direction. So, the advection of u velocity and in fact there is lot of change of enthalpy of the fluid in the x direction. So, advection of u velocity and temperature in the x which is horizontal which is the stream wise direction is balanced by the this actually right now the velocity gradients which you are getting is in which direction? It is along the flow direction or it is in the perpendicular direction. So, the diffusion momentum diffusion due to which results in momentum penetration and thermal diffusion which results in temperature penetration, but this is diffusion is occurring in which direction? Transverse direction. So, in the most of the real world situation advection in a particular direction is balanced by the diffusion in the perpendicular direction like here advection in the stream wise direction is balanced by the diffusion in the transverse direction. But the example here we are taking is advection is balanced by the diffusion in the same direction. So, this is a you can say hypothetical situation, but this is a good test problem. So, I was in this slide when I finished before T break where I mentioned that in the real world situation most of the time advection of velocity and temperature in stream wise direction is balanced by the diffusion of momentum and thermal diffusion in transverse direction. However, we are taking a test problem just because we wanted the problem to be one dimensional. We had taken a case where advection is balanced by the diffusion in the same direction.  So, what is being shown here is let us suppose we are taking a one dimensional problem. And let us suppose ice is at 0 degree on the left boundary and let us suppose there is a fire at 100 degree on the right boundary. And you know that if there is no flow and if you are sitting exactly in the middle pointed by let us say yellow circle at 4. If there is no flow you experience a temperature of mean of the two which is 50 degree centigrade this is what is shown here. Now, when there is a flow from the ice side the x location at which 50 degree centigrade is experienced will be at x greater than 0.5. Because if you are in the middle now you can see that when the flow starts from the ice side you will start feeling cold. So, the x location at which 50 degree centigrade is experienced will be further downstream. And if the value of the velocity from the ice side is very large then that location will be very close to 1. So, let us suppose if the flow is 1 meter per second if there is no flow let us suppose 50 degree is experienced by node 4. Now, let us suppose flow has started from the ice side then let us say 50 degree centigrade is experienced by the node 5. And let us say that the flow velocity has increased from 1 meter second to 10 meter per second then 50 degree is experienced by node 6. What I want to highlight is that under that situation the change in temperature from 0 to 50 degree centigrade occurs between node 1 and node 6 whereas the change from 50 degree centigrade to 100 degree centigrade occurs in a very small distance. So, under that situation where there is very sharp change in the temperature. Not that here we are talking of convection not pure advection ok. So, the velocities are not very very large still have diffusion vice versa if the flow is from the fire side at 100 degree centigrade. Now, in this case the x location at which 50 degree centigrade is experienced will shift towards x is equals to 0 with increasing velocity. So, when the flow is from the ice side the location at which 50 degree is experienced shifts towards fire side. When the flow is from the fire side the x location at which 50 degree is experienced shifts towards the ice side. Let us come back to the slide. So, that is what is being shown here. Now, why we are taking this one dimensional situation is because this situation has an analytical solution and it is always good that when you are developing a formulation when you are developing a program we take a situation for which we have an analytical solution. So, that when we run our program we can compare with the analytical solution and get a confidence and we can make other people believe in our results. So, as I mentioned physically this represents a situation where advection is balanced by diffusion in the stream wise direction where x is the stream wise direction. Here we define a non-dimensional number which is called a speclet number. It is ratio of strength of advection and that of diffusion. The strength of advection is denoted here by a and is expressed by the product of density and the velocity. The strength of diffusion is expressed in terms of diffusion coefficient divided by the length of the domain and this is the exact solution which you obtained if you integrate the differential equation. Note that the differential equation is this differential equation. So, for this differential equation with this boundary condition where at x equals to 0, phi is equal to phi 0, at x equals to l phi is equal to phi l, this is the exact solution. What you see in this exact solution when peclet number is 0, peclet number 0 means flow is 0. It is a pure conduction or diffusion phenomena. The variation is linear as you know that pure conduction temperature distributions are linear without polymetric heat generation. Whereas as I said when peclet number is greater than 0 means u velocity is greater than 0 which in our example case flow is from the ice side. Then I had mentioned that the sharp change from 50 to 100 degree centigrade occurs in a small distance. So, when the flow is from the ice side initially there is a slow change in the temperature. So, from 0 slowly there is an increase in temperature and suddenly there is a large change near to the accident. Why so much if the flow is from the fire side? There is a slow change in the negative x direction and then when it reaches close to the ice side there is a sharp change. What I discussed physically that is what is coming out from this analytical solution. So, this is what is written here also. So, if left boundary condition value let us say temperature on the left side is less than that on the right side. In case of small velocity peclet number is close to 0 and adduction can be neglected and solution is linear. Where peclet number is very large and it is positive 5 grows slowly with x then suddenly rises over short distance and vice versa for negative values of peclet number. Now the real challenge in this test case is there is a sharp change near to the exit near to the outlet and how to capture it accurately is a real test. This is the finite volume discretization. Now what I will do is that for that differential equation I am showing you the finite volume discretization for different advection scheme. So, in this slide I am taking the central difference scheme. So, when you use a central difference scheme this is the finite difference discretization. I am not sorry not finite difference finite volume discretization do not get confused that I am using a same ball i plus 1 i minus 1. So, this is finite difference however in this case finite difference scheme will also give you the same result because you are taking a uniform grid distribution for the interior grid points. But what I am showing you here is a finite volume discretization where this delta x is the surface area which we are taking sorry there is a mistake here this is not delta x this should be delta y. There is a mistake here you can correct it this is delta y because and this delta y comes will be unity as we are taking a one dimensional situation and here we have used a central difference scheme. I would like to point out that when you apply the advection scheme on the west face and the east face on the east face you get phi capital. So, here you get phi capital E plus phi capital P divided by 2 minus of phi capital P plus phi capital W divided by 2.  Now this linear algebraic equation this is the coefficient of P this is the coefficient of capital E this is the coefficient of capital W which are shown here. So, this you get a linear algebraic equation note that we are talking of steady state convection one dimensional steady state convection and let us see how is the nature of the coefficients.  Now when you look into this expression what you realize is let us suppose the pecklet number is 0 sorry pecklet number is greater than plus 2 then what you see is that this coefficient becomes negative. When pecklet number is greater than plus 2 this expression becomes negative when pecklet number is less than minus 2 this coefficient becomes negative then a situation comes like let us say if you have a equation z is equals to 3x minus 4y if you have z is equals to 3x plus 4y. So, when x increases as well as y increases z increases when there is a plus sign in between 2, but if it is minus sign that is z is equals to 3x minus 4y then when x increases z increases whereas, when y increases z decreases with this what I want to emphasize is the coefficients of the neighbors in the algebraic equations they should have same sign. If you follow the book of numerical heat transfer and fluid flow by Patankar he has given this as a rule that all the neighboring coefficients all the coefficients in fact this a i also should have same sign in fact a i should be equal to sigma a and b a i plus 1 plus a i minus 1 if this rule is not followed then what happens I will show you through example problems. So, with central difference scheme the rule is not been followed the neighbors are all the neighboring coefficients are of not same sign when pecklet number is greater than plus 2 or less than minus 2 note that otherwise it is obeyed. So, only when there is a pecklet number goes out of range if it is within the range minus 2 and plus 2 no problem, but when it goes out of range then the nature of algebraic equation is such that it results into some oscillations which I will show you through example problem this will answer the question which was asked in the next in the last lecture that why there is an oscillation in quick and second order of point scheme right now I am showing you through central difference scheme oscillations, but that this discussion is also applicable for the higher order schemes. Now if you do the finite volume discretization of the same equation in earlier slide it was for central difference scheme in this slide it is for first order of point scheme when you do the discretization you end up with the coefficients here you will see that the coefficients are will always be of same sign because if this u is negative then this minimum will give you 0 and if this u is negative here also this maximum will give you sorry if this u is negative then you will get a negative value and there is a negative sign outside with negative into negative it will become positive if u is negative here the maximum function will give you 0 if u is positive then this minimum function will give you 0. So, this term becomes 0 so you will never get our negative coefficients you will always get a positive coefficient. So, this is following that rule that all the neighboring coefficients are of same sign. So, when fou connections advection scheme is used all the coefficients of the resulting linear algebraic equations are positive thus increase in phi i will increase in the value of the variable will increase the if there is an increase or decrease in the value of the neighbors it will have the same effect on the grid point. So, phi i will increase with the increase in the neighboring phi values phi at a particular grid point will increase if the neighboring value is increasing it will decrease if the neighboring value is decreasing it is having the same effect that is what we want that is what happens physically also and that is what we want to be obeyed in the algebraic equations. Whereas, when you go to the central difference scheme a i plus 1 at when you earlier becomes negative when pecklet number is greater than 2 which will result in decrease in the value of phi i for a grid with an increase in the east neighbor value this result in non physical oscillation as I had mentioned earlier and I will show you through an example problem. So, we have taken we are taking an example problem where the length of the domain is 1 density is 1 u velocity is 1 diffusion coefficient is taken as 0.02 left ball boundary condition is 0 right ball boundary condition is 1 grid size is taken as 12 by 12 with 2 boundary points and 10 interior points if you in this case if you calculate pecklet number which is rho u l by gamma. So, rho is 1 u is 1 l is 1. So, rho u l is 1 divided by gamma what is gamma 0.02. So, if you take the inverse of this it is 50 this is the on a domain this is the pecklet number when you consider total length of the domain. Now, I will want to show you that in this expression the pecklet number which is shown here this is calculated using length total length of the domain or width of the control volume this pecklet number is calculated with width of the control volume. So, we want peck what we call as cell pecklet number not the domain length pecklet number to be less than 2. So, in this case that cell pecklet number is 5 this is what we have to note that this is greater than 2. And for this case let us see what happens if you use the central difference scheme and first order of point scheme. I will show this through an animation which will come in this window. This is a central difference scheme this is a first order of point scheme what I am showing you is that on the x axis you have x coordinate on the y axis you have a value of 5 I will play it once more this is central difference scheme. So, if there is you can see there is an oscillation and this is the steady state result when you use a first order of point scheme is smooth there is no oscillation. Let us come back to the slide and I will show you the steady state solution this is the steady state solution. And in this steady state solution you can observe there is an oscillation in the central difference scheme why because the cell pecklet number is greater than 5 which makes the east neighboring coefficient negative which results in oscillations value going oscillating about 0 by the way this oscillation is occurring in which region which x location what is the flow direction this is the x coordinate flow direction is positive x direction. So, this oscillation is occurring in the between x to between x equals to 0 to 0.5 or between x equals to 0.5. So, it is occurring near to the inlet or it is occurring near to the outlet note that this oscillations are occurring near to the outlet why because near to the outlet it is a sharp change in the temperature from 50 to 100 degree centigrade close from the ice side. So, you know that the location at which 50 degree centigrade is there is close to the outlet and close to the outlet there is a sharp change in the temperature. So, even when pecklet number is greater than 2 it creates problem in regions where most of the action is occurring it creates problem where sharp changes are occurring. So, if you generate a if you are clever enough if you know where real action is occurring you can use a non uniform grid and make sure that the self pecklet number in those regions are less than 2. Note that this I am discussing it for an convection problem where we have one dimensional advection diffusion equation when we solve the Neusdorff equation this is used as a guideline. Although right now whatever we have shown this is for this equation where there is no pressure gradient term. This is not directly applicable to Neusdorff equation which has other than the advection diffusion pressure gradient term but this is used as a guideline when using central difference scheme. Now, this is the now if you in earlier slide what was the grid size 12 by 12 if you increase the grid then what will happen to the self pecklet number? Self pecklet number is directly proportional to delta x rho u delta x by gamma. So, when you have more grid size your delta x reduces. So, your self pecklet number reduces like here in this case the interior grid point in earlier case was 10. Now, it is increased by 4 times. So, the sales size reduces by 1 fourth. Pecklet number reduces by 1 fourth. So, in earlier slide it was 5. In this slide self pecklet number is 5 by 4 and in this case you see that in central difference scheme there is no oscillation and as this case has an exact solution you can see that the central difference scheme result is having an excellent match with the exact solution. They are almost lying one over the other the green sorry the blue line is calculated value or computed value from the code and the black line is the exact solution which I had shown you earlier. This is the exact solution which is plotted there. When you go to the first order of print scheme now what you are seeing is that the result is not matching. Actually if you so the domain pecklet number is right now 50. Now, what I what you do is that go back to that exact solution.  Now, if I want to know create this exact solution which almost goes matches with the first order of print scheme then what I do is that in that exact solution this pecklet number I keep reducing. When I keep reducing the pecklet number in this expression. So, what I am saying is telling is that with the cell pecklet number 1.25 and right now let me tell you that the in this exact solution the pecklet number which is used this is which one cell or domain this is domain pecklet number. So, in that slide domain pecklet number was 50. However, with that 50 pecklet number or domain pecklet number the black line which I am getting from the exact solution the first order of print scheme is not matching. However, let us do one thing let us reduce this pecklet number. So, that black line exact solution will keep on changing and there will be a particular pecklet number for which the steady state solution of the first order scheme almost matches with this blue line and that pecklet number let us suppose in this case if you do an exercise comes out to be 18. So, the result if the result of first order of scheme of a particular at a particular domain pecklet number is matching with analytical solution at low pecklet number. What does that mean? Note that pecklet number is a ratio of strength of advection to diffusion. So, what is the meaning of low pecklet number? Low pecklet number means more diffusion. So, with this I want to highlight that first order scheme has what we call as numerical diffusion. So, due to this numerical diffusion although the domain pecklet number is 50 as it has additional diffusion which is called as numerical diffusion and as pecklet number is inversely proportional to numerical diffusion, inversely proportional to diffusion. So, if diffusion is increasing pecklet number will reduce. So, that is the reason that the solution of first order of scheme matches with the exact solution at a lower value of domain pecklet number at which simulation has been done. As this is not a we are not going into the numerical analysis we are discussing about the numerical methods in CFD here. I am not discussing here the why there is a numerical diffusion in first order of a scheme. For that we have to do Taylor series expansion if you for reference I will suggest you to read the book competition fluid dynamics by JD Anderson where mathematically it has been shown that which terms causes the numerical diffusion. So, the conclusion is the central difference scheme I will take one scheme at a time. So, let us start with the central difference scheme then go to the first order of a scheme. So, the central difference scheme exhibits several severe oscillation which disappears on fine grid as cell pecklet number becomes less than 2. No oscillation occur if pecklet number is less than 2 at every node. Note that this is sufficient, but not necessary condition for boundedness of the solution. Why? Why it is not necessary? The answer is the next point. Oscillation appears only when the solution changes rapidly in the region of high pecklet number as I showed you that where oscillation occurred near to the exit. So, this is condition which is sufficient for oscillation, but it is not necessary because so in the region in which not much action is occurring even if you have large cell pecklet number which is sufficient to cause oscillation, but it is not necessary because if there is not much action, there is not much change then in that region you may not get oscillation. So, it is not always necessary that when you have large pecklet number in central difference scheme you will have oscillation. So, the necessary condition is that in that region there should be large chain in the dependent variable. So, oscillation appears only when the solution changes rapidly in region of high pecklet number. On the other hand when you go to the first order of a scheme this overcomes the problem of oscillation as it unconditionally satisfies the boundedness criteria. I had shown you that in first order of a scheme we get the coefficients which are always positive. So, you will not have oscillations or boundedness problem your values will not go below 0 when oscillation occurs. So, this is robust this does not have that problem it is very good converges characteristics, but it introduces excessive numerical diffusion resulting in poor accuracy especially for convection dominated flows. For example, as I mentioned earlier the result of first order of wind at domain pecklet number of 50 matches with the exact solution of self-pecklet number approximately equal to 18. Thus the stable numerical solution is obtained at the price of truncation error which increases with the increase in the strength of convection. So, this is a very good converges characteristic, but it has artificial or numerical diffusion which reduces the accuracy and this is not goes in a convection dominated flows. Hence the quest for optimal what is the optimal advection scheme which is stable as well as accurate which does not have oscillation and is accurate because central difference has problem of stability and first order scheme has a problem of accuracy. Other promising alternatives are higher order schemes such as second order schemes and quick schemes and quick has been found from the literature to be better as compared to not only second order advection scheme, but first order of wind and central difference. So, I hope that has answered that the question which was asked in the earlier session that why do we get oscillation? We are getting oscillation due to change in the sign of the neighboring coefficients. Now, I am showing you as I mentioned that when there you have a steady state formulation you have two different types of method explicit and implicit. So, this is the expression where we calculate the total heat gain by conduction and enthalpy transport by using the temperature of the previous time level this is fully explicit and this is fully implicit. There is another method which are not discussed as far as which is called as Crank-Nickelson where they give the calculate 50 percent of heat transfer from the using the temperature of the previous time level and other 50 percent from the new time level which is second order accurate in time, but I had not considered that in this lecture. This is the total advection terms which represents total heat in this case it is east outflow minus inflow. So, this will represent total heat lost by enthalpy transport this is inlet minus outlet this was outflow minus inflow this is lost and this is inflow minus outflow this is the total heat gained by conduction and these are the different fluxes which are involved advection flux which is enthalpy flux conduction heat flux. Now, as I said that in pure diffusion there is a stability criteria fusion explicit method for pure reduction there is a stability criteria, but for combined that is convection combination of the two we do not have one equation for. So, what we do is that we calculate two values of time step one for pure diffusion second for pure advection denoted here as delta Td and delta Tc and we take the minimum of this two time step in our computation for a convection problem. Note that even while solving the new and stoke equation this is the way for explicit method we calculate the time step. So, the solution algorithm is first step in all the methods or all the modules is the user input material property geometrical parameter number of control volumes boundary condition inputs and the steady state criteria grid generations when you generate grid basically what we mean is that all the geometrical parameters like width of the control volume surface area volume of the control volume distance of a cell centre from its neighbouring cell centre all those are calculated in this step. Then we calculate time step from the stability criteria mentioned in the previous slide here as I said that we are not solving the fluid flow the problem we take flow field is prescribed. So, we can calculate the mass fluxes we set the initial condition for let us say temperature then the boundary condition before we go for the computation for the next time step whatever temperature we have we take it as an old value in this step we calculate total heat here you can see it is inflow minus outflow it will represent total heat gained by the enthalpy transport when you calculate total diffusion it represent total heat gained by conduction heat transfer I think there is a mistake in this sign this should be positive the way I have taken a here. So, this should be positive because here this is total heat gained by enthalpy transport plus total heat gained by conduction heat transfer this is the total term there should be no negative sign here. So, you can make a correction here and then check for steady state you calculate a value rms value and then compare with epsilon which is practically 0 if it is not reached the steady state go back to the step 7 and continue till it reaches to steady state. So, this completes the solution methodology what is the next thing next thing is the implementation details that I will show you through an animation. So, focus into this window. So, this is a control volume for temperature now this is the grid point which you have used to calculate the conduction heat flex for in the first lecture this is a second lecture first lecture was introduction the second thing is the total right now I am taking it as minus a x so minus a x a x will be heat lost by momentum transport and this is again. So, we are taking the combination of the heat transport by the enthalpy as well as conduction and this are the grid points for green square gives you the total advection diffusion in the x direction and inverted triangles gives you the same value in the y direction. So, we draw equi space horizontal and vertical lines we get certain grid points for temperature inside the domain certain other points at the boundary where we apply the boundary conditions note that we apply conservation law for the yellow circle inside the domain and boundary conditions for the point at the boundary these are the running indices these are the grid points for which we calculate the convection flux in the x direction these are the grid points at which we calculate the convection flux in the y direction and this is the computational stencil. Let us come back to the slide. So, this represents the ad actually I had shown this slide earlier in the earlier two lectures also because there it was in first case it was pure conduction then pure advection now we are taking the combination the loop is this loops I had shown earlier also for conduction pure conduction pure advection, but in pure conduction only you have to calculate q x and q y now here there is a combinations we have to calculate both in the x direction and in the y direction this is calculated on those green square points this is calculated on those red inverted triangle points and this is the balance of the two actually I write I am showing you ax but this adx which I am showing you is a sum of this two ax plus you do you do a balance and then you calculate this adx on each faces which will be the sum of this ax plus qx this is the total convection flux this is the convection flux on the west face which is entering this is the convection flux which is leaving in the x direction you are multiplied by the surface area of that vertical phase delta y this is the total convective heat transfer in the x direction this is the total convective heat transfer in the y direction and this is the total heat gained by convection which is a combination of enthalpy transport and the conduction transport. So, total heat gained by convection you multiply by this value delta T by rho Cp delta V and whatever temperature you get you added with the previous time level temperature. So, this is a pseudo code in the afternoon session you have been given codes for pure advection and convection and for convection you are given two different codes one dimensional and two dimensional. For one dimensional you will see oscillations and in a two dimensional you will solve the problem which I will discuss next the example problem. So, I had mentioned that we are taking a problem where there is a slug flow I had shown you in animation also in the beginning of this lecture of this topic where I had seen that we are taking a prescribed velocity field as u is equals to u infinity v is equals to 0 everywhere. However, temperature is changing because at the inlet temperature is ambient and the top and bottom wall of this channel is maintained at higher temperature Tw. Now, here before going into the results I want to mention that the boundary condition is written in non-dimensional form. So, theta is T minus Tw divided by T infinity minus Tw. So, at the bottom wall this T is Tw. So, theta becomes 0 and at the inlet T is T infinity. So, when T is T infinity theta becomes unity. So, the boundary condition is at the inlet non-dimensional temperature is unity and on the top and bottom wall it is 0 and this is the result which has been obtained at different axial location. This figure shows you the non-dimensional temperature profile at different axial location. There are two result the symbols represent the analytical solution proposed by Burmister. There is a book on convective transfer where this analytical solution is given and the lines here represent the result which has been obtained using the formulation and implementation details solution algorithm which has been discussed earlier. So, the red solid line and this red symbol you can see the line of a scalar as well as the symbol of the same color you can see they are exactly matching. So, which shows clearly that there is an excellent agreement or matching between the numerical and analytical solution. So, this is close to the inlet. So, as you move away from the inlet that so, near to the inlet the center line temperature is close to 1. But as you what happens is that when as the fluid enters heat transfer starts and thus what will happen. So, at the inlet fluid temperature is ambient wall temperature is higher, but as the fluid enters and passes across the channel then slowly the center line temperature will reduce sorry center line temperature will increase, but the way we have not done the non-dimensionalization the value of theta will reduce. So, there is a reduction in the center line temperature. Note that this is at axial location 2, this is at 6, this is at 12 h, this is at 18 h. So, this will continue. So, with this I had shown you the formulation, solution algorithm, implementation detail and the testing for two-dimensional convection problem. We had also taken one-dimensional steady state convection and there at shown you why oscillation occurs in central difference scheme. I had shown you for that there is an analytical solution. So, you can develop a 1D code and test with that problem and when you are developing a 2D code you can test with this problem. For both this problem you had been given a in the afternoon you will be solving both this problem and obtaining similar results. So, for teaching CFD we have given you sufficient material which you can use to prepare your lecture notes. So, with this I had come to the end of this topic and thank you for your attention. Let us have 5-minute interaction. Nithya Meenakshi, Institute of Technology Bangalore please ask the question. Yeah, the question is about the advection code you have developed and this actually tracks the temperature, but here we are not solving the Navier-Stokes equation. Is that right? Yes. So, which means that we can also solve this problem in totality by using the complete Navier-Stokes equation and energy equation? Yes, you are right. Can you just elaborate on this? The purpose is only for benchmarking or? So, the question is right now I have shown you advection taking an example of temperature, but indeed this is applicable for momentum transport and the question is can I elaborate further on it? I would request you to hold on because the next topic which I am taking I will be elaborating all those and there I will show you that the same advection we will apply for momentum transport across the control volume. So, if you have further question you can come back in the evening session. Thank you. Just one more sir, just one more. This free slip boundary condition and far field are the same? Yes, yes. VPCOE by Aramati please ask the question. Yes sir, my question is what is optimal advection discretization? Please elaborate it and what is the procedure for that? Slide number 27. Yes, it is an important and interesting question that what is the optimal advection scheme? As I said that each scheme has certain advantages and certain other disadvantages. So, we to know what is the optimal I will try to give you a flavor that optimal means that ultimately we want to achieve the accuracy by paying a price. So, what price we pay? Price we pay in terms of running the ACs and the computers. So, and unfortunately the optimal scheme is problem dependent in computational fluid dynamics. It is problem dependent, it is dependent on the range of Reynolds number also let us say. For low Reynolds number maybe you can find that first order of print is optimal, but at higher Reynolds number maybe if you can come up with a conclusion that quick scheme is optimal. So, what I am trying to do is that but that conclusion you can only draw if you take up a problem, run your code. However, in general for most of the cases quick scheme is considered to be better as compared to the other scheme as far as the price which we pay and the accuracy which we get. But this is highly dependent on problem and the range of governing parameter. If you want to confirm you have to run your own code for different schemes that is why in softwares you have all those options. We will stop the interaction here.


Good evening, everybody. You are here for the Lake Arlington Gravity Main Part 1 and Part 2 Community Design Meeting. Your project manager is Petima Pujol. We want you to, if you're, I think all of you can see the screen. So, if you have questions now or during the presentation, you can post them in chat and we'll answer those at the end of the presentation. The website link for this project, if we go to the chat, the link is in the chat box and Petima's contact information is also in the chat box. So, I am going to pass this over to Petima Pujol. Thank you, Sally. This is the agenda for today's meeting. I am going to introduce myself and the project design team. I'll provide you the project overview, project location. We'll discuss some of the frequently asked questions and I'll provide you the project timeline. My name is Petima Pujol and I'm a senior professional engineer with City of Fort Worth Water Department and I'm the project manager for this project. My number is<PHONE_NUMBER> and the email address is Pratima.Pujol at Phototexas.gov. D.O.T. Engineering is the design engineering firm for this project and Brian Jarby is the project manager and he's also present in this meeting. There are two parts on this like Arlington Gravity Main project. The first part we are calling it upstream gravity main and the second part is the downstream. The first part is in Council District 8 and the second part is in Council District 5 and I'll show you the locations in the next slide. The upstream gravity main is about 5000 linear foot and it is a 78-inch news sewer line. And the downstream gravity main, which is part 2, is about 3000 linear foot and it is 42-72-inch news sewer line. As you can see on this map here, the bold line over here, that's the part 1 upstream part that starts from just north of... Sorry, the south of Lawn Steffensen Road where it links to our existing sewer line M257 part 2 and then goes north towards and it ends at the Lake Arlington Lift Station. The Lake Arlington Lift Station is under construction right now and it is just north of Freeman Drive. The part 2, the downstream part of this project is over here. It starts between Arkinson Lane and East Rosedale Street and goes east towards and ends near the Cooks Lane and Lancaster Avenue and it connects to the 60-inch existing sewer line. Why we are doing this project, this is one of our master plan project. The green area you see on this map is our Village Creek sewer basin and part of this sewer basin, sewer collection system is at capacity and we need more capacity in this basin. And the increased capacity is necessary because of a projected population for four doors and also for our customer cities of Burleson and Crowley. What happens if the sewer system reaches capacity? Well, many trains since the system in this sewer site is at capacity, it overflows. We also call them way-to-ether overflows. This happens when untreated sewers in the city underground sewer system overflows and they're all sewer is released. Now I'm going to discuss a few of the frequently asked questions. What is a gravity main? A gravity main is a pipe system in which the sewer moves using gravity or just a mother nature. What is the force main? It is a pipe system, but in this system the sewer moves, in this system sewer moves are using the force and the pumps, comparations and this station provide that force, that energy to move the sewer through the pipe system. What is the lift station? Our lift station is a large size pump station where the sewer is generally lifted from the lower elevation to the higher elevation. It is basically an oversized grinder pump. I mentioned you about the Lake Arlington lift station. It is under construction and it is just north of Freeman Drive, south of I-20 and east of England Drive. And part one of this project is going to end on this lift station. Is it a part of bigger project? As I mentioned you earlier, it is one of several master plan projects we have and yes, it is a part of bigger projects. There are several projects linked upstream and downstream of this project. On the part one it links to another project M-257 part two on the downstream and it links to Lake Arlington lift station and force main project. The lift station is under construction. The force main is in design and it is about seven miles long. And the part two of this gravity main project connects to the part of that force main project and the downstream connects to the existing sewer main. I know there are several pieces connecting to it and if you'd like to know more about all these different projects, you can go to these project links and find out more about these projects. This is a design public meeting that makes it for us is to advertise this project for construction, open the base and then come to it, approve the bid to the contractor. And once we have the contract established with the contractor, we'll have a pre-construction meeting with the contractor and the stadium specter. And after that we'll come back to the community again with a Wavex community meeting to update you about the project before the construction. And after that the construction will start. Where can I get more information? You can have more information about this project and city website. There is a link for this project project which we update frequently so you can get updated information from that link. You can also go to www.photo-texas.gov and enter 101311 in the search bar. That's the project number for this project. The link for this meeting video, the project map, the project summary, if you're going to ask questions, it will be linked to the same project grade. Again, my name is Pratima Podial and my number is<PHONE_NUMBER>. And email address is Pratima.podial at photo-texas.gov. And the art engineering is the design engineering firm and Brian Darby is their PM. I also have another number over here for emergency water main bricks and sewer backup. It is a 24-hour service. The number is<PHONE_NUMBER>. And you will have to select option one. You can call the same number for non-emergency uses as well from 7 a.m. to 7 p.m. Monday through Friday. With that, this presentation is complete. If you have any questions, please go ahead. We don't have any questions in the chat right now. I did forget to introduce Sandy Bro. She's the District Director for Council of District 5. Sandy, if you want to say anything? I appreciate y'all being here. I think it's time we go have a cold beer. Craig, did you have any questions? You said you live on the other side of Lake Arlington. Yeah, correct. No, I don't at this time. Thank you. Okay. I think everybody else is internal. Does anybody from the City of Forth have any questions? I don't know whether we said this, Pratima. This is a design meeting. So we will be coming back in, do we have an idea when we'll have the construction community meeting? So we are at 90% design and we are doing our ecological survey. And then probably the construction probably start and fall of this year. So we'll probably come back in August or September and talk about this again and have the actual timeline then and a contractor on board. Yeah. Okay. Do y'all know if this will be online or if it'll be in person? We don't know at this time. I know transportation and public works is trying to work with that that the issue is We are reaching a lot of people we would not reach with the WebEx that don't feel safe coming to a meeting, but we also have people who want in person. So I know that they are talking to our communications department to see if there is a way to do both at the same time. So at this point we don't know, but I don't anticipate us making that move until at least August, September time. Okay. Thank you. Thank you, Brenda. Anybody else? Going once, going twice. Did not. Thank you, Sandy. Okay. I appreciate y'all being here and we will notify everybody again when we have the community construction meeting. Thank you. Thank you.


Still giving here, still giving. Mmm. Delicious. I hope you guys are having a good day. It's been a little topsy-turvy here, but we're gonna get through. Ladies and gentlemen, you have a story. You have a unique, personal, amazing story, no matter how boring you think your life might be. Okay? One of the most common comments that I receive down below or on Facebook or through Snapchat is that my life is boring. It's not worth vlogging. Ho-ho-ho-ho. Pause. Pause. No. Your life is worth vlogging, filming, documenting, sharing with the world. What to vlog? So, okay, before we dive into this topic, what to vlog, go back, pause, pause below, and go back and watch the video from two weeks ago that I made a video about why to vlog. That's really important to go watch that first before you watch the rest of this, because that will explain, and you can fast forward to like the six minute mark in that video, and I really get into the the intricacies of why you should consider or not consider starting a vlog. Okay. What to vlog? You just saw in there, spray paint. Life.  If you're alive, you have a story. I don't care what you say. You've got a story that is worth sharing. Never forget that in there. Never forget that. You have a story and a great story. Don't overthink it. I took some notes down. Keep it simple. When you're trying to figure out, man, I'm busy today. I don't have time to vlog. No. Film the busyness. Film the stress. Film the pulling your hair out, if you'd like, because guess what? That is your life. And that is reality and that is truth. And why sugarcoated? Life is hard. Today was a little hard in here in this, this here derriere office. It was a little hard, just like it was two days ago. But guess what? That's life. All right. Point number two. Point number two. Find your style when you are thinking about what to vlog. Now, I know a lot of people comment, not a lot, but a few people are like, yeah, there's another Casey Neistat. And that's fine. Hey, I'm honored by the comment. Yes. I used to watch Casey. I don't watch. I haven't watched him. I watched him for like three months right when he got going and then maybe another like three to four months, like eight months later. Anyway, I don't watch him anymore. He's great. He's amazing. Maybe Casey's watching me. Hey, Casey, you in there? Hey, hey, hey, you watching me stealing my, no. Casey, you can take my ideas anytime, anytime. No problem. Remember the camera? Okay. So what to blog? Find your style. Whatever that is. It could be very simple filming. It could be very intricate. So point number two, wrap it up. Find your style. It could be black and white videography. It could be close, close, tight micro shots. It could be big, big expansive shots. It could be quick cut, quick cuts. It could you get the idea. I digress. Point number three, make the ordinary, extraordinary. I don't know if I came up with that little phrase. Probably not. But hey, I love it. Make the ordinary, extraordinary. Life is, in my mind, life should be simple. Simplicity, strive for simplicity. So making the ordinary, extraordinary. What does that mean? What to vlog? Don't be afraid to vlog you going out to your car. Remember when I filmed this yesterday? I literally walked out to my car, took an extra two minutes to film those quick cuts for Michael. And just to make it spice it up a little bit. So make the ordinary, extraordinary. Maybe you're cooking lasagna tonight. Film it. Cut it up. Make it interesting to watch. You can do this. You can do this. Okay. Now I have to make one last point before we go home. What I'm getting at is don't be afraid to make the ordinary, extraordinary. All right. All right. Enough of talking. We're going home. What to vlog? I'm going to show you a couple of tricks of the trade. Actually, okay, next week is how to vlog. So I'm going to actually show you how to vlog at the house and be like, okay, I'm walking into the house. This is what is going through my mind as I'm walking into the house. P.S. Happy weekend. I hope it's grand for you. Did someone take get a haircut? Who did? Can I see it? Look at Seth. You look so handsome. What's a vlog? Throwing diapers in the trash can. Seth wants to help. All right. Here we go. And Joseph. Oh, you're going to pull them over. We're going to use the sled to pull the diapers over. Smart. Load me up, he says. Load me up with diapers. This is what you want. Make the ordinary. He comes bearing gifts. Brandon. How are you, brother? Amazing. Good to see you. There it is. Money. Thank you. Okay. It goes nothing. YouTube. Whoa. The pine needles up. Yeah, hold on. Have fun or what? You want to do it again? All right, making the ordinary extraordinary. This is awesome. This was a gift from our neighbors. Remember when the neighbors moved? They gave us all their stuff. That was this is from them. Clean it up. You like it? Good, buddy. Okay, you tell me when I can open them. Pull your hand up like this. We're going for the messy look. So when you have, when you grab some inside, where's the comb? Where's that comb? There it is.  And then so there's if you do it actually do it for one. See like how can you? That's one finger. And then you cut with that. Yes, it went and then you. So what's the difference between going here and there? That's still one finger. I just it was that show me more than one finger.   How long I was those two fingers? It's these two fingers. It's yeah. Okay, show me one finger again. Okay, so one finger was to one. I was doing one figure this way because I just get it away. So it's one finger underneath. Wow. Crushed it.  Hi. Could you do me a solid favor? Come back tomorrow and I'm going to do a better job at answering this question. What to vlog a part two if you if you will. I don't feel like I answered that question really well today and showed you really well today. So I feel like it was a start, but we're just scratching the surface to this question of what to vlog. Now, keep in mind, what's a vlog falls in your court because that's where your creativity comes into play, but I want to do a better job at helping you guys come up with ideas on what to vlog in your life. Don't forget next week is how to vlog and then of course the question the day is if you are a vlogger, what do you like to vlog? Like what do you like to film? And if you're not a vlogger, um, have you ever thought about if I was just going throughout my day? Oh, like that would be kind of cool to film. Is there anything that jumps out at you like a moment in your day? Uh, so that's the question of the day. It's kind of long and winded, but say lovey. All right, tested beauty. Work hard. Love each other. See you tomorrow.


This is a ceremony that has existed for 2500 years, something that millions of people participate in every year to honor those who've gone before. And so today, as over a billion people around the world honor and remember their ancestors, we are here to honor and remember the pioneers from China and around the world who have built Canada and made us who we are today. Today's ceremony is about recognizing how despite past hardship, Chinese pioneers, they have helped shape the Great Provinces into what it is today. A province of equality, a province of opportunity, and a province of respect for all. And thereby working together, we can build an even better future. This is believed to be the first time a provincial premier has participated in a Qingming ceremony. I am extremely, I am extremely proud and heartened that the leader of the province is respecting our culture. From deep from our hearts, thank you so much for being here today. And thank you very much, Minister Wang. They've done so much for our communities the last few years. It's just tremendous. And I'm so happy that we are here today too to help celebrate our Qingming celebration.


Okay, guys. What is up? How are you doing? So with interest rate shooting up, we've got buyer sediment very low right now And we've got market watch calling for 25% less transactions by the end of the summer We do have a lot to talk about here I want to give you my thoughts and I want to tell you where I think the whole is in the market where we can go and get More listings. I know inventory is low and it's really tough to go out there and get listings right now But I feel like there's a massive opportunity and we're seeing it over the last week here At my office with my team. We're having a lot more sellers Tell us that they're thinking about doing something very soon And it's because of what is happening in the market right now So I want to break all this stuff down for you and give you this You know opportunity that I feel like everyone should jump on 100% first. I want to apologize I haven't done a video here in about a week or so. I took my family to Puerto Rico We had an incredible time really unplugged It was the first vacation where it was zero work for me in a long time And I got a little kite surfing in and we just had a really incredible time really checked it out down there Outside of that I am doing cold call wars if you guys haven't seen it It's where we go head-to-head I have two agents go head-to-head and a cold call competition and we've done two of these so far And what I'm gonna do is I'm gonna take the the first eight winners eight different sessions I'm gonna take the eight winners and we're gonna do a bracket style competition sudden death rounds It's gonna be incredible. So we already have two winners and So we need six more So if you would like opportunity to compete in cold call wars right here live on this YouTube channel Then I'm gonna put a link in the description. You can go fill out that form and Hopefully get an opportunity to show us what you got But as far as the market is concerned there's a lot of things going on and The biggest thing right now is interest rates, of course mortgage rates went from they were in the mid threes about five weeks ago Now they're at five percent. That's a big jump now still historically Extremely low. We know back in 1980 1981 interest rates were 18 percent Coincidentally back then was the last time we had inflation like this which just hit 8.5 percent So we're in a very strange place There was a there was a prediction by one of the banks that said that we were gonna settle out at 4.5 mortgage rate and that was gonna be like that through 2024 that's not gonna do anything to this market. That's not gonna cure inflation. That's not gonna Put us in a position where we can balance the real estate market out. I Don't believe that prediction at all. I think there's gonna be something much more dramatic that happens But what I find interesting is that you know with the interest rates coming up We've had low interest rates for so long even lower than what they are now And we've got sellers who couldn't find a place to buy they didn't want to sell because they couldn't find a place to buy Well, that's gonna get worse because now not only are they not gonna be able to find a place to buy They're also locked into a lower interest rate So they don't want to go out there and pay, you know, these high prices weren't record high prices They don't want to go out there and pay these record prices and a higher interest rate than where they are right now we also have the largest generation coming into the prime buying season of home buying years of their life and That's gonna cause more problem with supply and demand So I don't see inventory changing very much But we are seeing sellers that we're reaching out to we're cold calling where we're following up with You know, we're doing our thing and we've had an uptick in the number of sellers that we talked to who have told us Yeah, we're thinking about doing something. We know why because they're they're seeing what's going on, too they see interest rates Raising and there's a lot of uncertainty moving forward for the rest of the year mean it trust me when I did the video about You know Get ready prepare for the upcoming housing crash. There was about half the comments So there's no way you're crazy that the markets are gonna crash us by the way I wasn't saying it's gonna crash All I was saying was that when it crashes regardless of when that is I want you to be prepared for it I don't want you to sit back and you know, do what most agents do kind of just pretend like it's not gonna happen And then when it happens get caught with your pants down No, I want us to be completely prepared and ready to take it on and not only survive but thrive through those moments because that's when I really shot up in my career in 2008 I got back in the business and and you know I took that moment and that's what got me to the hundred deals a year taking advantage of that time and Listen, we may not see that time all the fundamental Indicators in the market say, you know, we have a very healthy markets about half the people in the comments of that video They said yeah, I think it's gonna crash, too. Now. What are they basing that on not fundamentals necessarily? I mean you can figure inflation into the mix you can figure several other things But I really think we're in this place where nobody knows what's gonna happen, you know, and I'm ready for whatever I'm excited about this market. I'm thrilled that we're all here together trying to navigate this market I still stand behind we're gonna lose so many agents the question is and I did that video I'll link that video that we're gonna lose more agents than we ever have before in 2022 Also the prepare for the housing crash market. I'll link those two videos below But the only question is is will we get new aid? And you know as many new agents as we lose in the industry, you know Is that churn gonna hold firm or we're gonna be in a net negative and that positive by the end of the year I Think we're definitely gonna lose a lot of them just due to the fact that I do feel like we're gonna have less transactions I think that that is a very safe bet that we're gonna have less transactions. I don't know about 25% less I know I believe it is realtor.com and some of these others the National Association realtors I think they're calling for more like a you know a four to six percent decrease in transactions this year, but These predictions are just predictions, you know, there were predictions that you know Real estate prices were gonna go down in 2020 in May Zillow and maybe core logic It was said that real estate prices were gonna go down Or maybe core logic had it coming up just a tad Zillow had it at a negative two and we all know what happened in 2020 guys These predictions are just predictions and it really doesn't matter at the end of the day for our business We just kind of go out there work or build our database build relationships help people do what they're trying to do They're always gonna be trying to do something for some kind of reason. We got to figure out what that is So don't let this interest rate spike scare you don't let all these predictions scare you Nobody knows what's gonna happen. We got to stand firm on what we believe and that is Closings are gonna happen every day for the rest of your life regardless of what the market does Transactions will fluctuate there'll be less some years than others But we got to get out there and do what we got to do to build our database and build that business up the quicker we can build our database and build that business up the quicker we're gonna get to consistent transactions and You know hitting our goals so Where I think the hole is in the market the the huge opportunity right now honestly is absentee owners second-home owners vacation property owners investors Those are the kind of property owners who aren't living in the property so they don't have to worry about where they're gonna move to They're not living in these properties. I think this is the biggest opportunity right now because those type of property owners can take The money off the table right we're at all-time highs They can take that profit off the table and then either reinvested they can sit tight They can do whatever you want to do, but I think these type of owners are more apt. There's so many agents out there that are You know going after primary homeowners and they're telling me hey, I got a lot of people that would sell but there's nowhere to buy Okay quit beating that dead horse move over and go 100% and absentee owners vacation property owners investors Second-home owners stuff like that another thing that a lot of agents are coming to me saying is that they have all these buyers And they've wrote multiple offers and they lose every one and they don't know what to do, but they're not doing anything Okay, they're not doing anything to go after sellers to help connect that buyer to a seller And you know our job as a real estate agent is to connect the buyers and sellers And so if you're just sitting on a buyer wedding on things to come on the market to compete with all the other buyers You've only done half your job You've only found 50% of the transaction and you're just basically laying down and saying I'm just gonna wait for something to come On the market you better go all in on trying to connect with these sellers who own the type of properties that your buyer wants You should be doing everything door knocking phone calls letters Emails postcards everything you can think of you need to go all in you should have different projects where you're going after Particular subdivisions and complexes for specific buyers that you have you should be going after all the absentee owners and second-home owners You should be crushing social media. You should be spending an hour or two a day just commenting and liking and creating DMing and just responding and engaging. That's the biggest thing with social media. It's not really the posting and the content It's it's the engaging that you're doing on other people's profiles. Honestly I think that that is the biggest thing and the most overlooked strategy in in You know in the game I've been going harder there and I'm gonna go even harder because I see it paying off So yeah, if you guys are interested in going after absentee owners and stuff like that go to red X red X You can get all the absentee owners They also have for rent by owners which are investors trying to rent their properties get for rent by owners Those are people who own probably multiple rental properties commercial properties so on and so forth These are the kind of clients you want to start, you know stacking up as this market continues to navigate through Whatever direction it's gonna go in it's gonna be very interesting and again I'm super excited about this.  It's the cheapest lead generation source you're ever gonna find and You sit there look at all the people that we do Cold-call words with look at all the people that we do cold life cold-call sessions with these people are getting pickups They're picking up clients and they're doing deals. We have guys that I have two new agents That work with me who close 10 million in their first year I got 20 months in this guy started with me 20 months in he's closed a hundred deals strictly just using red X That's all he does doesn't do social media. It doesn't do anything. He does he does red X. He does the weekly email It's nothing crazy. I'm gonna put a link to my weekly email below that I sent out today You guys use my template guys just use all this stuff. This is free information guys And anything else I could do to help you I'm still answering all my messages on Instagram That's the best place to reach out to me if you need anything and the 60-day challenge People love it. It's going really well and you know, we're getting nothing but incredible reviews. So Don't let this market scare you. That's the whole point of this video You know, there is there's a lot of different data out there and you know I've read through a lot of it and from what I can tell nobody really knows what's gonna happen There's a lot of really smart people that think that we're going for, you know, a big recession, you know coming soon And there's a lot of people who think there's no way that you know, this real estate market can get knocked off. So Listen at the end of the day guys again you keep doing what you're supposed to do and Everything will work out. This is one of the toughest times I would think to be a real estate agent, which is why I think a lot of agents are Not gonna make it, you know through the year Especially when renewals come up they have to pay and go do CEs and different things like that on top of how tough it is as Transactions come down, but I want you guys to keep pushing. I want you guys to keep fighting I want you guys to keep chasing your dreams. All right. We'll see you guys on the next video


Mike, how is Will, have you gotten the test results back, and depending on his health, is it, do you have to weigh the fact that you're eliminated on whether or not you put him on the field? Well, I don't think that that necessarily weighs into, you know, the factor, the decision right now. I want to make sure that one that he can protect himself, that he can do his job up to the expectations that we have and that he, you know, really the most important thing is that any player can protect themselves out there during a game. So it's Monday right now, you know, he's sore obviously like a lot of guys, and we'll see, you know, how things go. Does it factor in maybe to a guy like Jeff or somebody like that who was expected to miss some time, maybe could have forced his way back in had you guys needed in for a playoff push. But now, how does that change your, well, I don't know if, you know, I think everybody's that's out is doing everything they can to get back until, you know, we have to decide to put him on injured reserve for, which would, you know, at this point in time end their season. So that hasn't happened. So I know that everybody that wasn't healthy enough to play in the game is doing everything they can to get back and realizing that, you know, every snap is meaningful, it means something to somebody. And, you know, so I wouldn't exclude Jeff from that or anybody else if they can play, we want him to play. How similar is Will's injury to what Ryan went through these last couple years? I think the mechanism is the same as similar and, you know, those are things that, you know, make it difficult.  Yeah, I mean, just kind of same thing he has been dealing with.  Well, there was a handful, but there was also some, you know, I don't want to, you know, get this, you know, but third and 15 and they handed off for 14 yards, you know, there was a couple of those third down and long situations where some of those yards were had. There were some snaps on first and second down and normal down and distances that weren't good enough. But then there was also, you know, a lot that were. So I think some of the numbers and again, I don't have a percentage, but there's somewhere on third and long where they handed off and we're in a substituted defense and, you know, either way, it's got to be better. There were some missed tackles and, you know, we have to be better all the way around in all three phases. What about on the interior of the D line? Like it seemed like a lot of the runs were between the tackles. What was happening there? The couple that were in inside were, you know, the third and long where, you know, Niko and Arden are playing on third down.  And then there were some good snaps where they tried to cut back and Marlon or Jaleel or, you know, Ciaran Dreher or, you know, one of those guys inside were there. At what point is determination to establish the run turn into stubbornness to do something that's been futile? Well, we don't ever want to be stubborn, but also knowing that, you know, some of those things that allow us to gain yards downfield in the play pass game are also set up through that run game. And, you know, so I don't think it's a stubbornness. We have to be balanced. We have to use those formations and those running plays, you know, to set up some of those play passes down the field and, you know, be able to, you know, create good pockets for the quarterback so that they can deliver to football so whoever's in there can step up and throw the ball downfield. You know, like we did a couple of times yesterday and that we have done, you know, in the past and then have to just try to stay as balanced as possible and let those things marry with each other. We've got to make over in the off season and it hasn't necessarily translated into better play. Do you need to maybe reevaluate what you look for in offensive linemen and how they play? Well, we're just focused on this week right now. We'll worry about and be as diligent as we can in evaluation at every position, you know, in the off season. But, you know, right now we're focused on and continuing to find ways to improve and most importantly find ways to win. And then in the evaluation process, that'll come after the season. Mike, when you talk about the off season and ask about the off season, kind of always pivot every time to worry about the next game or Paul asked yesterday about the offensive line and just talked about protecting as opposed to what happened in the off season. Is the accountability for the fans about what happened with the offensive line this year that kind of dodging a little bit? No. With the offensive linemen, they can talk to some of them. They said that it wasn't anything new that they saw, but they did have problems communicating and just picking up assignments. Is that something that, like, how do you handle the accountability for that? Is that the players, is that the coaching staff, collective? How do you handle that? It's all of it, but it's every single one of us. It starts with me and, you know, we knew that this was a fast defense, like, you know, there's good players, you know.  And if you're not good with your communications or staying, you know, you're good on your combinations. They create penetration, which then makes you loose and everything else. So we've said this, like, there's a call that goes in. At that point in time, it's on the 11 players in each phase to communicate, to work together with somebody to identify the mic, to know your assignment, to strain, to do everything that you can, to put yourself in a position, to protect the guy with the ball, whether it's a run, whether it's a keeper, whether it's a play pass, that's how it goes down, that the coach tries to give them as many details throughout the week and show them some things that are going to help them. And then you have to go out, and if there's new looks that you see, then you come over on the sidelines and you make adjustments or you, hey, this is what's happening now, I know we had talked about this. But for the most part, you know, they were pretty much, that was just structured that we had seen in the previous weeks. When it run at 17 times for 12 yards on first down, is that setting up play action? Are people biting on that, or are they having a fine time stopping the run with what they have up front? Did it establish anything for you to do in play action? We hit a strike behind the linebackers late in the game to Hopkins, so it must have done something. I mean, there was... Was that trade off worth it? Again, we didn't win the game, and you have to understand that some of these play pass protections are also advantageous to allowing the quarterback to move the spot, to change his launch location and give us an opportunity to protect, but also still run a route that we think is going to be good versus their coverage. What's the trade off there in terms of the frequent conversations we had about not being behind the sticks when out of all of those first downs, you're coming out generally at second and 10 or worse? Well, that was, you know, yesterday we've done well, and again, previous weeks of our average gain on first down, whether that be running or throwing it, trying to stay as balanced as possible, and also trying to do, you know, possess the football, try to find ways to win the football game, and didn't work out yesterday. What starts in how much freedom does Will have with the line of scrimmage and has he exercised it a lot to this point in terms of getting you in the right place? I think specifically, I'm thinking of a couple of instances yesterday where it looked like they were bringing run pressures and you essentially ran into it at the end. Yeah, and I think that there is some of that that we have to be able to expand on, or at least, you know, can it and try to, you know, maybe get it to the other side to give us a little better angle. You know, and there's some, you know, relief throws that we can make and things that are in there and, you know, I think it's important just to, you know, as long as everybody's on the same page between him and the receivers or him and the offensive line and what we're trying to do, that's what's most important, and, you know, we'll continue to work on that. Mike, what led you to your torque getting released and did he ask for his release at all? You know, I think we can touch on some of those personnel decisions, you know, at the end of the season. But, you know, we're excited about the guys that are here now and working with them and moving towards them and, you know, finding those guys that we can work with. Mike, I know all the guys, Mike, about finishing the season strong the right way after being eliminated. Yeah, I think that that's probably going to be something I'll try to, you know, make sure I'm consistent with when they come in here, you know, on Wednesday and making sure that, you know, it's not too watered down. I don't know, it's new, it's a new experience for me, you know, so I'll have to give it some thought and try to, you know, make sure that we're doing everything that we can to continue to try to teach them, to develop them, you know, inspire the ones the best that we can. Mike, are Derek's days as an elite running back in the NFL over? I don't think that, you know, I think that, you know, that we understand that Derek's got a certain running style and a great skill set and, you know, we have to be able to get him going and give him some space and get him to the second level and he in turn has to be able to, you know, help the line, help the receivers, help the tight end, you know, it all goes hand in hand, you know, just hand it to a guy and they beat three people, but there's also times where guys make a great cut or guys make a guy miss or Derek Stiff farms a guy, you know, so certainly after yesterday, nobody was good enough, everybody involved. All seven sacks yesterday were in the second half and over time, was there something that they did that made an adjustment that allowed them to get there or is it more breakdowns from the second half that didn't occur in the first half? Well, they, you know, two, you know, two through three quarters.  We'll probably waited it out a half account too late and it wasn't there. Would have liked for Jelinda block a little bit longer, but maybe we can help them out and just say, hey, they got us, they didn't bite up on, you know, the fake. You know, you go by case by case basis. There were some that, you know, tried to throw the ball on first and 10 one time and wasn't open, so it was a sack. So, you know, it's a lot of things. They're down, they show up there and long, you know. So it's just got to be, you know, cleaner, you know, with everybody involved with, you know, how quickly we get open, the concepts that we're giving them, how quickly we get open as receivers, how long and how well we block, you know, the quarterbacks movement in the pocket, all those little things that, again, that all goes into it.  We're currently starting two rookies on the left side of your offensive line that seemed to have a rough day yesterday. A lot of teaching tape there and what's the message to them is that that's bad. They'll keep working, they'll keep fighting, keep improving, try to, you know, keep taking the little details, the technique and, you know, it's not easy developing young offensive linemen, but we'll, you know, at this point in time in the season is what I'm saying with the amount of reps and, you know, where they're at physically, but, you know, working together is something that's critical, you know, using length, you know, not letting them get into your body, you know. But then they had some snaps where they blocked them well too, you know. You think that the last sack of Levis was a hip drop and I wonder if you had any more thoughts on that, I guess Deanna Fales looking to ban it next year? Yeah, I don't have any. It was a sack that led to a player getting injured. Levis, can I talk a little about the interception and how the corner kind of came off of Birx on the deep route and he had an alert, but he threw it to Hopkins. How do you take him through that whole process of, okay, I know Hopkins is a guy that you want to throw it to, but, you know, look at other options as well. I mean, I think just, you know, there's a primary and there's obviously things that you have to do before you throw it there and make sure you're looking out in front of the crosser and, you know, understand that you have time there to set up and, you know, wasn't, you know, we're trying to protect you to get to the edge and allow you to set up and, you know, maybe by doing that, he would be able to see trail and I know that he stayed on the move and, you know, thought he had hop and, you know, it's, you know, we gotta do a better job of protecting the football. So Mike, when it's all about winning, how frustrating is it for you like on Sunday nights when you've lost overtime games at home when there was a missed extra point involved?  I would say that losing is devastating.  Everybody feels better about the work that you put in when you win.   There might be two PITs away from two more wins. Thought about that in terms of how close you are to a different story. I think about a lot of things, you know, so can make points up other ways. You know, Nick's been really good for us. I'm sure he'd like to have that kickback yesterday. I'd like to have a lot of things back. You mentioned how these next three weeks are kind of a new experience for you as a head coach. How difficult do you expect it, or do you expect it to be difficult to keep the same messaging? No, I don't know what the messaging is going to be.   Challenges like keeping them around where it needs to be in these last two weeks? You know, gonna rely on the assistant coaches, rely on our leaders, be great every day, don't be phony, you know, be as authentic as possible and keep teaching them the things that are gonna help them. You talked about guys and how much you expect out of the defensive line because of the money that you pay those players. Using the 11th pick on Peter, are you disappointed with where his play is right now? No, I think Peter's been working hard and you know, again, the player evaluation, you know, we're putting a team together and Peter works, Peter's improved. Not sure what the first part of your question had anything to do with Peter, but we're just, okay, we all have high expectations. That's the nature of this business and we understand that and we need to continue to raise expectations with whoever's out there. What about his playoffs to coach for I guess now or these weeks that I guess you have to rely on why you got into coaching in the first place and competitiveness and love for the little things within the season? Well, certainly love football, I love helping players. Remember that, remember why you got into this and watching them improve and have success and you know, embracing their competitive spirit and making sure that we're doing everything that we can to put them in the best positions to go out and enjoy it, but enjoy it from having success and winning and making plays and it's a fine line each and every week. Do you use these last three games maybe to take a look at guys like Caleb Murphy or Otis Reese and some of them beyond maybe just special teams? I mean potentially, but you know, I don't, not ready to answer that, you know. Is it simply Ryan or do you have to assembly? I don't think, you know, Ryan would, you know, we'll see where we're at based on Will's health and we'll keep you updated. I'm sure every player that didn't finish the game could probably have missed some time and he was one of those players so we'll have to be ready for where he's at Wednesday of practice and moving forward but, you know, when you're not able to finish, you know, then then you have to, you know, then there's always concern. There's guys sometimes that finish the game and then come in with something and then there's guys that leave the game so I know that he wished he could have tried to finish but that wasn't gonna be a possibility. Well, you're not saying that the full review will come at the end of the season but yesterday there was some finality knowing you can't make the playoffs. When you went home last night or came in this morning, is there some, I guess, theme that you think about and why this season is where it is right now or other than you expected? No, no, we're focused on, you know, I appreciate the question I do. I just, we're focused on what we have to do today on who's injured and how they feel and how many guys are sick with the flu and all this other stuff, that's my focus is not going back and evaluating that right now. There's two more home games left and you're eliminated from the playoffs. You talked about high expectations. For what would be the team's message to the fans about the two home games to finish out the season and the belief in the program going forward into future seasons? Well, I think the belief going forward, you know, we can always discuss that.  But, you know, when we take the ball there at the end and three negative plays on defense that, you know, from guys that maybe have been here on the practice squad or just got here, you know, and obviously the plan with great effort is going to rally, you know, a fan base. Winning always is going to be the forefront of what we do. And if we can, you know, eliminate some of the plays that are going to get us beat, and, you know, there's still good football in there, there is. It's all over the place, we go down, we convert a fourth and one on first drive of the game, hit a couple X plays, third and 10, they jump off sides, we snap the ball, Will looks for the flag, we throw it down there to two yard line and we score, like, that's what good football teams do. But then there's just, you know, there's the plays that, you know, aren't consistent enough and not efficient enough. Defensively, get an interception, get a third down, stop. But then we give up some plays that cost us. Special teams, we do a good job, we're protecting a punter and get a penalty at a critical time in a game. So there's a lot of good in there. And again, I know that this sounds like it sounded a couple of weeks ago, you know, but unfortunately there's just a lot of too many, too many examples of the bad football that ultimately you can't overcome.