Good morning. So, about one hour behind schedule on conduction, but that is okay. Convection we have I think some amount of buffer time hopefully, but convection is again a topic which will have lot of questions, lot more questions I think than conduction. So, that is why we have kept about six modules, six sessions for convection. From what we had yesterday in your presentations, I think most universities when private institutions give convection to go by actually in some cases about eight lectures or ten lectures is what we have seen. I think that is a little bit too short for a topic as important as convection. And probably at the BTEC level students appreciate conduction a lot more than convection because convection it may seem actually and that is how I was taught and I think probably that is how you would have been taught. Choose the correct formula, apply it Reynolds number, Prandtl number, choose the correct formula, apply it, get Nusselt number, get H, 10 marks. So unfortunately the physics is completely lost and concept of it is a beautiful subject actually which combines fluid mechanics and heat transfer something which students just do not get the feel of at the end of the heat transfer course. And how to get that into the psych of the students I think that is a very challenging thing because fluid mechanics itself is a little bit difficult subject to teach and how it is taught we do not know, but I think looking at the way it was taught to us I think fluid mechanics also will be given by hand waving you know this is what it is, this is what it is kind of thing. So when fluid mechanics foundation itself is shaky, convection is shakier if there is a word like shakier. So students do not appreciate the point is that students do not appreciate convection, students find it difficult and probably teachers also find it difficult to communicate fluid mechanics they have not done why should I bother about it because it is unfortunately curriculum has become so compartmentalized that the connection is lost and I think we should ensure that the connection is given all the time and when connection is not there I do not think anybody will say what is the use of this every time we should say this is what you did in fluid mechanics see where it is coming here it is exactly the same thing why do not let us see these two together holistically when we are able to get connection between you know what we did in high school A B C D or you know L K G and see this adjective verb adverb all those things we are connecting all the time, but fluid mechanics heat transfer connection or for that matter I think it is the same in strength of materials and design all those things also. So it is very very important to establish that connection when we teach convective heat transfer. So fluid mechanics and these are like the two wheels of a train has to go together one is one cannot be separated from the other. So with that idea all of us I think will introduce convection the same way when there is a bulk motion of the fluid etc. This is what we say what would us to see every convection is one one subject or one topic which I think all of us including the students would have experience in some form or the other meaning h a delta t is that is the simplest equation that you can have q is equal to h a delta t product of three numbers how difficult can it be to get the solution what is so great about this equation why are we spending so much you know 10 lectures 15 lectures on it the problem is q is equal to h a delta t unfortunately that h is what is very very difficult to find. So if I have to get q correctly I have to get h correctly and getting that h correctly is next to impossible but of course nowadays things are much better. So the whole idea is to get that h correctly. So students you know we can say you know you have seen convection in so many applications in real life your hot water diesel you know flow or flat plate etc. is all you know very engineering concepts but whenever there is a flow cooling of some device or all you know cooling of t for example is a convection process you can just say leave it in a room where there is no fan it is going to cool much slower where where you turn on the fan it is going to cool much faster. You you start to feel better when you stand under the fan rather than when you are just without any kind of motion. So basically all these things you know people have experience convection and you can relate to it very very easily. One other thing which you can say is turn on the fan put it in one you do not feel that much better increase the speed you start to feel better why it is just that some quantity which is taking away the heat from the body is becoming better with the increase in the speed of the fan. So that quantity is what we will call by some name called as heat transfer coefficient. So when we give such examples and connect the dots I think it is it is beautiful. So convection for students is actually a scary subject. Now we have we have to remove the fear when we teach it. So all of us know classification this is the Newton's law of cooling. So H A T S minus T infinity T S T infinity are temperature of the surface and T infinity refers to the bulk fluid temperature. Now convection again this H for example is not a material property alone. So stagnant air or stationary air versus moving air will have a different convective heat transfer coefficient all of us know that. So I cool I cool the same cup of T in a stagnant air room where there is no motion of air it is going to take longer whereas I turn on the fan it is going to take a shorter amount of time. So it is the same air it is the same T it is the same T infinity what has changed is the H meaning the heat has been removed at a faster rate. So you get a colder T at a faster rate. So this H therefore is a function of many many many things type of the fluid. So that means all the property is associated with the fluid density viscosity specific heat and also the nature of flow of that fluid. Am I right? So if it is just stagnant air where it is just going around in the room without any pattern or with some kind of a slow pattern then it is a poor cooling. When you apply a force velocity by means of a fan or whatever external means it is a better means. So some characteristic velocity is there. So geometry I keep the same cup of T in a cup versus I pour it on a saucer and keep. So it is going to take a different shape. So the area exposed is also important. So geometry of the surface that is there it is important whether it is flow over a flat plate, flow over some other geometry all these things influence the heat transfer coefficient. Heat transfer coefficient can have values you know natural convection very very small numbers to tens of thousand when you talk of phase change applications. So this H going from 0 to a few thousand values we can classify it based on the type of the fluid. So typically you have values from single digit to a few thousands and what we are saying is heat transfer coefficient for natural or free convection for gases is about order of this is where this order of becomes very important. It is in order of tens you know 10 20 whatever. Liquids natural convection 50 onwards you know force convection slightly higher but gases are on the lower side force convection of liquids it is on the higher side again and boiling and condensation this the different topic anyway where you have the heat transfer coefficient very very high it is very common to get 10,000, 12,000 watt per meter square Kelvin. So with this idea let us just get back to so this H is a very very important concept and accurate measurement accurate value of H is very very important. So of course one other thing what we see in conduction we have there will be several problems which have been solved by the time we come to convection. Heat transfer coefficient of 25 watt per meter square Kelvin 50 watts these are things which were given as numbers to the students to solve the problem but till that time till we come to convection they do not know how it was obtained it is just a black box for them. What we are going to say is we will find out the value more importantly we will try to understand and appreciate the concept of an average value versus a local value of heat transfer coefficient what is this average versus local average means average over the entire geometry surface. So what we have given to the students during conduction course is only the average value H is 25 that is where assumptions become very very important one of the assumptions we will write is uniform heat transfer coefficient over the entire surface. What does it mean whether the plane wall is 10 meters in height or 1 meter in height H remains the same what is given in the problem H remains the same but now when we when we see we will appreciate that H is not going to remain the same what was given was an average value of the heat transfer coefficient. So heat transfer rate this airfoil diagram is very nice here. So it tells me that locally for a given area Das heat flux by convection is Q convicted that is given by H local times T surface minus T infinity. So H local times T surface minus T infinity times Das which represents the surface area associated with this element. Surface area would be this length this small length times width into the plane of the board. So Das times HL times delta T. So assuming the entire surface to be at constant temperature which we can make this assumption this comes out and what I get Q convection is nothing but H average. So I have probably just write this. So Q convicted is equal to H bar or H average surface area T s minus T infinity this equal to integral A s Q double prime convicted T s am I right one is the whole equation other represents an integral based on the heat flux locally. So this I am going to write it as T s minus T infinity A s H local Das. So this is H bar A s T s minus T infinity and I can cancel this off. So I will get H bar or average heat transfer coefficient is nothing but local value integrated with respect to. So till the student studies convection he or she is just going to get an average number which how it was obtained nobody cares we used to just give them a number but this local value. So this local quantity is something which we will now learn to calculate appreciate that it is going to change dramatically because of the nature of flow over the surface and the surface conditions. So this average value is what is used most of the time in engineering applications. Local measurements are very very important and of course lot of experiments are done nowadays to measure the local heat transfer coefficient by measurement of local surface temperature etc. But getting the local measurements is very very difficult. So you have taken that Q double bar convection D A s that is equal to T s minus T infinity into H local.  But in some application we are not finding out the uniform surface temperature and we are taking care of the average temperature of that. Like we are measuring the temperature at different points. Yeah it is here why we have taken this T s minus T infinity outside and understood your question. T s minus T infinity is because I have maintained the boundary condition here as constant wall temperature. Constant wall temperature. Now to come to your question let us say I devise a boundary condition constant heat flux. Then I cannot take this out. Yes. But what will be remaining constant? Q double dash. Q double dash will be same everywhere. T s will be different everywhere. But H also is going to be different everywhere. But so my question is when we are finding out the local heat transfer coefficient should we take the uniform temperature of the plate or? That is what I am telling you. It depends on the boundary condition what we have imposed in our experiment. If I am doing an experiment. But even if we are imposing the boundary condition say for example uniform heat flux which is getting out from the cylinder and we are having the embedded thermocouples over the surface and we are measuring temperature and then taking care of this averaging out. We should not average out. Yeah. We should not. If you average out you get some average heat transfer coefficient. Yes. But we should take local temperature and then get the local heat transfer coefficient. So this is with the assumption that it is a uniform constant temperature only. This is the constant wall temperature boundary condition is imposed here. If there is a variation of the temperature then it should not be T s minus T infinity. T local minus T infinity. That will be inside the integral. Yeah. So that is the expression would be a little bit more complicated. So you will probably have this way just to make it yes. Some T average minus T infinity integral a s h local. This will be T x or whatever coordinate you want to call it minus T infinity d a s. This d a s will also involve the characteristic dimension x. So yeah something like that. So it will not be a simple integral. But nevertheless you can do. We take a couple of temperatures even in our setup on the other day in the manual also says your 6 temperatures for flow over a pipe. I just take the average of those 6 temperatures and calculate the heat transfer coefficient. That is not right actually. That is not right because in Dittus-Polter all of our setups I am sure we would have been maintaining constant heat flux boundary condition. But we average all those temperatures. Averaging those temperatures has no meaning. I should compute heat transfer coefficient locally for everything. So that is what we will demonstrate when we do the experiments also. We should not average the temperatures and then take those temperatures. That is no meaning. We will understand that when we get to developing flow and fully develop the concept. Okay now I think we have to come to fluid mechanics whether we like it or not. So I will just put this slide and then take a recourse to the paper again. So whenever there is a flow everybody understands what no slip condition is. So first thing which we need to tell students. Do you understand what no slip condition is? I think that is very very important. Students probably know it but they do not know it with the correct terminology. So no slip condition does not mean the fluid is at rest at the flat plate. It means the fluid if the plate is moving the fluid also moves with the same velocity. So the relative velocity is 0 at that solid surface. So no slip condition just see fluid mechanics that is why it comes first. We are able to understand things related to velocity a little bit easier. So when there is a solid surface and there is a flow happening, you are going to have what is called as a boundary layer which is formed. What is this boundary layer? Boundary layer is nothing but a region which separates the flow into two parts. It is not a physically drawn plane or something. It is done for our convenience. Why is it done? We are going to see. Boundary what we say is within the boundary layer the effects of the fluid property called as viscosity plays an important role. Beyond the boundary layer viscosity effects are negligible. It is not 0 it does not vanish. It is negligible compared to the other forces which are going to be in place. So what happens in the boundary layer? If I have a flat plate and there is a so u comma t infinity I am just putting this t infinity for now. We will use this also a little later. So I have a flat plate which x is equal to 0 is at this location.  First we will see the fluid mechanics then come to the heat transfer part. So there is going to be what we call as a boundary layer which is formed over the flat plate and locally we will give it a symbol delta within parenthesis x which tells me boundary layer thickness is a function of the x direction. What is this locus of points? This line which I have drawn represents the locus of points at which u over u infinity is equal to 0.99. So what it means is everybody understands and appreciates that the fluid first layer of fluid. I always like to give this example it is like a ream of paper. So the bottom most ream is glued to the solid surface. If the surface moves, the bottom most sheet of paper is also moving at the same velocity. If the surface is stationary, the bottom most layer is also stationary. So same thing is for the fluid. Then I am trying to pull the fluid because there is a flow because that is the boundary condition which you are imposed. So what is happening? The next layer of paper is constrained by the layer below it. So it says I cannot move with the same velocity u infinity. This is pulling me to 0 whereas somebody is pushing me to u infinity. So it will take a value much closer to the solid surface value which is slightly greater than 0 but much further away from u infinity. Subsequent layers will see the effect of the solid plate lesser and lesser. And as I move away from the solid plate which is stationary in this case, this effect or this pull is going to die down slowly. And that is what we say. If I plot this as the velocity profile something like this, next layer is like this, next layer is like this, so on and so forth. And somewhere it is completely free from the presence or the effect of the solid surface. That point we will say is called as the point where we say u is approximately equal to 0.99 times u infinity. Locus of several such points which I am marking by x is will be joined to form the hydrodynamic boundary layer. And I think all students should know this part. I do not think there is any, is there any question on this boundary layer part? Now what is happening within the boundary layer? What is causing this velocity gradient? This is caused because of the inherent property of the fluid which is called as viscosity. What is wall shear stress? Wall shear stress is nothing but tau is equal to mu du by dy at y equal to 0 or at the wall. So the velocity gradient at the wall dictates the wall shear stress. Larger the gradient, larger is the wall shear stress. And how is this calculated? We just have to put it like this in the reverse way and see it. I think this is easy to understand. So this vertical axis now becomes a velocity and this is the y coordinate. So du by dy in this way will give you the velocity gradient. Steeper the line, greater is the velocity. Turbulent flow therefore, we will come to that. I am going little beyond what I should be going. Turbulent flow we will draw a velocity profile which is almost touching like this. We will draw a velocity profile which is like this.  The students do not appreciate it because they are not seeing it in the form du by dy. So all you have to do is flip the paper, rotate it and then you will see du by dy is much steeper slope for turbulent flow than for laminar flow. These are all things which we have suffered as students. So we should not make them suffer again. So now if I have this velocity boundary layer, there should be something similar in thermal boundary layer. Why should there be any difference? So what we are going to say is this flat plate. I am not drawing the velocity boundary layer now. I will focus on the thermal boundary layer. You can draw it on the same graph U infinity, T infinity. Surface temperature T s is greater than T infinity. So the plate is hotter than the fluid. So the plate is going to give heat to the fluid. Same logic that we have used for hydrodynamic boundary layer. The first sheet of paper, the first layer of fluid is by default going to be at the same temperature as the solid surface. So this value is T s. Next layer of fluid will see a slightly lower temperature than the solid surface and subsequent layers will see a lesser and lesser influence. This will end at a location which is given by T minus T s divided by T infinity minus T s is equal to point right away from the surface. There is a complication which we did not have in fluid mechanics. Fluid mechanics we said U by U infinity is equal to point 99, definition of boundary layer location. I had two velocities to deal with. One was the free stream velocity U infinity, other was the local velocity U. Now in heat transfer, moment I say there is a thermal boundary layer. We have not defined it as yet. I have three quantities which I have to deal with. Local temperature, surface temperature and one new thing which we call as T infinity which is analogous to U infinity. So I have all the three are going to take part in deciding how heat is going to flow through the fluid. Am I right? I cannot leave one or the other. The temperature locally is changing just as the velocity is changing locally. What is causing this? Surface temperature I cannot leave that. U infinity like T infinity is the imposed flow condition that also cannot be removed. So this ratio where it becomes equal to approximately point 99 that we will call as the locus of points which will form the so called thermal boundary layer. Thermal boundary layer is defined by the symbol delta T of x. Again it represents that it is going to go with increasing x the boundary layer thickness is going to increase. Now I told you the first layer of fluid. I am just going to shade this dark here. First layer of fluid. What is happening to that first layer of fluid? I am just going back to this fluid and the solid surface have the same temperature at the point of contact that is the first layer. This is called as the no temperature jump condition just as you had no slip condition, no temperature jump condition. Then what does this no temperature jump condition imply? It says for the first layer of fluid which is stationary or for the first layer of fluid which has 0 relative velocity between the solid and the fluid surface. There is no bulk fluid motion. So only conduction is going to contribute to the heat transfer. So heat transfer through that first layer of fluid is by conduction alone. Very good. How does it go out? E in minus E out plus E generated equal to E stored. Steady state E stored is 0. Single layer of fluid there is no generation of heat. E generated is 0. E in minus E out equal to 0 which means E in equal to E out. E in is coming by conduction. So if I take the control surface between the first layer of fluid and the second layer of fluid heat has to go out because of bulk fluid motion by convective heat transfer. Q convected from the first layer is equal to Q conducted through the first layer of fluid. This is very very important. Therefore I can write Q convected is what? H times T minus T infinity that is a heat flux convective heat flux T surface minus T infinity. Why is it T surface? Because of low temperature jump boundary condition that is what is given there. Low temperature jump boundary condition dictates that this layer of fluid is at T surface temperature only. So T s minus T infinity is the bulk fluid temperature. It has given the heat to the subsequent layers of fluid that is equal to minus K fluid. Why? We are doing the energy balance for the first layer of fluid. We are not doing the energy balance for the solid flat plate. The energy balance is for the fluid therefore it is K fluid dT by dy at the wall. Am I clear in this? So what I get because of this is a very very very important definition for the heat transfer coefficient which tells me minus K dT by dy at y equal to 0. dT by dy at y equal to 0. What does it represent? dT by dy temperature gradient at the wall. du by dy at y equal to 0 represented velocity gradient at the wall. So analogous, mu du by dy represented shear stress, K dT by dy represents identical in form. This is equal to h T s minus T infinity. And this is the definition of heat transfer coefficient. I do not have h was never defined so far. It was just h heat transfer coefficient. We never gave a definition for it. So it represents therefore h this is very very important. h is equal to minus K fluid dT by dy at y equal to 0 divided by T s minus T infinity. Larger the temperature gradient at the wall, larger the heat transfer coefficient. Now I have drawn this picture here. This is a snapshot of the temperature distribution at this location x1. Everybody remembers the velocity distribution and this is going to keep this here. Velocity distribution is going to be at another x2 something like this. This will be like this. x2 let us say x2 is here. What will happen to the temperature profile? Will it have the same slope or a different slope? Different slope. How many say different slope? It is okay if you do not have an opinion it is okay but we need to different slope. How many say same slope? See this is anchored T s. It is fixed. That is a boundary condition. Between x1 and x2 what has changed? Fluid has gotten more amount of heat. So it has to have a larger energy content. Energy content is manifested by temperature. So this being fixed the gradient I am drawing it bad really sorry about it. See like this. So it will become fatter than this profile. It is not drawn that well but it will be a flatter profile. That is the imposed boundary condition. Surface temperature fluid thermal conductivity value is less only. So naturally it will resist the heat flow through. Fluid thermal conductivity value is less. Whatever be the fluid thermal conductivity value correspondingly the heat transfer rate will change. It might not take away that much amount of heat. If one fluid has thermal conductivity value 0.7 and another has a very large thermal conductivity the magnitude of heat transfer will change will be smaller. But that does not prevent the surface boundary condition to be violated. I mean that does not allow the surface boundary condition to be violated. So T s has in no way related directly or T s should not guide the heat transfer rate. Same T s if I have honey versus oil versus liquid metal what will be different is the heat transfer rate. But whether honey flows or liquid metal flows the first layer of fluid will still remain at T s because that is a no temperature jump boundary condition. What will be different is this one minus kf dt by y. dt by dy will change to adjust to give you a smaller value of Q because k is very very small. So boundary condition is sacred. We cannot violate any boundary condition. So your question is liquids have some liquids I mean liquids have lower thermal conductivity it does not matter it will take away lesser amount of heat. But that does not prevent I mean that does not allow me to have a different boundary condition at the surface whether I am at x1 x2 or x infinity. So what I am trying to say is more heat has been added. So we will have a fuller fatter profile here at 2 and at 1. Now this brings us to a very very important concept. So if I have infinitely long plate what will happen to the temperature profiles later? Will it be a straight line ever? So it will become bulkier and bulkier velocity distribution. Will the nature of the velocity distribution change?  Let us say it is so long that it is still laminar then do not bring turbulent because it makes life difficult. Will anything change to the velocity profile? Nature will it does not become fat it will not become thin nothing will happen. So what does it tell me? Have you all heard of fully developed flow? What is fully developed flow? What is fully developed flow? What is the flow because at all we would find any kind of change in velocity profile. So if I take a snapshot of the velocity distribution at a given x location and move downstream to other x locations identical profiles are there. That is fully developed. Can I say the same thing about temperature? Because at both the end the temperature are fixed. The blood temperature is fixed and the fluid bulk temperature is fixed. So in nature of the profile. Nature will always be this kind of concave surface. I have added more heat to it right. Conditions have changed from this point to this point. So fully developed thermally is it possible? We will answer this question when we come to internal flow. I just want to leave this as a thought provoking question. It will become clear. Can it attain? If it attains wall temperature what happens to heat transfer? Fully developed. No, I just wanted to bring this issue of continuous change in the temperature of this profile as opposed to velocity profile. That is all I wanted to bring and this question what he raised that is what I wanted to trigger. So tomorrow when we do internal flow whether a flow can become thermally fully developed or no we will understand. This is a local heat transfer versus average value problem very straightforward. H is given as a function of x and you are asked to find the average heat transfer coefficient just obtained by integration. So it comes out to be 1.11 times the local value. So average value is about 11 percent greater than the local value and this is plotted there. So nothing difficult about it. I will take care of it. This Nusselt number we will define a little later. It is come here. We will define this a little later. This is Professor Prabhu likes to put in a historical perspective. So this is Professor Nusselt. Dr. Nusselt his thesis was on thermal conductivity of insulating materials and this contributed in the area of film condensation. This is theory of condensation then combustion of pulverized coal and of course heat transfer mass transfer analogy in evaporation and his work till the age of 70 and probably one of the pioneers in heat transfer we can call. Classification of convection I am going to leave there is nothing to teach here. So internal, external, laminar versus turbulent, natural versus forced all these things like that. All of us know definition of Reynolds number, rho, some characteristic velocity times some characteristic dimension divided by the viscosity. So what those characteristic dimension and velocity are those will change if the flow is internal or external and depends on the geometry whether it is a flow across a bank of tube, cylinder, sphere or flat plate correspondingly the velocities and the length scale is going to change. So physically it represents inertial forces to viscous forces and characteristic velocity distribution in laminar flow. I would like to draw this little bit to ask you a few questions. Now this is the pipe and what is drawn here is velocity distribution for laminar flow. Everybody agrees that this is for laminar flow? Now please draw this velocity as I have drawn and on the same graph that is at the same location X please draw the turbulent velocity profile. I need you to draw the turbulent velocity profile for the same mass flow rate. M dot is fixed, area of the pipe is fixed density it is an incompressible fluid. So I want you to draw the turbulent velocity profile one minute, drawn okay. How will it be? Laminar sub layer okay. I have drawn this something like this. How many of you have drawn like this? This is turbulent, this is laminar. Hope all of you have drawn like this. What does this tell me? What is the area enclosed by this velocity distribution? It represents the mass flow rate right and my way of looking at this is this way. So larger gradient at the wall is there for the turbulent flow. Therefore mu du by dy at the wall is larger for turbulent flow. Therefore wall shear stress is much larger for turbulent flow compared to laminar flow okay. So this is my arc coordinate okay which is y like this and this is the velocity vector direction okay. Mass flow rate is fixed. So there is apparent excess area here which is compensated by a change in the area there okay. Now what is the characteristic of turbulent flows? How would you explain turbulent flow to a student? Introduction. Random motion yes. Chaotic 3 dimensional. Chaotic 3 dimensional random. What are the words? Half hazard random okay. Eddies okay. Fluid chunks. What do you mean by fluid chunks? Group of molecules okay I have not come across this way okay. Any other? Discuss. Laminar also can be discussed. What else? Vortex. Mixing okay. Okay. All these are English. How will you tell real life turbulence example? Household. How many of us have seen honeycomb honeybees? Correct. What you are saying is correct. Correct. What else? Washing machine. Parade versus crowd okay. Very good example. So traffic in a I mean that is all correct example okay. So if I open that tap very very slowly small opening it falls down beautifully okay versus I am in a hurry I just open it fully it splutters splashes all around okay. So turbulence is there everywhere okay. We all have to deal with turbulence whether we like it or no and because of that we will say mathematically to quantify turbulence we will say any turbulent quantity be it velocity, pressure, temperature or any quantity can be defined in terms of see at every point there is some kind of chaos okay. So I will say let me define a hypothetical mean quantity so that that mean is there it is like a pendulum okay. I have a mean position and it is oscillation oscillating periodically about that position. Now in a pendulum it is the same amplitude both locations whereas in turbulent it can be small here large here next time small large here small here but if I plot these fluctuations with respect to time the actual velocity distribution could be something like this the signal would come out something like this this I say I do not like this let me just break this into a mean component which is u bar this is actual velocity u I break this into a u bar and a fluctuating component of velocity. So this is u prime and I say u local at any given instant of time and position is equal to u bar plus u prime similarly y component of the velocity v is equal to v bar plus v prime z component of the velocity is w bar plus w prime if I can do it for velocities I can do it for the pressure so I can say p is equal to p bar plus fluctuating component of the pressure temperature is a scalar quantity mean temperature plus the fluctuating component of the temperature. So what is this telling me there is always some kind of a mean about which these fluctuations in that particular quantity is going to occur these fluctuations I cannot quantify it is random that is what is the characteristic of turbulence when these fluctuations die out is going to 0 I get perfectly nice orderly flow this disorder is manifesting itself in the form of these quantities who told me this I am putting this because I like to make life simple mathematical if I want to quantify u v w p and t life is going to become difficult so I say this mean velocity plus this fluctuating component is what is equal to the actual velocity and these bars here represent the mean what is this mean have you heard of the word time average what is time average so time average mean what is time average 0 to some t any other definition of time average and one other question you can take over for t in your differential equation for momentum mass conservation we have not derived the energy equation you will see terms of this nature one of the terms typical terms you will see like this correct. So this if I want to put for the turbulent part it will be u bar plus u prime and similarly some such thing would be there so what it tells me is that a very very simple equation which I could write in about six lines now when I put things in turbulence it is going to have product of several terms which will have one mean component and one fluctuating component two fluctuating components derivative of those fluctuating components it is a nightmare to do it okay so why are we studying this then we will basically say these fluctuating components mean components all these things the product of these when I do a time average we will say the product of these components time average that is given here as one of the examples is given here I am not going to go into the definition right now u prime v prime bar that above bar represents the time average value so I write the full governing equation Navier-Stokes equation one of the terms I have written here u du by dx right so several such terms I will write I will expand the bracket take the sum of the derivatives multiplied by the term in front of it so I will get u bar du bar dx plus u bar du prime dx plus u prime du bar dx plus u prime du prime dx so I will get four terms each of which is a product of two quantities I will take the time average of the entire equation so that means I will have terms which will be u bar du bar dx time average each of these term will be time average and then we say time average of the mean quantity is essentially the mean quantity mean quantity does not change with respect to time so that is essentially equal to the mean quantity itself product of the mean quantity time average will give you the product of the averages okay then we will say u prime u prime time average u prime v prime time average these will not go to 0 okay and then you will say product of this mean and a fluctuating quantity time average of that so if I have terms of this nature u bar u prime and a time average of this this will be made equal to stop at this okay we have to write this and show and we will do that.


Brandon Marshall is here. What a weekend and the NFL so happy to have him as my guest. It had it all. History was made, dramatic finishes, controversial finishes and plays as well. We are breaking it down with B-Marsh plus. Matt Hamilton, live in studio. He made the trip. Show, look at the hammer, little love. There we go. Hammer cam, I got zebra pants on, let's do it. Week 15, like my pants. Wild, it all matches, it all fits. Welcome to the show. Up in Adams Happy Monday to everybody in NFL record. 12 games come down to the final possession, 12 games. Listen, we had our Up in Adams holiday party. Brandon Marshall was invited, he didn't want to come. That's fine, we'll get to that in a minute. But we all win as a team of producers and I thought, I was looking at one of our producers, Owen Reynoldson. And every time he had another drink, I was like, he can't possibly be more entertaining than he is right now. And then he'd have another drink and it would get better and the show would improve. And so I really liken that to what this NFL season has been because even just that 12 finished, unbelievable what's going on with these games this weekend. But last weekend I said it was the best week ever. And the week before that I said it was the best week ever. So this NFL season, Ipso facto, what so have you is the Owen Reynoldson of the NFL. Did it kind of make things? I don't know, I think it does. Listen, we also got some answers and I love getting answers. That playoff picture when things were loopy and gray and like you got to use your number two pencil with the eraser on the back. I don't like it. Sharpie vibes. And here's what we got. Six of the 14 playoff teams got decided. The Eagles, the Bills, the Cowboys, they punched their ticket to the office to the post season and then the Vikings, the Niners and the Chiefs, they lock up their division titles. And like, did Mahomes is the MVP? I'm sorry, Marissa.  I don't think you can. I don't think you can. I think it's Patrick Mahomes game and everybody's just playing in it. All right, we want to start with a rematch of what was a nightmarish tie between the Giants and the Commanders. And this time the Giants defense finished the game. There was a goal line stand involved and New York beats them 20 to 12. And let's take a look at what the shakes up in the playoff picture. The Giants move up a full game on Washington. They hold the head to head tiebreaker there. Then they're also a game and a half up on Detroit and Seattle. The Commanders, they're clinging to that final wildcard spot, but the Lions and the Seahawks, oh, they're right there. They're breathing down their necks, just a half game back. Like Hamilton's breathing down my neck to execute this show perfectly because he stayed up all night working on it. But when it comes to this game, this was the, and I think I've said this before too, biggest win, biggest game Jalen Jones' career is a giant. And the numbers, they might not jump off the page like you might think when I'm saying that sort of thing, but he made some really big throws and key situations to move the ball. On this number four, by the way, ranked Washington, Ron Rivera led defense and look at this fourth down play. Here we go, Daniel Jones, he's not trippin', that's his biggest highlight. Big game, big win, and look at that. Richie James, he keeps the drive alive. He leads to the touchdown that put the Giants up 14-3. That's brilliant football right there. That's what you wanna see. And the defense was phenomenal, by the way. Kavon Timbadoe, we talked about him all off season, all draft process, he goes to the Giants and we finally see this incredible breakout game. 12 tackles, he had the strip sack that he recovered himself for a touchdown, I can't imagine that's easy to do, but this was all about Daniel Jones and this was that moment. He gets the Giants one step closer to the playoffs. In the season where no one gave them a prayer, a lot of, oh, Dabel's gonna improve the team, nobody gave them a prayer for the playoffs or any success, or that Daniel Jones could potentially be the guy for this franchise. And all of his receivers are banged up, they're all injured. And so I do think Daniel Jones deserves to get a little bit of credit. Maybe we'll talk about that a little bit later this week, but to break down this game and everything that was crazy and fun and entertaining that happened yesterday and controversial, we bring in all-per-receiver, the IAM athlete, architect, and Brock Purdy's number one fan, Brandon Marshall, good morning. Good morning, what's up?  Gotta throw a loop in there. I didn't come to the holiday party because you keep calling me a guest on the show. Oh, so you want to be a family member, co-host, what would you like? Guest host. Guest host, I'm into that. I thought you were gonna say we didn't invite you, in which case your friend, Richard Issacow, failed miserably, because we would have loved to have you at the holiday party. Guest host, let's do guest host. Okay, great, somebody fix the copy for next time, Brandon comes on. Guest host, Brandon Marshall, and I'm so happy you're here. And who do you have in studio sitting in my seat? Matthew Hamilton, so Matthew Hamilton was with me for my first day, you guys can show him, for my first day at Good Morning Football. He is, in my opinion, the most brilliant mind, NFL-wise and football-wise, so he's here feeding me nuggets.  You wanna come work on I Am Athlete? No, don't, no. You can work with me. No! You cannot take him. No, stop. I'm gonna call. I think Richard has your number, I got you. That would happen to me.  I'm athletes taking over. No, Kay's better. Can I come work with you? Kay's better, she's easier to work with. That's not true. Can I come work at? Can I come work at I Am Athlete? Are you Ellen DeGeneres over there? Oh my God! No, I'm not, but I love you, Brandon Marshall. Let's talk about this. Giants win. Where do we stand on Daniel Jones? I don't know if you think I'm making it too much about him, but do you think he's done enough for the Giants to bring him back next year? Right, so our guy Hamilton will understand where I'm going here. Last week, I was able to do a little bit of work on the Giants, right? Because I know this question was gonna come up on Daniel Jones towards the end of this year if they weren't having a success, right? Obviously over the last couple of weeks, they haven't gotten it done. When you break down this team, Kay, please tell me what's going on with the right tackle. Can you please tell me what's going on with the offensive line? Kay, I like Kenny Galladay. Like, I like him a lot, but he hasn't showed up since he's been there, right? For several reasons, not just him. There's some other factors as well, given the quarterback in last year and then also offensive coordinator last year. I don't know what the heck's going on this year, but who's the number one right receiver, right? Which also makes me talk more about Odell Beckham Jr. coming in and helping out. But look, outside of Saquon Barkley, I just don't see the help, right? So when you wanna judge this kid, you have to also look at who's around him. I think they find a way to get it done with him this off season. I don't know what that looks like. They are already passed on his fifth year option, but this guy can play ball. I like him and Brian Daybaugh together, but can we please get him some help at the offensive line position? Look at those couple games where they struggle. I mean, he didn't have a second to throw the ball at times. Guys were right in his face on a three-step draw. So before we can judge Danny Dimes, he needs help. He looked great last night. They got the win. I didn't believe in them. I had the commanders winning and winning big, and this just shows the oomph that Brian Daybaugh have and Danny Dimes. So here's what, so let's play GM then. Saquon, you mentioned, Daniel Jones and Brian Daybaugh are making this happen with banged up receivers. They trade away Cadarius Tony. They did acquire, they thought Kenny Gull, they paid him, they thought that this is gonna be the guy. Number one guy for Detroit, bring him in, big bodied receiver, lots of talent. This is gonna be the guy, not the guy. So if you're the GM, are you bringing back Saquon next year? That's, he's a free agent. You gotta make a deal with Saquon. And Saquon's the one that's helping him, despite the offensive line, get it done.  What do you do? Yeah, yes. Hammy, really quick, Hamilton, can you look up how many yards Saquon Barkley had last night? I will say this while you're looking up with Saquon went for last night. If you look at the last couple of games, he didn't have any big games. Why? Because everybody loaded the box. This guy was having a phenomenal year. He's still having a phenomenal year. But because you don't have the wide receivers on the outside to attract and pull coverage and keep defenses from loading the box, now you're gonna have a Saquon Barkley struggling. No, Saquon Barkley deserves a big time contract. If the Giants don't do it, then somebody else will. But when you bring Saquon back, you need to do what, Kay? You need to go make sure you go get Odell Beckham Jr. Find a way. Don't let him go to the Cowboys. You need him on the outside, creating those seven-man boxes, making teams play cover two. It's not easy with the money situation. I don't envy Joe Shane. He's got, you know. I know you brought that up. You brought that up last week about the cat. It's true. Because I'm thinking about Saquon. What do you pay Saquon Barkley at this point in his career? What do you pay for him? And then if you don't have him. Yeah, listen, I'm a player. Give him all the money. Yeah, me too, I like that. Right at check, write the check. Okay, we have to get to this. There's some controversy that was at the end of this game that I just wanna get your thoughts on because there's a couple of things. It's a very weird game. There was the illegal formation and this wipes out a Brian Robinson touchdown. And a lot of people, and we're looking at it here, I mean, the NBC rules expert, he was talking about this. It's all about Terry McLaurin, who clearly Brandon checks with the line guy and says, hey, am I good here? And everything's all fine. And then what do you make of this? Yeah, as a wide receiver, that's our number one job, right? Once we break that huddle, alignment is number one. So am I plus two from the numbers? Am I on the numbers? Am I inside edge of the numbers? And once we define that, then we check outside with the ref and we tell him we're on or we're off, right? He did that. He did his job. The referee didn't. That's on them. Super weird. And then fourth and goal, the game is on the line and you have Darnay Holmes breaking up the pass. When you're looking at this, I mean, he interferes with Curtis Daniel. I think that's pretty obvious. Is it a good no-call given the magnitude of the moment? Because sometimes we look at the TV and I say, let him play, let him play. What do you make of that? Yeah, this is playoff football, the divisional game. I'm okay with this. This is, I'm okay with letting guys play. It gets a little iffy right here at the end, right?  But for me, I would say I'm okay with this because as a wide receiver, what I'm gonna be doing in this moment, I'm gonna be extra aggressive in making sure that I'm coming down with the ball. That wide receiver had an opportunity to be more aggressive. He let the DB take the fight to him instead of him taking a fight to the DB. So as a referee, I like the no-call. All right, that's Brandon Marshall's survival. Brandon Marshall agreeable on a Monday morning. We love to see it. Okay, we got the Lions. The Lions beat the Jets. It was 20 to 17. It was a thrilling game. Zach Wilson, good and bad. And if you look at the playoff picture here, this win for the Lions, I mean, they're alive. They're within a half game, Brandon, of a playoff spot in the NFC, and now they've won six of their last seven. They're legit one of the hottest teams in the league. Nobody wants to play the Lions. The Jets, meanwhile, are a gameback of both the Dolphins and the Chargers, I believe, in the AFC wildcard race. So they're very much in this thing as well. Zach Wilson looked okay. He looked pretty good. Over 300 yards, two touchdowns, good and bad. What did you think? Well, so first off, let's go to the Lions. Man, the Lions is a tough team. We know that, and it starts with the head coach. Dan Campbell, I was with him when I was with the Miami Dolphins. He was our tight ends coach. I left before he got the interim job. My last cup of tea with the New Orleans Saints, he was there at the tight ends position as a tight ends coach for the Saints. He's a guy, man. That's how he was as a player. That's how he is as a head coach. That's how he shows up every single day. And that's a trickle down effect, right? You take on the personality as your leader. He's not a guy that's gonna hang his head ever. If anything, he's gonna be emotional. We've seen that, the tears. We've seen the emotions worn on his sleeve. We've seen that. That shows up well in the locker room. So when a lot of people ask like, what's happening with this team? Well, they're changing the culture, right? And it takes time. And if you had the wrong guy in that situation, that's gonna put their hoodie on. Josh McDaniels, when times get bad, you know, even maybe even a guy, I don't wanna throw another guy under the bus right now because no, I can't do it. You look at you want, you want Taylor to have something to tweet. No, no, but I knew it, but I can't, you know, when the Raiders won yesterday, I knew you were coming on the show and it was such like a lucky situation for them. I couldn't wait to ask you about it. We'll get there though, finish your thought. Yeah, so listen, there's nothing spectacular about this team outside of them being a tough team, right? Right, the offense, they've been showing up all year, but they're not the Cincinnati Bengals. They're not, you know, Pat, they don't have Patrick Mahomes. They're just super efficient, right? And this quarterback has given them an opportunity to be successful. And these young wide receivers are coming along. And then obviously you have two guys at the running back position that can hit a home run at any time. So this is a really good offense and defensively they're tough as hell. But if anything, I would say the emotion around this team, the mindset of this team, understanding that they are at the bottom of the NFL and we have to fight our way out. And so I think that type of energy is what's creating this magic in this locker room. Cause it's crazy, I'm looking at them, just what they've, I mean, this team was one in six. So when you're talking about bottom, that's rock bottom, rock bottom, they turn it around. And I love, by the way, cause you know, Dan can't, I like the story. So like Dan Campbell's this backup tight end and then how do they win this game? The backup tight end goes and like makes a play and like wins, I just like with everything that's going on with this Lions team. But if we go back to the Jets, I can say the same thing you're saying about the Lions, bottom of the barrel, know they need to do something, know whatever. And then it's just not working as well as you'd like it to work. What'd you think of Zach Wilson and do the Jets need Mike Whiteback ASAP to make the playoffs? Did you play short week Thursday night? No, I think he did a good job, right? He's been on the bench for a couple of weeks.  You were the number one guy, okay? They took you over Justin Fields. Now there's a few million people watching. We're talking about on your show. They're talking about on other shows, right? There's a lot that this dude had to fight through over the last couple of weeks for him to come in and play the way he did. I have a lot of respect for him. Now I don't know what happened in the locker room. So I don't know how he's connecting with the guys which is the most important part. I don't know how he's controlling the huddle which is extremely important as well but I think he deserves the right to go out there and play again. 100%, you let Mike get healthy. And look, let's see how he shows up this time around but they played against, like you just said it, an extremely hot team, a really tough team, a team that got talent in a lot of places and this was the unfortunate outcome. I have really played attention to what Zach Wilson said. I mean, you early in the season and early in one of your appearances as guest host here on Up and Adams talked about with you. I like what you did there. You talked about Zach Wilson and how, you know, the whole Elijah Morthing and like, he has to be careful. Before the whole thing blew over before he got benched you were the one that said, I don't know if I like how he handles things in front of the media. I think that might trickle into the locker room. You called it weeks before it happened, it's true. Why are you doing that for? Because, and I'll say it, I like to get messy, you know, on our platform and I'm outspoken and I keep it real but when I made that comment on your show, you know how many people from the Jets organization called me? You know how many people? Three, let me put it over here. Three people called me and they were like, Brandon, like, we don't agree with what you said and why you said and I was trying to explain it. You know, like, if my quarterback stands up and says, answers the question the way he did and it wasn't nothing terribly wrong, but it's like, we got a guy that said, I'm not showing up. Right? Do we want this guy back if we do then we can't go out there and say, look, I know you didn't get any targets over the last two, three games but I'm just going through my progression, right? Hell, that doesn't make any sense. How many times have we seen quarterbacks drop back and throw it in double coverage because they just believed in a guy? How many times have we seen an offensive coordinator just throw a bubble screen or jailbreak screen or smoke just to get the guy a touch? That's not a hard thing to do to get a guy involved. So when I said that there was a few people in the organization upset and then, you know, a couple of weeks later, this happened and guess what I did, Kay? What? I called them saying three people and I said, you owe me apology. Yes, of course I did. You broke out the Robert Salo receipts on them? I love that. Yeah, but they said, you know what, it's different. They felt like it was different. We had a great, healthy conversation. Well, here's the thing, because you and I talked about this on Friday. It's a, we both agreed, it's a good thing to get bench sometimes. It's a good thing to see it from a lens of sitting on the bench. And we saw, I think Zach Wilson looked a lot better, but I'll also say after the game, because he knows everyone today is going to be asking, should he start? And if they've got, I mean, they got the Jags on Thursday. Nobody should look at that and say, that's a hot team. The Jags are a hot team right now on a short week. So we'll see if it's Zach Wilson or Mike White, but he of course was asked post game, all those vicious New York beat reporters saying, should you be the starter baiting him? And I was like, oh no, because the whole point is you taught me to pay attention to Zach Wilson. I listened to every word now. And his answer was, that's not up to me. My job is to watch the tape and try to get better. And I was like, thank goodness. And he had a perfect answer. And all those reporters were like, probably. And that's just how it went. And I loved seeing that out of him. So we'll see what happens on Thursday. Before we take a break, I want to ask you about the Bengals and the Bucks. So this was such a fun game. 17's it, Bengals are down. Then they ripped off 34 straight points to beat the Buccaneers. And so if we set the playoff fixture for people, as we see it here, this one vaulted the Bengals into the AFC North lead up to number three seed. One game back in the top spot in the AFC, yeah, overall. The story was though, and we loved the Bengals, but the story was the Bucks collapse. They turned it over on four straight drives, my friend. Brady throwing picks, Brady fumbling handoffs. This is unthinkable. You give such good answers, Brandon. You never give me a straight answer on what's going on with Brady and Mike Evans and that offense and the play calling. Why is it not working with Brady? It's a chemistry thing. Everything matters. Before the season even started, you had how many offense alignment go down. That is a big deal. And even looking at the running game. My God, hammy, hammy. Can we look at, maybe at the end, all these things I'm asking, maybe at the end of the show, you got to say, Brandon's questions and here's the answers, right? But what's the yards per carry from the running back position? You got Tom Brady. Tom Brady, I'm sorry. How did they win a Super Bowl the first year? They won a Super Bowl by saying, you know what? Let's not throw it 40, 50 times a game. Let's week 12, let's start running it more and then start throwing it, right? Let's have more of a balanced attack. Right now, we're asking Tom Brady to win the game. Tom Brady is, Tom Brady is the GOAT, but Tom Brady, he needs some help around him. So it's not all Tom Brady.  You're telling me Tom Brady doesn't have enough help around him and that's why it's not working. It's, it's, it's, it's, it's, sometimes you need a little bit more. Sometimes when you got guys in and out of line up, you can't overcompensate.  Tom Brady, we've seen him do that in the past, but now Tom Brady is how old, 45, 46 of age and you're asking him to deal with guys in and out of the lineup. I think that's asking Tom Brady a little too much. 3.3 yards per carry, worst in the NFL. There you go. How did they win the Super Bowl? This is simple. This is simple. Okay, listen to me. Playoff land. No, listen, you had a running game that popped late in the season. Remember, there was a lot of back and forth, a lot of clash between Tom Brady and Bruce Arians. Right around week 12, I could be off a week or so here or there. Right around week 12, they started running the ball and then Tom Brady, he started doing his thing in the passing game and then defensively they were good all year, but they start destroying guys. They start running through tackles. They start demolishing quarterbacks. That's the formula for this team. Todd Bowles in that defense, top five defense. Are you guys getting to the quarterback or are you guys turning the ball over? On the offensive side, can we get to that running game going? If we can, everything else falls in place and that hasn't happened all year. It's the O-line. It sounds like it's the O-line. So it's a few things. It's a few things. You also have a receiver coming off injury and then you have an aging Julio Jones. You don't have Bromkowski. There's a lot of things there. There's a lot of things there. You know what they should have did? I would say if you're, look at, I mean, Mahomes is a different animal. Mahomes has Kelsey's, you can, whatever. You have Mike Evans and Chris Gottlin. Hey, all pro receiver. You have future Hall of Famer potentially. Mike Evans and Chris Gottlin. Really? But is Chris still the same? Is he still, is he still, is he a hundred? Is he back yet? I don't know, but I get, I mean, it's the O-line. I guess chemistry sounds like a weird, something it's weird, it's weirder than it is. Why can't the goat just have one bad year? Why can't the goat have one bad year? I'm not saying that. I'm not saying, I think there's a confidence thing that's missing on the team too. It's more, it's one of the, when you're watching it, it's intangible. Like it's, I mean, are you telling, he's not even checking to runs, like when he has the numbers in the box. He's not, and he's fumble, like what is that? Listen, the goat can have one bad year. Is he back next year? You want me to create this magical actor right now? Your press to be like the New York media. You're not in New York anymore. You're in LA. Is he, is he back next year? Huh? Is he back next year? Heck yeah, you the goat? What? Yes. I hope so. He's coming back, he ain't going out like this. I don't know, is he back with the buccaneers? Mmm, that's a great question. 50-50. I wanna ask you about this because I don't know how to feel about it and I know that you'll help me because there are some fans and I obviously hear a lot from Bangles fans. People are in their feelings about how Brady reacted to Joe Bro. Did you see any of this? Mmm, let me see, where is he at? Yeah, I see Joe. We'll play it a couple, so yeah. It's a very brief handshake. Very brief, but he hugged Brock Purdy last week. He embraced him. And then I want you to listen to this. This is, you know, Tom Brady, well he made it the last question in his press conference after the game. Listen. Tom, what can you say about Joe Burrow seeing him on the sidelines and the way he was able to rally back in that second half for his team? Yeah, he's a really good quarterback. All right, thanks guys. What do you think of that?  We know that, which I saw last week, he tried, he tried to appease us, okay? He didn't wanna go, say hello to Brock Purdy. He didn't wanna do that, right? And then he tried to take in a moment, being back in San Francisco. He tried to play into the media thing, right? I think that was his first time back in San Francisco in a long time, or maybe the first, I'm not sure, right? So like this, this is Tom Brady. This is the Tom Brady at the Chicago Bears game and how he treated Nick Boles. And we've seen this before. But is that okay? The greatest player in our, in our sport. I'm just asking, is it okay that he's inconsistent in how he dishes out daff, like daff-ups after the game? Yes, yes, America. Football players have emotions too. Tom Brady, he knows we're gonna be talking about them losing today. So right after the game, he has so many things happening. So many things going through his head. He's not gonna be perfect all the time. Like he, he don't wanna go out there and say, hey, great job, and let me walk you through some things you can do better, or I'm super excited about you. No, talk to me in the off-season. We'll talk about that then. I take it as a compliment. I mean, he got, he got Matt Ryan against this team. And there's no other way to call it. This team came back from a huge deficit. And this was, you got 28 to three, my friend, in this match, it's just true. Season stuff, season stuff on the line. I wanna show, here's my take on this. It's a compliment. It's a huge compliment. People don't compare. Nobody says my homes is the next Brady. No, Josh, he's his own thing. Josh Allen's his own thing. The comparison made, who's the next Tom Brady? The way he plays, care all of that, it's Joe Burrow. So I think that really does play into it a little bit. I don't think I'm feeding into it. I think that exists. First time these two face each other, he gets Matt Ryan and smacked around by this kid who's gonna be him, and people are crowning him for the future. But I will say, here's my take on this. And I wanna show the clip, Sarushi, back there, our director. Again, of the on the field stuff, if we can loop that. Joe cannot not look cool.  Joe, Joe's like, hey, man, yes, up, and goes back. Right, right, right. He cannot get got. Can he look like a little bit of a mess at all, ever? No, like this, he makes, it was the coolest thing I've ever seen Joe Burrow do. He's one of the coolest people I've ever met. He's an awesome person as well. Back when he was going into the NFL, remember when the middle of the pandemic, you had the COVID-19 hitting hard, I reached out to him and a lot of athletes to support. He supported, he donated without even question, right? Last year, going into training camp, he opened up the doors to us. He took us in the cafeteria, broke bread with us, and he gave us a great line. I said, who are you listening to in music? He said, Gunna Wanna Wanna, right? Like who? You're listening to Gunna? You're listening to what in hip hop? Like he's just the coolest dude the way he dressed, the way he talks, his whole demeanor. I love him, he's the best. I'm trying to think of the demeanor and coolness comparison to Tom Brady. That doesn't exist, those two things. I aren't to say. No, what do you mean? You don't think Tom Brady's cool? I don't know if I think Tom Brady's cool. No, I don't. I personally think Tom Brady's one of the coolest cats that's played football or maybe played sports. You gotta think about this. He is the goal. He's not only one of the best football players, he's one of the best athletes ever. Tom Brady ascended to, he's up there with Michael Jordan, he's up there with Tiger Woods, he's up there with Serena Williams. And for that guy to treat his teammates the way he treats his teammates, maybe not this opponent, but the way he treats people, the way he conducts himself is first class. Do you want me to play that loop again where he's yelling at everybody or is that what you're talking about? I'm confused. It's football. Oh my goodness. I'm kidding, we're gonna have to take a break after this, Brandon Marshall joins. I mean, we're half, we literally are 30 minutes in. We have not taken a break.  He's going. We'll be back. He's going, Richard. Back on up now, I'm just with my guest host, Brandon Marshall, saying he got five minutes for us, so let's get to it. You know we have to talk about the Patriots Raiders game of Ramondry Stevenson. End of the game. They're tied. He takes off. That's great. Well, great. Amazing. They're tied. Let's go. Josh McDonald's with an advisor is going to lose. He suffers for some reason, pitches it back to Jacoby Myers, who then inexplicably throws it to former Patriots, Super Bowl champion, Chandler Jones, who stiff arms Mac in the face and takes it for the game-winning touchdown to beat his former team. I mean, your favorite guy, Josh McDonald, gets the win, but this might cost the Patriots a playoff spot. That loss puts them outside looking in. Jacoby Myers, after the game right away, was like, I take full blame, but this is, you know, in my head I'm like, maybe that's not play calling out, but it's discipline, right? It's what are we thinking? Where are we? Should Belichick take heat for this? Well, listen, I don't know how the play was put together, right? I don't know if there's more that came out. You know, I don't know what Bill Belichick said, but is this like that play where you just throw it around? Or was this just on him, right? So, you know, they keep things tight internally, so I can't really call it. I just think that, you know, if I'm in that situation, I'm not throwing the ball around.  Bill Belichick needs to stand up and address this and really be open and honest so the kids not taking all the blame. Ooh. The bigger issue is that it's uncharacteristic. I've never seen this before. The belt, even if it wasn't how they drew it up, first of all, it's a tie, go to overtime, what are you doing? But how does the player not know, how does the player, the players out there not prepared for this? That would be on Belichick. Well, we've never seen this before, right? We've seen this play, this type of design before where guys are throwing it around, but never seen it picked off and taken it to the house, right? Or it's not even a pick, it was like a fumble. I don't know, what is it? It was a pass, it was a pass to Chandler Jones. That's what it was. No, it was backwards, so I don't even know how that shows up on the stat sheet. But anyways, you know what popped up for me watching this? Was how cool, same game parlays are? Like, I know this whole, this is not because we're on Fando, but hey, I gotta be honest, right? I gotta be honest with you guys. Never was a betting guy, never was into it.   So now, this is my first time doing same game parlays. It makes the game so much more interesting. It's ridiculous. It's crazy. Like, because at first I thought I was like, you know what, I'm an athlete, and like the integrity of the game, I just want to root for my team to win, but now I'm looking at, can this running back get an anytime score? Can this guy go over a hundred? And it's like, ah! It's fun. I love it. And that's what it should be. It should be a little bit of fun, and I love that.  Okay, one last one. Maybe you gotta teach me a little bit more. I don't know anything. Money line, parlays. I literally grounded myself from parlays because I'm so bad at that. Unders, overs. One last one for you, because we have this. Super boost. Super boost. That's what it's about. That's like that McAfee thing.  I've done them and they don't hit, so. I mean, I grounded myself. I'm gonna do one this week though. Just like with the same, do the same game parlays. Just do a three leg. Maybe we should team up for one, Brandon. Let's do it. Since we're guest hosts together. Let's do it. I wanna ask you one more. Before I know you have to go, the Jags dramatic overtime win. They're in it. They're doing their thing. There was a pick six. Oh, Ray Sean Jenkins. Hello. They come back. They beat the Cowboys 40 to 34. And one of the best games of the year. They also pulled to within a game. If we look at the playoff picture of the Titans for the AFC South lead after their loss to the Chargers. Now, Trevor Lawrence, he's been great. He's been on fire lately. What do you think is clicked for him? Woof. This is hard. I don't know. I don't know because he doesn't give us a lot. The coaching, right? Because this guy came in and he was, he had the story around him that he was a once in a lifetime type of talent or once in a generation type talent, right? And then he came in and we didn't see that. There were some people saying that he was a potential bust. I mean, his feet looked terrible in the pocket. You know, as far as accuracy, he was way off. I know early in the year, you know, you had the coach come out and say, look, it's, he's getting it now. He's starting to understand what we're asking him to do. So I have to say coaching, right? You know, so- That's what he said. Brayshon Jenkins has that pick and after the game, he asked what's different this year and he goes coaching. That's what he says. And I have, I mean, and by the way, the Jags might win the division because the Titans, they've lost four straight. They're in an absolute tailspin. And then I look at the other side and Cowboys, I just can't trust them. One last thing before we go. Yeah. So on the AFC side, we talked about the Cincinnati Bengals. You have the Kansas City Chiefs. You have the Buffalo Bills. On the NFC side, right? Cowboys still there. I know you say you can't trust them, but you have the Philadelphia Eagles and who am I missing? The San Francisco 49ers, really strong teams. But, okay, looking at this weekend, my biggest takeaway was, hell, could the Giants make a run? You just talked about the Lions, right? There's some teams out there, even the Vikings. The Vikings sing at 11-3. It doesn't feel like a strong 11-3 because it's the team over the last seven games have given up, what, 300 plus yards in offense, right? Their defense has struggled. I don't think anybody, you know, at the top was like scared of the Vikings, right? Right. So I'm saying that because you have these... Who is the team? And then, you know, on the AFC side, who is the team? Who is the team? You said it was the commanders last week. No, I did not. No, I did not. I don't... Taylor, why'd you tweet that? Brandon Marshall, I am athlete podcast, fan dual friend and guest host of Uffin Adams. We love you, thank you for taking the time this morning. Same game parlays, that's right. Don't bring up same game parlays.  I'm cursed. Though I was at the Chargers game and they won. So I think my curse is broken. I do. Love seeing that. Welcome, ho. Oh, okay. I don't have it in me to dance to that. We had a bit of a holiday party on the Uffin Adams show yesterday and Hamilton flew in for it. What's up, Hammer? What's up? How are you? I'm great. You think of our studio, you've never seen it before. I love it here. I love that I had the little box. I could be like the old men from the Muppets and just hackle you from the side. It's great. Well, you used to when we were on Good Morning Football together in our very first studio. We used to sit in a glass cage, I would call it. Yeah, it was a little. You legitimately sat in the glass cage and I would just look at you with behind Peter Schrager and I'd be like, what's happening? Remember? Yeah, and sometimes you'd be like, was that a good question? I'd be like. Yeah, you'd be like, all right. Okay, well here you are. Listen, we had a great time with Brandon Marshall. He ate up all the time in the show. He happens and likes to do. But so much happened Saturday. Crazy game. So let's go over. We don't want it to get lost in the shuffle. So let's start with Miami at Buffalo. Okay, I was told this was a shot, but it's not here. This is some snow that was happening. Bills win a snowy Conrad. Beating the Dolphins 32 to 29 Miami. Now my friend has lost three straight. There is Butler will be on tomorrow. Talk about it, but are you worried? I'm not worried. I think if you look at it, it was three high quality opponents. And I thought the Dolphins actually played really well in that game. I expected the Bills to, you know, I think everybody expected the Bills, especially given the weather to kind of control that game. The Dolphins gave them everything they could handle. So what in Buffalo is not a good mix? I know, but you saw it. I thought he played pretty well. And I liked how they got the run game going. I think that was a really critical thing for them. They rushed for the second few yards a game this year. And I think, you know, we've seen defenses really try to take away the passing game and key on Tua and those receivers and really, you know, go with a light box to try to take away the speed of this receiving course. So you have to be able to run the ball and especially as the weather gets bad. And we saw Mostard have a massive game. They averaged seven and a half yards per carry on the ground. If they can get the run game going like this, and you saw it as that game progressed, it opened things up in the passing game. So if they can keep this running game going, I think it's going to get Tua back to playing the football we saw in playing earlier. And he played well, right? Bounce back, tough defense, all of that. Great, threw two touchdowns over 230 yards. But the defense gave up 32 points. That's the real worry here. They're getting their run game going, Tua maybe looks a little bit better. 26th ranked defense in the league this year. So that's a huge concern. Yeah, it definitely is. And we've seen them, they make plays. They've come up with some big sacks at points, some big turnovers at points, but they can't get consistent stops. And you know, everybody loves to make everything about Tua, but I agree with you. I think that's the bigger concern. What do you make of, I know the strength of schedule gets kind of nitty gritty, right? We know what teams are and how good they are and there's momentum and everything. So to get this, there are three losses we're against really high quality opponents. The Niners, the Chargers and the Bills. So they got the Packers, I think, next. Yeah. What do you think? So I think they bounce back. I think we saw them, they looked like the Dolphins on Saturday, the Dolphins team that we saw early in the year. I think they get back on track and take care of the Packers and make their way into the playoffs. I know Dolphins fans are getting a little nervous now because they're right on that ball playoff bubble, but I think they get in. I'd like to see them in. Conrad, do we have an actual shot here? Okay, great. Here we go. For a spot for Minnesota. Good, I appreciate y'all's support. Hey, I know we scared y'all in the first half, but stick with us. We gonna hold y'all on our back and we gonna fight to the end. Y'all know it's good. I mean, there was a 33 point colds lead. I don't even know what to say about the sheer madness of this game. This was like one of the biggest comeback. Was it the biggest comeback? Yeah. In NFL history, right? I don't even know what to say. I don't even have the question for what this was. What do you got? I mean, it was remarkable. I mean, I landed. I had to catch up on it after because I landed here in LA, saw it was 33-nothing and I'm like, how did this even happen? Because Jeff Saturday was playing on a Saturday, said Twitter. It's true. And then to see the comeback. But when I went back and I watched the film of this, you know, you see how the colds built that lead. It's not like they were like running up and down the field and Matt Ryan was playing amazing. It was a little janky.   They got a few lucky plays to kind of jump out to that lead and that Vikings offense caught fire. So it's more about that it was like fool's gold with the colds did to the glass yesterday. I was like, what was the point? What was the momentum switch? And it didn't really exist, right? But the Vikings keep, you say this to me more than anybody, the Vikings somehow keep doing this weird stuff. And we are always like, is this sustainable? Can they keep doing this? It's the, you know, the seventh comeback win of the year for her cousins who could never do this before this year. He's been so clutched down the stretch in games. And I guess it is sustainable. That's our answer. Yeah, they just, they keep doing it. If they can keep repeating it, then yeah, it's sustainable. We saw them do it to the bills in that wild game. This is, they just find a way to one up themselves. But I think there were a few significant things to come out of this. I think seeing a guy like KJ Osborne emerge, they need a big play threat opposite Justin Jefferson. And Thielen isn't quite the player that he was with Osborne being able to make big plays like that. It opened things up for Jefferson later in the game. It was, it was really important. And if they could get consistent production there, it makes this whole offense more complete. I feel like I slammed their defense a lot. I always have questions, but I mean, Eric Hendrick's going to be on our show this week. Great game. The defense made plays when they need to. Yeah, they did.  And they did a great job. So they are in the two seed thanks to that epic comeback, historic comeback. So if they lost, the Niners would have jumped them. And now they have the Giants. They have the Packers and they have the Bears to end the season. So we'll see what happens in the NFC. All right, let's hit Baltimore and Cleveland. The Browns beat the Ravens. It was 13 to three afternoon game. Kind of a good place to take a nap potentially on your flight, because it wasn't that riveting of a game, Ravens. Do, by the way, Jacobi Prasad, anyone? Anybody missing Jacobi Prasad? No, okay. Do the Ravens just miss Lamar? Are there other reasons to be concerned? Well, I do think a lot of it is Lamar. I think when Lamar comes back, obviously, it's gonna be a big shot in the arm for them. And I think the significant takeaway from what we've seen in the last two weeks is what J.K. Dobbins has done. You talked about it last week. He had 125 yards again on 13 carries. And he's still clearly not himself. Like you see it when he gets into the open field. He just doesn't, that breakaway gear isn't there. Like he's not gonna get better, right? That's the thing, because like, you think he could get healthier? He should continue to get healthier as he gets out there and gets back. You know, he's gonna be getting in better and better shape every week. They're kinda slow playing things with him. So I would expect him to keep this going. Do you think the Ravens could still, you know, like we're not talking about them in the big, there's the big three, right? Chiefs, Bills, which is by the way, Bills, how impressive are the Bills that we're talking? They're peace. They're $126 million piece that they got to help them get over the hump and fill the need, the only boy that they have. He's out for the season, but we have not moved them from our thoughts on how impressive is that, honestly. That is really impressive. With the Bills. That is really impressive. I don't know, like you lose, if they kept Jamar Chase out, one of their prime pieces, even it's different, you know, whatever side of the ball, we would not be talking about the Bengals in the same way we're talking about them, but the Bills lose Von Miller and they're still bang right there. It's true, it's true. And as for the Ravens being on that, in that tier, I really, they need to find some playmakers. I think we saw them are struggling for a while, you know, before he got hurt. And I think losing Rashad Bateman, losing some of these receivers, they haven't been able to really make up for it. And I think that's something that we need to watch. Well, Bateman's on IR. They never replaced Hollywood. And by the way, here's the stats. None of them had over 30 yards receiving in this game. So what, I mean, we've been saying for, take a swing on a big receiver. Do I not talk to DeCosta all the time into, like from the New York good morning football camera to this one on Up and Adams on my new show in LA, make a big swing because a lack of investment in the wide receiver position is what is slowing this Ravens team down and you hate to see it. All right, and that's why Lamar was having some struggles. Great job by you. Lots of fun at our holiday party. Wanna know how much fun Hamilton was?  The whole time we're there, we're having fun, not you. Okay, I know we only have a little bit of time left. What is so funny? I don't know what's happening. We gotta get into this. Let's bring up the tweet. Oh God.  Here's what happened. No, no, no, here's what happened. This is actually incredible. Meeting Santa Claus for the first time. This is the anti-Joborro. Could I be less cool? The game ends, I've had some shots, I've had some shots, and I run, make Hamilton, I run over there and I'm acting like I'm there, I'm their coach, smacking their butts, they're going to lock them in, I'm like, add a boy, add a boy, go win me a Super Bowl. Hey, and I'm in, and Derwent James is like, yeah, cool lady, like great, like, you know, like Austin Echler's like, yeah. And I'm just like, yeah, I was so juiced. I was like standing on a stool, like, yeah. I mean, that's embarrassing. There was a stool there, which makes it more embarrassing because he looks like he's five times your size and you are standing on a stool. Well, that's not what we're talking about. We're talking about just me being a fan girl.  Packers game, like you don't get anywhere, near the guys, whatever. And I'm sitting there and I'm part of the team. It was a win for me. I'm happy for them, but I'm happy for you. Unhinged.  I'm so glad. I'm so glad. I'm really glad everyone had a good time. Bye.


One World Initiative for Sustainable Development Group has given over 44 out-of-school children certificates of scholarship in the federal capital territory in a project designed for special intervention in education. The group's president, Timothy Achamiya, while giving his remark at the flag of its SAVA future project in the federal capital, agreed, urged stakeholders to put more effort into promoting the culture of peace through dynamic conflict transformation strategies for poverty reduction and sustainable development. Under the effect of all this on Nigeria, it has a very high unemployment rate, high level of insecurity, galloping cases of hunger, malnutrition, and very low health indices. As a result, we have become deeply entrenched in the moral, paramount, and economic privation. We are beginning our intervention from Abuja Municipality, from here we will spread across the country. We aim to provide the rest scholarship to children beginning from today. We would work to establish community-based homeschools in Grasswood, and mothers will be equipped with requisite knowledge to serve as the first line of defense in our project of taking the children out of the street. We shall provide a certified literacy and vocational education program for the youth. The best way among others to address the issue of out-of-school children is to cut them young. Through the effective provision of early childhood care education, this is because various research comes have shown that early stimulation of children at the primary school level is very critical as it serves as an important foundation for the overall future development of the child. Most of these children you see are not all of them are not from FCT, but because of our capacity as a capital, everybody run down here to take refuge. And we cannot send them back. And that is why we are here to support this initiative, to make sure that we bring the students that are out of school in a way of encouraging them that life is not still lost, as we hope for them. And that's why we are here to also collaborate with these initiatives. If the children are out of school, they are prone to crime, they are prone to so many things. So I've been to Ghana Embassy, I've been to South Africa Embassy and some other embassies that are still in my world like the American Embassy have written to all of them to see how they can support this initiative, to see that we bring our children back to school and also to encourage the children that life is they see hope for them at the end of the day. Hello, hope you enjoyed the news. Please do subscribe to our YouTube channel and don't forget to hit the notification button so you get notified about fresh news updates.


Spring Cleaning is here and Appalachian Wireless has the deal to get you started. Get a Samsung Galaxy S8 for a penny or a Galaxy S8 Plus for only $89.99 on the region's best network. Better service, bigger savings, that's today's Appalachian Wireless. So your agreement requires you to store for details. Following an escape, back in March, the Department of Corrections is investigating the work release program at the Big Sandy Regional Detention Center. Because of the investigation, the Big Sandy Regional Detention Center Board voted last night to restrict inmates from being signed out on work detail. Until the investigation is complete, inmates will only be allowed to work in or around the facility and a jail guard must be present. Once the investigation is complete, I would like to see us get to use the inmates for projects and cleanups in our communities. The Big Sandy Regional Detention Center serves Johnson, Lawrence, McGuffin and Martin counties. Inmates are typically signed out to help with odd jobs around each county. I've had this position for two terms and this is my eighth year and this is the first instance I've ever had anyone to walk out from a detail. Johnson County Sheriff Dwayne Price uses the work release program frequently. He says it will be a huge loss to the Sheriff's Office. There's a certain individual that we use all the time if he's not available, we'll use somebody else, but for 99% of the time we use the same guy. He's very well mannered. He helps out over at the office, he's good at filing papers because we have a lot of paperwork here that needs filed. He helps us keep the place up, takes the garbage out, never had an issue out of him. So he's been a great asset to us. We pick him up two or three times a week. Those signed out for work detail are usually Class C or Class D inmates. Those in charge of those inmates are trained and certified to supervise. In Paintsville, Shelby Porter, EKB News.


Well, in January, Cayuna Regional Medical Center opened a new menopause center at their clinic in Crosby. The center is one of only a few in the state and offers important care and treatments of issues and symptoms caused by menopause. Reporter Rachel Johnson has more. Since you've had a chance to cut a... Cayuna Regional Medical Center has recently added a new state-of-the-art menopause center at their Crosby clinic. We've noticed in our area that it's certainly an aging population and the fastest growing segment of the population is postmenopausal women. And so there's a big need for postmenopausal care. The menopause center opened in January and offers care and treat symptoms caused by menopause and perimenopause.  The center treats medical symptoms associated with menopause but also helps women live healthier and happier postmenopausal lifestyles. There's so many things that we address are more addressed towards more like healthy living. Can we do something to help you sleep better? Can we do something to help with low libido, pain within our course, incontinence? The menopause center aims to offer a unique and personalized patient experience. To make the experience calming and relaxing, they have added amenities such as heated blankets, comfortable robes, oils and candles. For CRMC, it was important for them to offer these services to the surrounding lakes area. Nationally, there really is not very many menopause centers. You see them more in large cities, but even in that setting, there really is very few certified menopause centers where there's kind of a multi-specialty approach. And so we felt like we had those pieces here at CRMC and that we could provide that in a more streamlined approach. The providers at the menopause center hope that by offering their services, more women will live healthy and happy postmenopausal lives. Reporting from Crosby, Rachel Johnson, Lakeland News. And CRMC will be hosting an informational event on the menopause center on April 23rd at the woods in Merrifield. If you enjoyed this segment of Lakeland News, please consider making a tax-deductible contribution to Lakeland PBS.