we will take over from where we had left that is so far till this problem we have considered effect of we have considered lumped capacitance.  But so what does it mean situations where lumped capacitance is not valid we do not solve the problem now that is not the case. So, what we do is situations where lumped capacitance is not valid or bio bio number is less greater than 0.1 we have to take into account the special variation in the temperature which means we have to take into account the fact that temperature is going to change with respect to the coordinate position and apply not so simplified lumped capacitance approach, but a slightly more elaborate approach to try to solve the problem. I am not sure how many colleges how many universities cover topics beyond lumped capacitance and transient conduction for those of you who cover it definitely is going to be very useful for others who are not covering this topic as a part of their undergraduate curriculum. Still I am sure this is going to be useful because we are going to cover certain mathematical formula certain charts and graphs which we can use directly for getting the solution it is not complicated it is just initially it looks little bit cumbersome, but it is not so. So, what are we doing here spatial effects means temperature change with respect to space with respect to the coordinate position that is what is meant by spatial effect. So, if I have if you look at this diagram here you have a plane wall which is a large plane wall you have a long cylinder you have a sphere now why is this a large plane wall why is the word large important why is the word long cylinder important that we will we will see when we come in and deal with a plane wall of you know finite dimension or a short cylinder at that time we will see because in case the dimension in the other direction let us take a cylinder this radial direction is here and the length is comparable to the radius then my two multidimensional or two dimensional conduction effects come into place. So, I will have a transient two dimensional conduction problem if I have a l by d ratio of the order of 1. So, that is why we are not dealing with short cylinders or plane wall of a finite dimension when we say a plane wall large plane wall it means it is of a finite thickness and extends in both directions to whatever length which we are not concerned with. Similarly, long cylinder would refer to a cylinder whose length is much greater than the characteristic dimension which is the diameter and of course sphere there is no such issue. So, what are we doing here we are saying we want to take care of variation of temperature with respect to space along with variation with respect to time what did we do in lumped capacitance in lumped capacitance we said well temperature is uniform. So, if I if I go to the white board and try to draw this for you in case of lumped capacitance method we said temperature at all x y z is equal to t at any given instant we did not have different numbers. Now, what we are saying is spatial effects when I am talking of spatial variation in temperature I am going to say that t at is a function of x probably a function of y and function of z, but we are restricting ourselves to only one dimensional because we are considering a long cylinder or a large plane wall with a finite characteristic dimension. And we want to take the effects of this variation in the heat transfer direction it is not some random direction it is the heat transfer direction. So, what it means is let me just go to the next figure that is a little bit this figure is actually very nice maybe I will draw this and explain that is better. Suppose I have a plane wall and center line is shown here let us say initially it is at temperature t i. So, at time t equal to 0 temperature is equal to t i and all through this surface I mean all through the plane wall my temperature is uniform because you are not started any change in the boundary condition. Now, let us apply a convective boundary condition let me say sorry this is t i is here let us say t i is here it is high. So, we will not look at this we will look at t i being high the body is at a high temperature initially. And now I am going to establish cooling at t greater than 0 at the boundary surfaces both surfaces I am going to have convective cooling given by h comma t infinity h comma t infinity at the this let me call x is equal to 0 and this is plus l this is minus l at the surfaces x is equal to plus minus l we have h comma t infinity as the boundary condition. So, at a given instant. So, this is a common thing which you which we will have in case of cooling quenching of hot metals metallurgical various metallurgical processes we are going to have this kind of a phenomena. So, it is not something which is out of ordinary we are going to see it every time. So, one hot body is suddenly subjected to a cold environment and we want to see what happens to the temperature what will happen I do not know any heat transfer I just know logic. So, let us use logic and try to find out what is going to happen. First thing I have applied a convective boundary condition at the free surface the complete layout is here. So, I am going to now say this temperature was the this temperature was the initial temperature I want to see let us say let us even take a number say 600 degree centigrade and h t infinity t infinity is say 30 degree centigrade. So, when I apply this boundary condition what happens logic tells me that first the two phases are going to reach the fluid temperature. So, it is not going to happen instantaneously. So, I have applied h comma t infinity what will happen is just at t greater than 0 I will have the boundary coming to t this is t infinity let us say this is t infinity here. This portion alone x is equal to l and minus l this will come to t infinity and everywhere else the temperature is going to be high. So, from the surface to the inside the effect of the change in the boundary condition is going to propagate that means at any distance at a small distance inside the wall inside the solid I would have a temperature slightly greater than 30 further inside I am going to have a temperature slightly greater than 30 further much more greater than 30 and at some distance you will see it is almost equal to the initial temperature of the solid. Why go to all these examples those of us who have cooked will know if you have boiled a full potato in the pressure cooker and you are trying to peel it common sense tells me you put it under tap water. So, outside surface is cool you try to peel it and then you try to you want to break it into small pieces. So, you use your thumb to press it and you will see the inside is still very very hot that is exactly what is happening here. You have t infinity the effect of the cold boundary condition which is propagated not all the way through in the in just because you have put cold water on the potato you have your surfaces become relatively cooler or maybe it is become much more easy to handle. So, you peel it off the surface is cool tap water is running you feel nice.  So, this is for let me call this as curve 2 at t slightly greater than 0 when the after boundary condition is imposed. Let us say t equal to t 1 we get curve 2 if I go further in time that means if I am going to say now t is equal to t 2 which is greater than t 1 the effect of this change in the boundary condition is going to propagate further. And I will see a curve which is generated like this that means further inside from the boundary the effect of the coldness associated with the boundary condition is felt. So, this curve 3 can be a situation where you have still some portion at t i depending on your time and depending on your boundary condition it can be a situation where even the center line portion where the hottest portion was there is has started to come below t i. Now, let us just go and look and see whether we are doing it correctly yes we are doing it correctly t equal to 0 t i is the horizontal line at t greater than 0 I see the first curve which is going like this and coming. Now, I come back at t equal to t 3 which is greater than t 2 I am going to draw curve 4 which it says that something like this this is curve 4 that means the effect of the cold boundary condition has propagated further inwards and has caused the center line temperature also to drop from t i value further increase in time if I wait for some more time this effect would be felt further you get a curve which is resembling curve 5 that center line temperature has dropped what am I keeping constant here this is anchored this is t infinity this is anchored here that does not change because that is the boundary condition t infinity is fixed t i is coming down. So, this curves come in as t increases. So, with increase in t my nature of the temperature distribution I do not know any heat transfer I am just using common sense it is going to come in further and if I wait for time t equal to infinity that is very long time I will achieve a temperature distribution which is almost uniform equal to t infinity whether we want that or know that we will see later, but qualitatively temperature changes in this manner in case of a situation where spatial variations are important that means for cases where bio number is large is greater than 0.1 0.1 was the criteria we have chosen here we are having bio number greater than 0.1 for bio number greater than 0.1 this is the nature of the variation. So, you start with almost uniform temperature further increase in time after application of the boundary condition you get curve 2 next you get curve 3 4 5 6 7 so on and so forth I have just drawn few representative curves but the point I am trying to make is the temperature trend if I close this part and have a line of symmetry here we notice that the curve is symmetric about the center line why is it symmetric it is symmetric because our impose boundary conditions are symmetric h comma t infinity is same on both sides of the plane wall if it were different then this half would behave slightly differently this half would behave slightly differently you would have a non-symmetry associated with the temperature distribution, but the overall behavior is going to be the same. So, the maximum temperature in that case would in a non-symmetric boundary condition would occur on the side of the one with the lower heat transfer coefficient. So, if the right hand side h is low if this was low then the peak would be on the right hand side if this was if the left hand side was low the peak would be on the left hand side nevertheless you would have a temperature distribution which looked like this in this case we are doing the symmetry boundary condition so we get a nice set of curves. So, that is what is shown in this graph and as t tends to infinity you come up with a horizontal line. So, all that is given in words here when the wall is first exposed to a surrounding medium t infinity greater than t i at t equal to 0 the entire wall is at initial temperature once the boundary condition is established flow is established wall temperature at and near the surface starts to drop because of increased heat transfer creates a temperature gradient what can we say about the temperature gradient what is the temperature gradient temperature gradient is nothing, but the slope the steepness of this curve very high temperature gradient initially temperature gradient is going to decrease as time progresses can that tell me something about the heat transfer rate yeah because of temperature gradient d t by d x is directly related to the heat transfer. So, larger the temperature gradient larger is the heat transfer that is why when you have this potato and you have put it under cold water you feel things are very nice because lot of heat has been taken off. So, the surface has gotten cool very nicely and the moment you stick your hand in and try to open it you see the effect of the special non uniformity that is why you have to spend if you want the entire potato to become cool you will realize that you have to spend lot of time holding it under the cold water rather if you just want the surface to be cool to get a reasonable temperature it requires a very less amount of time. So, heat transfer rate is also non uniform because the temperature gradient is non uniform heat conduction from the inner parts towards the outer surface note that temperature at the center point remains at T i until some finite time that I have already told. So, depending on the time at which you are plotting you will have a large portion of the near the center still at the initial temperature temperature profile gets flatter as time progresses and results in and as a result of heat transfer eventually becomes equal to T infinity which is the horizontal line wall reaches thermal equilibrium with its surrounding that typically happens after a very very long time that the wall reaches thermal equilibrium at this point there will be 0 heat transfer because there is no driving temperature difference between the fluid and the solid. So, similar discussion of course we can have for other geometries now what we are trying to say because of all this is all this I can write a story write a book how do I solve this mathematical for mathematics we still have the same heat diffusion equation this is something which those universities those colleges which cover this transient conduction spatial effects etcetera. You can have questions of this type where you ask for qualitative variation sketch this draw this please explain like this rather than asking them you know to write just instead of just writing graphically explain what happens when this kind of boundary conditions are imposed if bio number is greater than 0.1 give them a non symmetric boundary condition and see how they are able to do it in terms of the explanation. So, that you can test them on this concepts also so the governing equation for this case of course is the same whether it was lumped or non lumped it is the same equation, but now we have initial and boundary condition which are given like this initial condition at T at x is equal to 0 and sorry T at all x and time equal to 0 temperature initially time T equal to 0 and all x everywhere is equal to T i second one boundary condition this is an initial condition initial condition is required for all problems involving transient behavior. So, we want to know where the problem has started from at what temperature was the initial was the surface initially. So, that is why we have to give a initial condition boundary conditions we need to because this is second order in space first one of course is a very nice one easy symmetry boundary condition dT by dx is equal to 0 at x is equal to 0 this is true for all times. So, at all times so I will write this as dT by dx at 0 comma T equal to 0 I will write this in this fashion. So, initial condition T at all x and time T equal to 0 is T i boundary condition first one dT by dx at x is equal to 0 and at all times is equal to 0 this boundary condition is possible only only only if I have symmetry on for the size if I have the same boundary condition imposed on the exposed surface of the plane wall remember we had the plane wall x is equal to minus l n plus l was exposed to the same h and same T infinity only then I will see this symmetry here. If I have h 1 T infinity 1 and h 2 T infinity 2 I will not be able to write this boundary condition like this in that case I will have to know the line of maxima or minimum maximum temperature based on some kind of a analytical solution. So, I have to have a line of symmetry x is equal to some value depending on the boundary condition. So, that becomes a little bit more complicated right now let us just stick with the symmetrical boundary condition therefore, this is the boundary condition as a result of that symmetry the second boundary condition in space is minus k dT by dx at x is equal to l or minus l does not matter whichever you say is a convective boundary condition h times T at l special location is l at all times that is why the general time is used minus T infinity what are the assumptions here h on both sides is the same h is uniform throughout T infinity remains fixed of course properties are all constant. So, this body could be at 800 degree centigrade initially is coming down to 30 degree or 100 degree centigrade after a long time still we are saying this rho v C p all these properties remain the same with respect to this problem. So, that is a big assumption in reality it would not be the case we can account for this of course, once we get if you are going to solve this numerically or anything you can have a next temperature at the next time next time so on and so forth and once you can you get that temperature you can iterate you can get the new set of properties and apply that whatever be the case this is the boundary condition that would be there and we have to solve this how do I solve this. So, the differential equation and the boundary conditions are given by this bio number is greater than 0.1 spatial variation in temperatures do exist and this is the nature of the distribution now to solve this problem we have to take recourse to some kind of a series solution. So, that is what is given in the next few pages and many universities where post graduate heat transfer is there definitely cover this topic. So, for them definitely it would be useful others if you are not seen this I am sure there will be lot of questions. So, please make a note and ask them after the discussion is over on this topic. So, now let us get to the solution there are two methodologies one is the analytical solution which is obtained by using paper and pen the other is a graphical solution both are not two different solutions it is the graphical solution is just a graphical representation of the analytical solution. So, that you can if you are hard pressed for time you can just use the graph and get a approximate answer. So, what we do first thing we do is we have to non dimensionalize this equation. So, the formulation of the problem for determination of 1 D transient temperature in a wall results in a PDE which can be solved using advanced mathematical techniques. The solution however involves infinite series. So, those of you have mathematics you would have seen solution of this would have infinite series which are inconvenient and time consuming to evaluate. So, what do we do we do not do it that is not the thing we say that we can do it with restricting ourselves to 1 or 2 terms in the solution or go to the graphical approximation etcetera. So, what are the variables that are involved parameters are x independent variable time another independent variable L which is the dimension characteristic dimension k alpha which are material properties T i T infinity initial temperature boundary temperature H which is the heat transfer coefficient which are far too many we have 1 2 3 4 5 6 7 8 variables to handle. So, the obvious logical thing to do is non dimensionalize the governing equation. So, what do we do we say let us take a non dimensional temperature generally when we non dimensionalize any quantity we try to take the two extremities associated with that quantity. So, non dimensional parameter typically let us take for example, length scale x divided by L. So, when x is equal to 0 when you are at the center line this non dimensional capital X would become equal to 0 when small x is equal to capital L the non dimensional capital capital X would become equal to 1 or minus 1 depending on which side you are. So, that is the way non dimensionalization is typically done temperature the largest temperature difference you have is T i minus T infinity whether it is heating or cooling this is the largest temperature difference and local or T at any location at any given time minus T infinity divided by T i minus T infinity is your non dimensional temperature. Bio number is a non dimensional heat transfer coefficient do not take this like the you will see Nusselt number later on. So, do not get confused with this this is only for this lumped capacitance approach H L c by k of the solid and last thing is the non dimensional time which is called as the Fourier number alpha T by L c square. So, we have 8 variables combined together as 4 theta capital X bio number and tau. So, what do we want in doing all this once we start mathematics most of us forget why we are doing what we are doing we want let me write down what we want we want T as a function of X comma T this is what I want let us not lose focus of this. That means in a non dimensional thing I want theta so, if I want theta as the dependent variable. So, it has to therefore, depend on the all other parameters we know Buckingham pi theorem says many pi groups are there you can relate one with respect to the other same thing I am doing here theta is a function of what are the other non dimensional variables capital X this involves small x and L bio number it involves H L c by k what was the other number non dimensional time which is Fourier number which is alpha T by L c square. So, this is T minus T infinity local divided by T i minus T infinity is therefore, of function of all these 3 parameters and that is what we have written non dimensionalization enables us to give a temperature in terms of only 3 parameters capital X bio number and non dimensional time. So, what I do I have non dimensional I want to cast this let us actually look at what has happened. So, a partial differential equation with two independent variables X and T and one dependent variable capital T you will see now it is going to get transformed into something else. So, these were the boundary conditions T of X comma 0 is T i d T by d X is equal to 0 minus k d T by d X at X is equal to L is this these are the boundary conditions we wrote. Now, I am going to transform this equation by using the non dimensionalization which I have given and let me start here itself. So, theta is given like this. So, d T by d T has to be transformed to d theta by d tau because we do not have T anymore we do not have small t anymore we have replace this by theta we have to replace this by non dimensional time. So, let me take a look d T by d tau d time therefore, can be written as question mark for this we need to go to the definition of these quantities theta is equal to T minus T infinity by T i minus T infinity all of you please do this with me. So, I can write I am going to do this step by step later on when we do non dimensional analysis for convection we are going to do it fast because this is probably the first time we are doing this T i minus T infinity times theta plus T infinity is equal to T. Therefore, also we have alpha T by L square is equal to tau implies T is equal to L square tau by alpha. So, d T by d T is equal to T infinity therefore, can be written as if I take derivative of this this is my temperature expression in terms of theta derivative of T infinity is 0 whatever be the independent variable because it is a constant T i minus T infinity is the constant it is a number initial temperature minus the free stream temperature. So, I can write this as T i minus T infinity d T would be replaced by d theta now derivative with respect to time we have to take now. So, I am going to transform time in terms of this one. So, this d T would be equivalent to L square by alpha. So, this is going to be L square by alpha theta tau. Therefore, I would get alpha T i minus T infinity by L square d theta by T tau this is my transient term in the governing equation which I have non dimensional. Let me just go back and see if I have done it correct we do not have the intermediate steps, but let us proceed. Second thing is the left hand side which is d square theta by d x square I want to non dimensional as this.  So, capital x is equal to small x by L. So, capital x is equal to small x by L therefore, d capital x is equal to d small x by L I take the L on the left hand side I will have this. So, now I will write. So, this is going to be d by d x small x I will keep it like this d T by d x I have temperature here the derivative with respect to x or whatever is going to be just T i minus T infinity d theta d by d x would become L d by d capital x this quantity can just come out. So, I will write this as T i minus T infinity by L d by d x here can therefore, be replaced as this way and when I just go to the next step I will write this as T i minus T infinity by capital L square d square theta by d capital x square equal to d square T by d x square small x square. So, this was the left hand side of the governing equation right hand side we already wrote d T by d T is equal to I have already written that as alpha T i minus T infinity by L square d theta by d tau. So, what was my fundamental governing equation basic governing equation is this one. So, I am going to now ask this in a nice form put this non dimensional things together I will say d square T by d x square is the left hand side that is nothing but T i minus T infinity by L square d square theta by d capital x square is equal to 1 over alpha d T by d T I will substitute as alpha T i minus T infinity by L square d theta by d tau alpha cancels T i minus T infinity by L square occurs on both sides that also can be cancelled off and my governing equation therefore, looks like this. So, what have I done one p d e to another p d e that is all why why did I do so much why did I talk so much about this. Well this equation if you look though it is a partial differential equation with capital x and tau as the independent variables and theta as the dependent variable it does not have the effect of all other parameters which were sitting k h so on and so forth that is why this is a far more convenient equation the boundary conditions also have to be transformed. So, we transform the governing equation we have not transformed the boundary condition let us go back to the boundary condition T at x is equal to 0 all time is equal to T i that is very easy to transform go back to the substitution T i minus T infinity by T i minus T infinity theta would be equal to 1 that is what we have here theta equal to 1 at any small x it is equivalent to any capital x time T equal to 0 time T equal to 0 same thing except that instead of T i it is becoming equal to 1 d T by d x at x is equal to 0 we have taken the first derivative of temperature with respect to the spatial coordinate let me just go back first derivative of temperature with respect to spatial coordinate is this one d T by d x has become T i minus T infinity by L d theta by d capital x when I apply this to the center line small x is equal to 0 it is equivalent of saying at capital x equal to 0. So, the boundary condition would have been second boundary condition or rather the first boundary condition was we have written it as d T by d x at x is equal to 0 is 0. So, transforming this would be d theta by d capital x 1 over L at capital x is equal to 0 is 0. So, because x capital x is equal to small x by L when small x is 0 capital x is also 0 this 1 by L is there take it to the other side. So, the boundary condition remains almost identical the second boundary condition is what minus k d T by d x at x is equal to L is equal to h T minus T infinity that has to be transformed minus k d T by d x at x is equal to L is given by h times T at the boundary L at all times T infinity this is what was the boundary condition this needs to be transformed. So, this left hand side would be minus k d theta by d T by d x we wrote here the previous step here also we have written d T by d x is 1 by L. So, that k by L this k is from here already minus sign is there already k by L d theta by d capital x when x is equal to small L capital x is equal to 1 because capital x is equal to small x by L L over L becomes 1 right hand side would be h fine T L comma T minus T infinity that is nothing but theta L pi why is that. So, theta is equal to local temperature x comma T minus T infinity divided by T i minus T infinity. So, when x is equal to L I get T of L comma T minus T infinity divided by T i minus T infinity. So, I have theta L times T i minus T infinity. So, this T i minus T infinity. So, this temperature is nothing but T i minus T infinity will be there here. So, boundary condition would become not it completed it let me just go back to it. So, T i minus T infinity will be there there is a minus sign x is equal to 1 theta h L c by k T i minus T infinity is there x is equal to 1 L comma T T i minus T infinity. So, the boundary condition therefore, would become minus k by L d theta by d x at x is equal to 1 is equal to h this is nothing but T i minus T infinity. So, this is the T i minus T infinity times theta L and one of you did not catch me here when I did a small error d T by d x when I transform to d theta by d x I had a T i minus T infinity here also. So, there is a minus sign there is a T i minus T infinity which is sitting here. So, let me just rewrite it instead of causing confusion T i minus T infinity minus k by L d theta by d x at x is equal to 1 is equal to h T i minus T infinity at theta at I should not retain L I will retain make this as 1 because x is equal to L implies capital X is equal to 1 T is equal to general T implies tau is equal to general tau. So, it will be like this where did this come from this I had forgotten in the previous slide here and I had missed out T i minus T infinity here also I had missed out T i minus T infinity let me just you please write down this here I will show it to you here where I had made a mistake yeah d T by d x is not just 1 by L d theta by d x it is T i minus T infinity by L d theta by d x I had forgotten to carry this T i minus T infinity in the next page here. So, here it should be T i minus T infinity by L in this portion T i minus T infinity by L I am circling this times d theta by d x it does not matter in the final equation because it is a constant you have the right hand side equal to 0. So, this remains the same here I am going to have T i minus T infinity which is sticking here I have written that in the next part. So, T i minus T infinity times d theta by d x divided by L now things look correct this will cancel off this theta because we are doing it at x is equal to L it corresponds to capital X is equal to 1 T equal to general T corresponds to tau equal to a general tau and therefore, this boundary condition becomes d theta by d capital X at capital X is equal to 1 equal to h L by k that is nothing but bio number there is a minus sign. So, minus bio number times theta at 1 comma tau. So, this is my second boundary condition first boundary condition was very straight forward we could write it as d theta by d capital X at X is equal to 0 is equal to 0 this was the first boundary condition this was the second boundary condition. And your temperature related condition we have already written there let us just go back d theta by T T condition we have already written this to the straight forward time dependent condition initial condition was already written. So, the transformed governing equation looks like this with the transformed boundary condition once this is done correctly. And how do we know that actually how did I know I made a mistake here meaning how did I know I forgot to have this T i minus T infinity is because on the right hand side I was getting this T i minus T infinity it should not occur when I have a non dimensional equation everything has to be non dimensionalized h L by k I know it looks like bio number. So, that is a non dimensional quantity theta is non dimensional capital X is non dimensional this theta is non dimensional. So, this T i minus T infinity cannot occur here alone it cannot stand alone therefore, it has to get cancelled somewhere that is how I figured that there was a mistake in this path. So, this T i minus T infinity has to come and this is your transformed boundary conditions. Now, once this is done we are just going to present the solution to you. So, theta therefore, function of capital X tau and bio number and the exact solution of this partial differential equation looks like this it is theta at X comma T is nothing, but this series solution summation of T i minus n is equal to 1 to infinity a n e to the minus lambda n squared tau cos of X n time sorry X by L times lambda n where a n the coefficient is given by 4 sin lambda n by 2 lambda n plus sin 2 lambda n. I hope all of you can see this part clearly and what is this so called lambda n the discrete values of lambda n are positive roots of this transcendental equation given by lambda n tan lambda n equal to bio number. So, what is to be done I have this theta it is given by a series solution what is this a n what is this lambda n all these things we are trying to explain a n is given by this equation and a n requires lambda n which is nothing, but a solution of this equation X times tan X is equal to bio number something of that form. So, I have to have a solution for X or in this case solution for lambda n and we do not have to worry about this solution these are all given to us in mathematical tables. So, what do I do theta I have to calculate I need suppose let us take first two terms I will have n equal to 1 it will be a 1 let me write it for theta of minus t divided by t i minus t infinity this is nothing, but the definition of theta. So, this is nothing new now I want to write the series solution the series solution you had was this one. So, we want to write one or two terms associated we want to write the first term associated with this expansion.  So, on and so forth what is this a 1 a 2 we have a 1 is equal to 4 sin lambda 1 divided by 2 e to the power minus lambda 2 squared tau cos of lambda 2 x by l plus. So, on and so forth what is this a 1 a 2 we have a 1 is equal to 4 sin lambda 1 divided by 2 e to the power minus 2 lambda 1 plus sin of 2 lambda 1. Now, what is this lambda 1 lambda 1 is obtained by solution of this equation lambda 1 times tan lambda 1 is equal to biot number. So, the solution of this equation will be given will be used here and that is going to be used here. I have written for a 1 we can write similar expression for a 2 a 2 would be 4 sin lambda 2 divided by 2 lambda 2 plus sin 2 lambda 2 the transcendental equation for lambda 2 would be lambda 2 tan lambda 2 equal to biot number. So, what we are saying is I have the solution I have n terms n going from 1 to infinity how many terms do I have to take 1 2 4 14 50 well logic tells me more the number of terms better it is for me, but in this case what we are saying is many times it is given here very nicely and just go back to the power point we will come to this. This is what I have written first this is only the first term a 1 e to the minus lambda squared tau cos lambda 1 x by l we are doing it for plane wall. So, this is the solution for the plane wall I have written this term on the white board first term and the second term I have written this slide here shows the first term alone and what is being told is that it can be shown that values for values of tau greater than 0.2 when tau is greater than 0.2 this series solution can be approximated by only the first term in the series. So, I do not have to take care of second third term also only the first term is almost equal to the correct solution in case tau equal to tau is greater than 0.2 what is tau let us remember what is tau tau is non dimensional time alpha t by l squared. So, for a given problem alpha is the material property we know the characteristic dimension l at what time I want the temperature distribution that is going to be specified you have seen problems 200 seconds after the process has begun 50 seconds. So, that tau is known. So, I can calculate tau because alpha t and l squared are known and once we know tau is greater than 0.2 what we are saying is that in such situations this big series solution though it has infinite terms only the first term is sufficient to give a reasonably correct solution. So, that is what is given here for a plane wall we have given this solution first term approximation this is called as the first term approximation where constants a 1 and lambda 1 are functions of bionumber only how do I know this because of this a 1 I put instead of n n equal to 1 where lambda 1 lambda 1 lambda 1 will be there what is lambda 1 lambda 1 is of this form lambda 1 tan lambda 1 is equal to bionumber. This equation will have multiple solutions because tan is a tan function is a periodic function sorry it is not it is going to have various values from 0 to infinity. Therefore, I am going to have different values of lambda 1 and these values are tabulated for us in this table. So, most of the text books would have this table where the first column for those of you who cannot read this first column is the bionumber going from 0.001 to infinity why are we using 0.001 this whole exercise started because we are saying bionumber was greater than 0.1 lumped capacitance is not valid does this mean that this mathematical solution is invalid for small bionumber no we are saying this is the general solution lumped capacitance is a special case where I do not have to deal with these kind of big mathematics I can just use uniform temperature. So, we do not normally care about these tables for lower bionumber less than 0.1 does not mean that solutions do not exist. So, bionumber ranging from 0 to infinity we have these values and this table gives this is psi right psi psi 1 psi 2 psi 3 psi 4 which is nothing but lambda 1 lambda 2 lambda 3 lambda 4 this is zeta and this is zeta zeta 1 zeta 2 zeta 3 zeta 4 is given in your slides it is nothing but lambda 1 lambda 2 lambda 3 lambda 4. So, the first 4 roots of this equation are given in this table. So, you know the bionumber you have calculated tau.  So, once lambda 1 is known a 1 can be given obtained. So, it will be 4 times sin 0.8603 divided by 2 times 0.8603 plus sin 2 times 0.8603 remember these sin functions are in radiance. So, you can have sin greater than 1. So, you will get a 1 once a 1 is known very nicely I have written everything here a 1 is known lambda 1 0.8603 square tau we have calculated was greater than 0.2 cos lambda 1 I have calculated from the table x what location I want the temperature is it mid plane is it 0.25 from the mid plane is it at the surface whatever. So, x by l is already there. So, the ratio of x by l is there everything here is known I can get this right hand side only first term I need in case I need the second term I do the same thing from this table I go get for bio number is equal to 1 get the second lambda 2 3.4256 if I need the third term I have this one 6.4373 so on and so forth. So, the point I am trying to make is though things look very complicated on face value it is not. So, and it is just good book keeping that is going to give us a proper solution. So, once all these are known theta is obtained we have an example cooked up example problem which we will do after the t break let me just go here I will just show you this cooked up example problem is there we are going to do the analytical part from 1130 onwards we will have t n assemble here by 1115 or 1120. So, we will sign off for now thank you.


Dr. Phil McGraw has worked extremely hard over the years so you can't blame him for wanting to relax in a multi-million dollar home. The iconic TV show host is the owner of a luxurious Alamos-Tel mansion where he currently lives with his longtime wife Robin McGraw. This massive estate in Beverly Hills ran Dr. Phil almost 30 million dollars but it offers more privacy than one can usually find in overcrowded Los Angeles. We'll take a look at this not so humble abode, all the crazy decorations he's got in this mansion and some of the other properties he's owned in the past. In these videos we don't reveal any addresses and even though I've done a house tour of my own place please do not show up at any private residences because it's not safe for anyone. Philip Calvin McGraw known to us all as Dr. Phil is a TV personality, author and host of the television show Dr. Phil. The show draws on 25 years of experience in psychology, sociology and observation. He holds a doctorate in clinical psychology but ceased to renew his license to practice psychological therapy in 2006. But I mean when you're doing as well as Dr. Phil is who has time for that anyways? I've actually met Dr. Phil, I was once upon a time on the Dr. Phil show and the guy is a genius. Like he was the best TV host I've ever seen.  I kind of want to be Dr. Phil, I should have got more education. McGraw rose to fame with appearances on the Oprah Winfrey show in the late 1990s where he was the resident expert on human behavior and then Oprah helped him launch his own TV program. Dr. Phil aired in September 2002, is formatted as an advice show and has been going strong since. Dr. Phil continues to deal with real issues in his signature blunt style. In October 2003 he launched the Dr. Phil Foundation which funds organizations that help disadvantaged families and their children. Dr. Phil and his wife Robin McGraw have been married for over 30 years and she's a New York Times bestselling author herself. It's said that the McGraws have a current estimated net worth of $460 million. So it makes sense that the couple are able to drop a casual $29 million or more on the place they currently call home. Not to mention they've also spared some millions on homes for others like when they bought their adult son Jordan a lavish pad or two. But I'll get into that shortly. Hey guys it's Kara. And I'm Michael McCrudden. Now some of you don't know who I am but I'm actually Kara's boyfriend and I'm kind of your boss. Yeah both. Awkward. But we work together. We work on many YouTube channels and we're having a lot of fun doing this and huge congrats to Kara because she's absolutely blown up. Now if you guys haven't subscribed to this channel you gotta do it because we noticed that 95% of you are not even subscribed. So get that done and I'm gonna let Kara finish this video. Bye baby. Thanks. I cut you off I'm sorry. Okay. I'd kiss you but that'd be awkward. I'm just gonna go. Okay. Bye. Today we'll be looking at a few beautiful homes owned by Dr. Phil McGraw and his wife Robin including their current Beverly Hills estate. We've also done house tours in the likes of Howard Stern and Joe Rogan and we'll link to some at the end. Follow me over on Instagram to chat and as usual let me know who's house tour is next in those comments down below. Now let's get into this video. We'll take a look at Dr. Phil's previous home. In 2010 it was reported that the McGraws put their Mediterranean villa in Beverly Hills on the market for 16.5 million just before they upgraded to their current digs. Property records revealed that Dr. Phil purchased this home in the 90210 hood back in 2002 for 7.5 million in cash. While listing info didn't show square footage of the home, the tax man shows it measures over 11,000 square feet and sits on a lot nearly three-quarters of an acre. Dr. Phil's previous home was in a prime location just north of Sunset Boulevard and was completely walled and gated for celeb style privacy. The masterpiece mansion offered eight beds and seven baths as well as a generous sized public rooms and designer finishings throughout. Elsewhere on the property there was a detached two-bedroom guesthouse for some extra space. Walking in there's a glamorous two-story rotunda entry hall with diamond patterned stone floors and a sweeping dual staircase for making dramatic entrances and exits. Nearby you'll find a luxe-looking great room with Julia Balconies and an ornate chandelier and another living room with fireplace. And those are just a few of the many rooms in this mansion. Other amenities include a formal dining room, library, family room, colossal kitchen and a half-circle shaped breakfast room with mirrored walls. There's also a billiards room, home theater, fitness center, media room, his and hers offices, staff quarters, a beauty boutique and three fireplaces throughout. Not to mention Dr. Phil and Robin were able to share a lavish master retreat with sitting area, private balcony, two baths and custom fitted dressing rooms. A wide dining terrace extends off the back of the house with an outdoor fireplace and media center for watching TV outside. A pathway leads at the large swimming pool and raised circular spa. In the end the McGraws had to adjust the price but ended up letting Gold this mansion for closer to 13 million dollars. The TV shrink hadn't even sold his old house yet before closing on his current one, located on three acres of hilltop land in Beverly Hills overlooking their former house. Apparently the celebrity couple had their eye on the massive home for a while and jumped on it when it came to the market. It's still the mega mansion where Dr. Phil and Robin lived to this day. The luxurious Alamo style mansion boasts around 15,000 square feet not including the separate guest house out back as well as five beds, nine full baths and two half baths. Dr. Phil and Robin loved the home so much they were willing to spend a whopping 29.5 million on it. But it is quite impressive to say the least.  While there weren't many listing photos circling online of the very privately situated property, we've also been able to catch glimpses from Dr. Phil and Robin themselves. There's a two story entrance hall with sweeping stairs, a formal dining room, library, games room and a kitchen family room complex. If the couple's previous estate is anything to go by, Mrs. McGraw likely decorated to her heart's contents with glittery touches and Tuscan extravagance. Since they've been spending a lot of time at home during the ongoing pandemic, Dr. Phil has shown fans a glimpse of his home office captioning it, my desk during quarantine. I grew up with a chalkboard. Times they are changing. His classy office also boasts a fireplace and wall mounted TV. The living room is grand with vaulted ceilings, gorgeous wood beams, modern decker and zark finish eggs. There's also couch space for the couple to unwind with their docks. In the multiple living areas, it seems the family loves to spend time in this spacious kitchen cooking together, which is fitted with the best appliances. There's also marble countertops, a massive island and bar style seating. All four of the family bedrooms are located on the second floor with their own bathroom and the master suite that Dr. Phil and Robin share has dual baths, a private sitting room and a terrace. The property offers some of the best views of Los Angeles and outside the space is just as nice. There's a covered lounge without their fireplace faulted ceiling and terracotta tile floors, which runs along the back of the house, leading to the flat lawn. By the looks of his Instagram, Dr. Phil likes spending time playing at the full size and lighted tennis court they have. Not to mention, there's a swimming pool and panoramic city lights view back here. The couple also loves decorating for the holidays. So now that Halloween is over, we'll see what Robin throws together for Christmas at their mega mansion. Before we wrap up this video, let's take a look at the home that Dr. Phil owned but never lived in. Rarely this year, mansion in Beverly Hills went up for sale for 5.7 million where Dr. Phil's rocker son Jordan McGraw had been living with his bandmates and the place was quite an eye-fall. Part Playhouse, part Tim Burton inspired this outrageous and expensive design sparked some controversy on the web. Ever since listing photos were published, social media went to town poking fun at the unconventional designs that only a 20-something year old with unlimited funds could have dreamed up. I gotta say, I do like these weird interiors. In summer 2016, a then 28-year-old Jordan offered the Daily Mail a tour of the estate and said, the idea is kind of Tim Burton threw up on a canvas and turned it into a house. Black velvet wallpaper aside, the 6,170 square foot estate sits on a gated half-faker just minutes from the Beverly Hills Hotel and offers five bedrooms. It's quite the home and if you can't get behind the designs like me, there's definite remodel potential. Jordan dreamed up the wild wonderland with the help of LA Design for Mogul. As you enter the property, there's a snake fountain, a reference to a nightmare before Christmas, giving guests just a hint of the trip to come. In the entry hall, there's a bedazzled bar at the bottom of the entry, which is meant to look like the rabbit hole in Alice in Wonderland. And the showstopper, the jaw-dropping glassed-in walls of guns in the dining room. While this modern estate isn't for everyone, I would totally live here. What about you guys? So now we've taken a look at the homes of Dr. Phil McGraw and his wife Robin and even one that once belonged to his son Jordan. After seeing the three Beverly Hills properties, which was your fave? The couple's current sprawling $29 million plus home, their previous one? Honestly, don't judge me, but my fave was actually the last home his son lived in. It's way more my style. And nobody would have an estate anything like it. And plus, I'm also a Tim Burton fan, so if the shoe fits. Be sure to rate Dr. Phil's homes in the comments down below. I'd also love it if you guys subscribed to my personal channel. I post a video every Sunday and I'm trying to get to 1,000 subs. We'll link you my latest video. He was inside, but he kept falling and horrifying the dogs as well. So he's out here for a time out right now. Thanks for tuning in. Don't forget to follow me on Instagram and let me know which celebrity houses you wanna see next. I'll see you all in the next video. Bye.


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So welcome everybody today. We're going to do a quick review of github co-pilot I have two extensions installed one is the co-pilot extension. The other is the co-pilot chat extension So this is the co-pilot extension this you need you'll need to connect it to your github account And then there's the co-pilot chat extension This is a second extension that allows you to actually open a chat window And this one's really powerful and this is the one that I get the most value out of Basically minus setup using all the defaults. I haven't changed a thing. Okay So one of the things that co-pilot has is this The what they call the sparkle command. So if you are looking for Some sort of a VS code setting save on format You know, I save on format Or something that our format on save or whatever You have this option that will appear that says ask github co-pilot. Okay, so when you click that it then Does its thing and it says It seems that you want to save on save the current file and visual studio code You can do this by control s if you're on windows command s if you're on Mac Okay, but it has additional Additional things so then this down here you see that the sparkle they call this the sparkle icon You will begin to see that once you installed in many different places This is the Saraswati project and this is the custom Google Drive Loader this is a hodgepodge of GitHub co-pilot going absolutely nuts and spitting out all kinds of code right things that I don't even understand Okay, but that's all right because one of the great things about This tool is if you open up the chat window here with this line selected I can do Explain Don't have to type anything else So it's looking at this line and in theory it's going to give me an explanation of what it does and what it is including examples and you can see down here the Sparkle icon again, that's a follow-up question. It's really remarkable Could you please show you an example of the explain of like an API cool with Where the documentation isn't necessarily like go into the library like sure that Sure, so Jerome, what do you exactly want to know for example? What are the parameters? Yeah, so like for example the doc the example that she gave in the video was called to the database where it added various Extra flags to the cool right the API cool and she was saying that these are examples from an old version of the documentation I'm wondering how well and your solution to it and adding random Extra flags and things is to say it can actually help explain these things to you And I want to see like how well it works when it's given Like an API cool where the documentation isn't necessarily like Gonna be indexed or it might be indexed, but maybe not the most recent version Do you know what I mean? Like if you've made a call to Google slides API, which you seem to have somewhere here Yeah, so for example can If you ask it like what does this the source mean in the Google slides API result something like that like something really specific that's like All right, you can do you can just ask you questions for example No, let's say so you want to know What does the source? Attribute mean Where does it come from What does It represent for example, right Yeah, so maybe it's maybe it's just like here. I see a scope and am I I'm just Right, so it's looking at the thing is it's looking at what I've selected right here So if I just if I come in here like this and I just select say You know this this bit here Above question using the selected code. This is exactly correct by the way. This is 100% accurate I'll give that a can you Pretty amazing pretty amazing This is a specific Python construct and you can see down here it ends with yield, right? That is used quite a bit by and it's an advanced programming Python programming language feature that is very low memory use and Should be used whenever possible So it looks like a loop, right, but it's actually it's a memory Low memory use loop. It's a generator function. That's what it is. Yeah, so exactly correct It's a generator function. It's done using the yield keyword Exiterating over the list of files returning the most recent it's incredible Yeah, the advantage of generator is that it doesn't need to compute all values up front Which can be very useful for large data sets Just one of the reasons Python is so is used so heavily in data science This is the let me show you some of the some really cool things that this can do, all right Watch this. We'll just we'll just write on it So when we're you know when we're developing new products focus really isn't on getting the code, right? The focus is on getting it working and the tests passing Then we'll go back and we'll look at how we can refactor to improve the quality of the maintainability of the code so As you can see we've got some work to do Right list all the code smells look we got quite a few we have nine code smells here Let's do this. I want to give you another demo that that has a very interesting approach and Over here what you can do is You can open the chat window right here, for example, so you could say And you can do the same thing. I don't know how to fix the latch Type hints in this file and the difference is it's the UI that changes And I think it's easier to work with when you do when you do it this way Okay Now this looks really awful Okay, and it basically just it it's not a very elegant approach and on a tiny screen like this It's really annoying right so here's what I do I go like this There's this option here discard to new file Okay, because I don't want to accept these changes without reviewing them I want to see what the hell it's actually doing. So if you create a new file, that's pretty cool It opens it up like this and you can begin to sorry you can go through and you can Analyze What the changes consist of so it's starting about right here? Sorry, this isn't a great approach as you can see because it does thing You know when you create a new file, it's not including all of the context So Python starts complaining about indentation and things like that But you can begin to go through and see where the missing Type hints are so let's look at oh, I'm sorry The first thing that it did was it included list and dictionary to our typing our Call for the typing library. Okay. Well, that's cool. So it did definitely add some so the first one here is discussed Custom Google Drive loader. Let's give it a little more space and you can see this line right here. It's added String a dictionary with a string or any subtype type script people will recognize this Annotation immediately. So then I think it may have added some to Yeah, see there's a Boolean. I don't yeah recursive equals false it added the Boolean type right there So this is one approach you can use for adding For going through and fixing stuff that's broken What's the shortcut for this check window? command-i So you can think of it that way and We're doing the same sort of thing and so it's going through and it's finding all of the instances of multiple Responsibilities and it's going to try to ferret them out into separate classes With varying degrees of success and failure. Mind you. This is not this is this is an it, you know, mega advanced sort of Behavior and to expect it to just get it right from the you know from the get-go is You know come on really so Interesting what it did here. It's hard to say exactly what it's done. I don't really know what it's done here It's odd that it removed the comment But it's doing super in the in it. Yeah, I'm too though, so I Don't know if any of you see what it's done. Let me know Well, it's got a load method, but that was there anyway, oh No, no, no the London initialized service as well.  I know the road I don't know what it's done. Well, yeah, no initialized service. That's a new one. It's done that That's nice. That's helpful. It's one that I had in mind, but I just haven't had time to get to This load there is the base class has its own load Function and it's overriding it for some reason. I'm not really sure why I guess because it's doing the initialization here. Okay Let's just let it go Hello They got confused it doesn't know what it should do. Oh, there we go. Oh Tomah Okay, and then look also by the way when sometimes you'll get multiple completion recommendations or suggestions and if you roll if you mouse over you can go you can navigate through them, right? so This is really interesting. I Just said yes to all of this Who will dockloader not a great name, you know, but you can modify that sort of thing by by clarifying up here in your comment What exactly you're looking for? But you can you can see I'm not gonna go too much further into this because this is like this.  So this bit's kind of lame. Okay, but It can work. I don't really have any good examples, but let me just give you this one example Okay, so like if I come up here and and I want to commit this one file that I've staged You'll see I have the sparkle icon if I click that it's gonna generate the commit message Really lame. Sorry co-pilot on that one. No, that's a fail. Sorry about that Because it's like, of course, I'm adding it, but what's the feature that I'm that I'm modifying So in my notes file here, I have I've added some data on some test runs that I created And if I select that and then I come up here and I do the same Fix bug There's no bug. I don't even know where it came up with that. That's why I said lower your expectations It's gonna get things wrong. I don't usually use the terminal in VS code that this one feature may Convince me to start using it. Okay, so Let's say I'm trying to do something and I execute the command WTF it goes. Hey WTF hasn't found but look there's my little icon. So if I click that Explain using co-pilot Right Okay, cool. Thank you for letting me know. Let's we could try brew install WTF util Who knows if that's even a real package that could just be a complete elucination, all right And with that So really good stuff Cool. Thank you all for listening. I appreciate it. I hope we got something interesting out of this


So, thank you Arpeth and good afternoon everyone, so I am going to give you a quick update on what Open Networking Foundation has been doing for last year or more and also tell you that in the process of kind of driving SDN, NFV with disaggregation and open source, we ended up kind of inventing or creating a unique open source model that we call curated open source and I will try to both tell you what we have been doing and then also try to tell you why and how we ended up inventing this unique open source model that we call curated open source. So, the first thing is that I hope you all know that Open Networking Foundation's mission has been to help network operators transform their infrastructure and services. And the idea is to help operators bring lot more CAPEX and OPEX efficiencies as well as help network operators invent new revenue generating services on top of that infrastructure under which the city of AT&T keeps saying that I want to turn my network infrastructure into a platform for innovation and a platform for innovative services and that is what we are trying to do. And the way we are trying to do this is by pushing SDN and NFV cloudification as innovative architectures forward, but in addition to that using leveraging disaggregation and white boxes and open source. So, what is important to recognize about ONF and the mission we are after is we are not only about open source, we are not only about SDN or we are not only about disaggregation, we strongly believe that if we are going to bring about this transformation and if we are going to help operators succeed in this transformation, we have to drive all these three things SDN, NFV architecturally, we have to push for disaggregation to bring that economies and all that and we have to push for open source. And when we drive all of these things together that is how we can bring about this transformation. But now when you look at if you want to drive disaggregation, open source, SDN, NFV together what that leads to is you transform a network either today's network or future network built using close proprietary boxes to something like this where you are building this infrastructure with simpler forwarding devices built with merchant silicon and white boxes. The SDN and the NFV control plane that is realized using you can call network operating system and then on top of that you have network and management control applications, you have virtual network functions, you may have services and all of that and that is what you build on top of this infrastructure. Now what I want to emphasize is that when we are doing this disaggregation and bringing open source and NFV, we are not only talking about doing it to package switches in data centers, we are bringing this approach to open line systems or OLT for broadband access that is how you build Gpawn, XGSpawn and these network for broadband access. We are bringing the same approach to radio access network with disaggregation with RUDU and bringing this to the 4G and 5G networks and we are trying to do the same thing with the optical networks, optical transport networks with open line systems and disaggregated RUDU. Now when you look at all of this together, I hope you recognize that this represents a major disruptive innovation in some sense and this is a disruptive innovation for network architecture and more importantly this is a disruptive innovation for the business model of networking industry of last 40, 50 years and when you think about it that way, you are not surprised that most of our leading OEMs find it very difficult to decide how to deal with this disruptive innovation, should they embrace it? If they embrace it that means they are going to cannibalizing their products and revenues of today and so not surprising we find it difficult to get developers committed to our platforms and solution from the leading OEMs because today most of the developers in the networking industry are in these OEMs and what that means is that we have found it difficult to build developer communities around our open source platforms and solutions. So what that meant is open networking foundation and our operators ended up creating inventing a new open source model that we call curated open source and curated communities and that is how we have been building some amazing open source platforms and solutions but before I get to them let me tell you what we mean by curated open source and curated open source community. So let us begin with the operators. So when you think about AT&T, Deutsche Telekom, NTT, China Unicom, these are some of the operators that we worked with. These are the operators that operate, own and operate some of the largest infrastructure in the world. They are all committed to the transformation I was talking about, transforming that infrastructure so they can build it with this aggregation, open source, SDN, VPN, VNF and all of that. Now these are the operators that know how they are going to go through this transformation. What are the use cases that are important to them? What are the priorities for them? And so that is why we start with them and then with these operators we decide what are the particular solutions, particular use cases that we are going to focus on and that is what they are the ones that prioritize what is important and what is ONF and this community should pursue. Then we have ONF and an engineering team. So we have a team of maybe 30 people that are part of Open Networking Foundation. Sometimes our board members and others in the industry have described this team of 30 people as small and mighty team and the interesting thing is that this team has no legacy to protect. They are not trying to push particular agenda except the mission that we are after and so they are able to pursue disruptive architectures, disruptive solution with lot of passion and number of times we have done things then people said this is impossible to do or this is crazy to do and that is the kinds of things we have done again and again with our platform. Then another important thing is now operators also bring a supply chain partners into this ecosystem and these are the supply chain partners that are committed to this mission, mission of desegregation, mission of SDN, NFV and open source. So once these supply chain partners are part of this ecosystem then they work closely with the operators. They work on platforms and solutions that the operators care about and operators want to take it into deployment. As a result they do not have to do lot of guess work about what operators want and what operators are going to deploy. They are working hand in hand with the operators. As a result for these supply chain partners there is significant benefit in terms of reduced time to market and because the supply chain partners are complementary with each other that is they are not competing head on or they are working together they also realize lot of benefits of shared R&D and that is significantly reduced R&D cost for creating these platforms and solutions that operators are wanting to deploy. So in some sense this is kind of what we mean by this curated open source model and the community that we have been building. Now here in the community that it looks like for all the reasons I mentioned it's not surprising that we have our top operators these are our board members. These are the people that own and operate the network they know what the strategic priorities ought to be and they provide the strategic direction and guidance to open network foundation. These are the supply chain partners that the operators have recruited and they work together to create these platforms and solutions that the operators want to take it into deployment. Of course we extend this value proposition to many more operators that are members of ONF and our ecosystem and on top of that we have supply chain people and the collaborators. So this ecosystem is approximately 150, 160 companies but this is how this ecosystem works which is kind of unique in open source and how we do things. So that was all about our mission, how we operate, how this curated open source model is. Now let me quickly walk you through what are the open source platforms and solutions that we have been building for last few years. So let me begin with stratum. So if you take a packet switch a white box packet switch stratum is a thin switch operating system that sits on top of the white box packet switch for example and it supports these SDN interfaces. We call them next generation SDN interfaces that is beyond open flow. So supports like P4, P4 runtime, open config, GNMI, GNUI and I will talk about that in just a minute more. Similar to stratum we have another open source platform that we call Volta. It is again a thin software layer that creates the open flow abstraction or a uniform hardware abstraction on top of variety of OLT devices that make up the GPON and the broadband access networks. So again you have a uniform open flow abstraction on this particular device. Similarly we have built an XRAN controller that does the same thing makes radio access network, a disaggregated radio access network that is SDN enabled and on top of that you can build services and similarly we use disaggregated open line systems and rodents and then on top of that we use ONOS as the SDN controller or you can think of that as an SDN network operating system and that is designed for scale performance and high availability and then on top of that we have this open source disaggregated and virtualized EPC thanks to Intel and Sprint. We got this release 13 compliant implementation that is again disaggregated and virtualized and this is the almost production ready that is going into production in Sprint and DT sometime later this year. Then on top of that we build a variety of services and these you can think of them as virtual network functions you can think of them as services but we have a portfolio of 30 or so services that are a part of this portfolio and then finally we have a platform that we call XOS so this is the platform that is you can think of it as a service operating system or a platform that does service lifecycle management service composition and putting service graphs or service meshes together and managing those services. So for a second if you look at this particular software stack that we have built you can see this is a software stack that you can take it into broadband access you can take that into mobile wireless packet core and much more and now this is only the half of the story because now the challenge is on one hand to do the innovation you do need this aggregation and this open source platform but when it comes to deployment the operators do want integrated solutions they don't want disaggregated component there are very very few operator that can afford to take all this disaggregated component put it together and deploy that in the production network. So you do need integrated solution and that represents a challenge and that's what ONF kind of because of the requirement we kind of stepped up to create some integrated solutions as well and let me briefly tell you about some of them. So the first one is what we call trellis as the NFV fabric okay and so what that particular solution does it brings together open flow white box switches okay those are kind of what I already mentioned they may right now they may be running OFDPA but in the future they will run stratum on top of that onus as the network operating system or SDN control plane and then there are set up application that turn this into a distributed leaf spine fabric okay and the good news here is that there is a tier one operator in the US that has already deployed this distributed leaf spine fabric into their production network in multiple geographies and that is carrying traffic from many I mean thousands of live customers and if you look at their plan they're going to scale it to many many geographies in 2019 and there are plans to deploy that in some other operator networks as well. The second solution that integrated solution that we have enabled is something called SIBA it stands for SDN Enabled Broadband Access okay and this is kind of bringing SDN to the GPON XGS PON and some of the broadband access networks where we bring in this solution we bring again open flow enabled switches white box switches the OLT devices that I mentioned to you that's run Volta on the top and become part of SDN and then of course onus of the operating system XOS and NEM and a set of services this software stack that is sitting on top of these devices also provides F caps capability that all the operators want and then this software stack integrates with the OSS BSS of the operators and here AT&T, Deutsche Telecom, Turk Telecom, Telefonica are some of the operators that have publicly stated that they are doing trials with this and they have plans to take this into production in 2019 and beyond the next solution that we are building is you can think of that we haven't picked the name yet we informally call this next generation SDN stack and again it begins with white box switches and stratum and as I mentioned stratum is the one that supports all the next generation interfaces P4 P4 runtime and all of that and then now we are also building the next generation onus and then on top of that a set of services and now this particular next generation SDN stack is going to become the foundation for all the other solutions that we build so we are going to transition from open flow base SDN to P4 open config GNMI and all of that as we go forward so to just give you a little more context about this so as you know we started with open flow at the SDN thing separation of control and forwarding open flow was the protocol that defined that but that protocol was a standard it was kind of defined and relatively static and as a result it was really not allowing you to specify the forwarding behavior dynamically in software and making it easy also we didn't have much of configuration we didn't have much operation that were part of the SDN architecture okay now what we have done with all the advancements that have happened that you can have a programmable forwarding plane forwarding thing or you can have fixed function but what we can do is to allow a network operator to be able to specify the forwarding behavior they want in P4 in a higher level domain specific programming language and through a compiler you can compile that forwarding behavior and then instantiate that in the switching or in the forwarding plane as well as in the control plane using something called P4 runtime okay and then we are also trying to support configuration now and the operations for configuration we are supporting open config and GNMI and for operations we are supporting the GNI protocol and these are the interfaces that Google have successfully used in their network and we are not trying to adopt them in this next generation SDN okay and then and so that is what makes the stratum and as I mentioned now we have begun some work on next generation or not where on one hand we want to support the next generation SDN interfaces but also we are re-architecting onos so we can bring microservices based ideas and try to make that onos very very what should I say tighter footprint for a given use case so that for a given use case you can definitely customize it for that particular use case and so together our goal is to bring two big benefits to the network operators so the first big benefit we want to bring to the network operators with this is enable operators to completely control of the network they can specify their behavior in the P4 and compile it and then be able to achieve the zero touch networking for verification for network debugging change management and lifecycle management okay okay so briefly I am going to talk about another particular thing that's a converged multi access and core in some sense this is the most important thing so here what we're trying to do is to bring all these pieces together into a converged access and edge okay and this is there are many operators that are supporting us but let me give you the problem statement and you know what we are trying to enable so the first thing is that the network operators operate many networks you may know this right for every access technology wireline for wireless different kinds of wireless network they end up operating many infrastructures okay and they end up deploying lots of physical devices in order to operate this infrastructure as you can imagine this is very capex and OPEX intensive and it makes their life much harder and this is only going to get worse with 5G and IoT so the holy grail in the operator world is can you build a single infrastructure where only the access link is unique depending on the access technology but rest of the infrastructure can be the same okay and that is what we are trying to enable where not only the infrastructure is the same you can also have seamless services that is a service can migrate from one network to another and a user can migrate in a seamless fashion without having to worry about which access network you are on okay so I'm just so the interesting thing here is that because of all these innovations I'm talking about what is considered the holy holy grail of conversion becomes possible because if you have all this desegregation you have this virtualization then you can combine these functionalities for multiple access technologies and you don't have to have multiple network so all these innovations I was talking about we are able to bring them together and be able to build a single platform that brings all of these together for wireless as well as wireline network I'm sorry I'm running out of time so I will not go in but give me one minute to wrap it up so but the idea is we are able to now show that everything that we did for wireline as well as the wireless because we did that with desegregation and because we did this is virtual software function we are able to bring them together and in fact if you are familiar with our architecture called called it actually brings all of these pieces together and now we are leveraging all of this to create this converge multi access with number of operators okay my last slide I will jump to this okay so thanks for sitting through all these PowerPoint slides and very high level overview but interesting thing is that everything I said is here on the floor you can go and check out all these develop I mean the platform solutions integrated things I talked about all of them are here lot of developers are there from the community go and ask hard questions about implementations and what we have done and the last comment if you like what you see don't be shy come and join us and together we can make this transformation happen thank you.


News update. Good afternoon folks Steve Rhodes coming to you live from the shores of very sunny Delray Beach Florida this year one PM update currently of all the U.S. indices trading to the upside the Dow is up half a percent that's a hundred seventy nine points the Nasdaq is up two and a quarter percent three hundred thirty points the S&P one and a quarter percent fifty three points the upside the Russell's up two and a quarter points forty four points semis up nearly four percent hundred twenty two points he straight out at thirty four twenty six out there gold is up eleven bucks silver ten cents lights recruit up ninety two pennies she's traded eighty seven seventy four let's go take a look at our market update charts out here we begin by look at the ES many would we know about it well it completed and formed to buy the D point did that last Monday when it generated that bullish hammer candle then a couple days later you have a bullish structured profile that formed Friday's close was above the center of that profile forty three thirty nine forty three ninety six I should say as long as price close above that we may see a price target of forty six twenty five that is the top of the daily profile look at the spot ball until next it's still below so I'm sorry still above its fifty day exponential moving average that's pretty to two twenty two twenty three more likely than not that is the target if there's one day rate of change below minus ten percent than that really confirms that that is the target or the minimum target of twenty two twenty three the NQ is trading with inside its daily profile like the ES many like each of the equity future contracts they formed bottoming patterns last Monday and now the ES are the NQ should go target the top of its profile that's a fourteen eight seventy four level out there the US dollar index confirmed eighty nine count top that has a new profile attempting to form below price so price should go target the top of that profile that's should become support that's at the ninety six twenty six level gold is re is gotten back above the center of its bullish structure weekly profile that's at the seventeen ninety level so the next price target for gold the next level of resistance going to be eighteen oh eight and eighteen eighteen silver made a found support at the center of its bullish structured weekly profile and that's at the twenty two twenty three level if we see precious metals rally sober it's counter trend if it's only a counter trend move would find resistance at about twenty three oh nine like sweet crude forming a new daily profile out here still looks bullish to Stevie with a price target of at least eighty nine oh three out there natural gas got an A to B equal seeding to the upside assuming there's no bearish reversal candle price should go target the five fifteen level folks they told for the trader said show if you're off to start your Monday have a magnificent we'll look forward to seeing you get some


Hey, it's Sifu David, the Wing Chun master of online Wing Chun training. Want to give you an update right now on the virtual Wing Chun training system, which is coming out in the next few days. So I know all of you are really excited about this. I've been working on this with my team for a long time, and now it's almost ready and ready to launch in a few days. So stay tuned and we'll show you how you can learn Wing Chun without going to a physical class. We're going to show you how to learn Wing Chun even if you don't have time or you have a really busy schedule. And of course, you're going to show you how to learn Wing Chun even without a training partner or anybody to practice with. All these things are going to be solved with this virtual Wing Chun online system. So in this Wing Chun training system, you're going to see how you can learn Wing Chun in ways you've never thought of before. So make sure you get all the notifications on this channel, click the bell next to subscribe button so you know when the course is releasing. Also subscribe to my newsletter on combativewingchin.com so you'll be the first to know when it launches. As the first ones who launch, there's going to be a special bonus for those who want to participate as the first few students in this training program. So I'll see you soon in the next video.