Good morning everybody. So, let us start off with the heat transfer. The overall plan is that I will just take a recap for the next 5 minutes, whatever we taught you in the yesterday's class. So, what we said is that there are 3 modes of heat transfer. One is conduction, convection and radiation and conduction is essentially quantified by 4 years law of conduction and we have T 1, T 2 and Q double dash and T 1 and T 2 should be visualized as electrical potential and heat transfer rate as the current and convection is quantified by Newton's law of cooling that is heat flux equal to heat transfer coefficient into T infinity minus T s. Here at least it would be important to recollect that h is not dependent on the plate material, but it is dependent on the fluid properties and the velocity and the radiation does not require any medium and the radiation heat transfer is quantified by Stefan Boltzmann law. So, conduction essentially takes place even when there is no bulk motion that is if the gases are there even if it is still and if the liquid is there it is still and solids of course are still all the time. So, the conduction is essentially an atomic or the molecular activity when there is no bulk motion and this is quantified by Fourier's law of conduction and there is a minus sign. So, that we tell that the heat flux is transferring from in the positive direction. So, this negative sign is to make the heat flux positive in the x direction and we did solve a problem and we said the convection is essentially because of the conduction within the thermal boundary layer and fluid mechanics is very much essential and we are going to spend indeed around 5 to 6 classes in taking the recapitulation of or brushing up our memories on fluid mechanics itself. There are various types of convection, forced convection, natural convection, boiling and condensation also falls under the classification of convection only. And then this is the Newton's law of cooling and these are the typical values of h as you can see natural convective heat transfer coefficients are lower compared to that of the forced convection, but for liquids generally whether it is forced or free the heat transfer coefficients are high compared to that of gases. Essentially this is coming out because of fluid properties that is thermo physical properties that is Prandtl number, what is Prandtl number we will come to that when we come to convection. Then we have Stefan Boltzmann law which is given by MSU power or you can take it as heat flux for now equal to sigma T s to the power of 4 where sigma is the Stefan Boltzmann constant given by 5.67 into 10 to the power of minus 8 Watt per meter square Kelvin to the power of 4 quite easy to remember and of course we have real surface which introduces emissivity. So we went ahead and this is the summary which tells the mechanism and the rate equation and the important concept professor Arun taught us is E dot in minus E dot out plus E dot g is equal to E dot s t and E dot g will not be there when there is no volumetric heat generation or volumetric heat depletion if you want to call and E dot s t is if there is no transient thing that is if my things are all steady then E dot s t would not be there then it would be only E dot in equal to E dot out. So this is budgeting of thermal energy and we specified where are what are the applications of heat transfer there are plethora or plenty of applications of heat transfer all over all around us every in day to day's life. So we solved couple of problems and we reminded ourselves that if it is 1 D conduction temperature is either a function of x or y or z and if it is 2 D it will be function of x y or y z or x z and 3 D means it will be function of x y z and transient means of course it will be function of temperature also and then we took a recap of conduction rate equation in a vectorial form and there was lot of discussion about this isotropy. Isotropy only means that the properties in this case let us say the thermal conductivity is independent of direction iso means same tropic means sort of direction so it is same in all directions and of course we studied what is thermal conductivity and we said that the thermal conductivity of a conductor is quite large compared to that of non conductor that is for example insulating material. So for solids it is quite high and for liquids it is of the order of 1 and gases it is of the order of 0.1 so then we saw that for the alloys generally the thermal conductivity is lower than the individual thermal conductivity of the material. So we have not answered the question yet why it is so but one of the one of my students sitting here has offered an answer that is the resistance is essentially going to be that is what he says is that if I have thermal conductivity of material k a let us say in this case copper and thermal conductivity k b let us say it is nickel the thermal conductivity of copper is around 400 and nickel is around 100 so copper nickel combination would be less than 100 how he explains that it is because the net resistance that is 1 by k equal to 1 upon k a plus 1 upon k b that is k equal to k equal to k a k b upon k a plus k b which is going to be lower than the lower than the independent thermal conductivity this is one way of explaining why k l i is going to be less than k a r k b sounds plausible but still we will check up check out the validity of this explanation as we go along and we said that the thermal conductivity is two components because of free electrons and another one is the lattice arrangement. So and then we define what is called as thermal diffusivity which is k upon rho Cp so then we define derived heat diffusion equation so the heat diffusion equation states that I will take the final equation that is this is the conduction in the x direction conduction in y direction conduction in z direction this is the energy generation or energy depletion this is the energy stored term that is rho Cp dt dt okay. So with this we will move on to today's thing I will not take recap of 1D conduction so what I will do is on 1D conduction we had solved a problem so I will just take recap of 1D conduction in all coordinates we will solve this problem now before we solve that so we said that this is the 1D conduction equation for plane wall cylinder and spherical and sphere this is plane wall cylindrical wall spherical so this is linear temperature distribution this is logarithmic and this is non-linear and this is the heat flux so here we should realize that the heat transfer heat flux is not independent of r in case of cylindrical wall and spherical wall but here in heat flux at any location it is going to be that is it is independent of x so the resistances are l by k a for plane wall and for cylinder it is log r2 by r1 upon 2 pi lk and spherical wall it is 1 by r1 minus 1 by r2 upon 4 pi k so let us just quickly solve this problem which I had skipped intentionally yesterday that is this is about a furnace we have a furnace that is a leading manufacturer of household appliances is proposing a self-cleaning oven design that involves a composite window separating the oven cavity from the room air that is you have the oven and this is the window what is made of two materials A and B and the two materials are having each thickness L A and L B and it so happens that the thickness of L A is twice that of L B and thermal conductivity of A and B are 0.15 and 0.08 you can note that these values are very less because we do not want the heat to be lost from oven to the outside atmosphere and the oven wall is maintained at 400 degree Celsius and ambient air is at 25 degree Celsius so now interesting thing is that he has given that the convective heat transfer coefficient and radiation heat transfer coefficient and the outside heat transfer coefficient that is convective heat transfer coefficient inside because of perhaps because of natural convection and there is some radiation but instead of accounting radiation he has given an equivalent heat transfer coefficient this is little hard to understand but instead of writing sigma epsilon Ts to the power of four minus T infinity to the power of four we we are writing that equal to h into T s minus T infinity. So, this is just artificial way of looking at it there is no physical meaning as such. So, h r is also same as 25 and h i is 25 and h o that is the outside wall to the atmosphere is also 25. And the minimum window thickness is to be found out to ensure that the outer surface of the window is 50 degree Celsius that is inner wall it is T s i is this temperature T s o should not exceed 50 degree Celsius. If I draw the resistance circuit for this remember both convection and radiation are simultaneously occurring. When I say simultaneously you can imagine that convection and radiation and see that the temperature potentials are same when I say temperature potentials you see here it is told that the wall temperature and the air temperature is given to be 25 degree Celsius. You see here sorry wall temperature and the air temperature not at 25 400 degree Celsius. The air temperature the air inside the oven and the wall temperatures are given to be 400 degree Celsius that means potential is same and only the resistances are that is the heat transfer by convection and heat transfer by radiation are simultaneously occurring that means we can imagine that the resistances are parallel to each other because potentials are same they cannot be in series if the potentials are same. So, that is essentially is what is occurring here. If you understand this the rest all is straight forward this is the resistance because of the material A of the thermal window and this is the resistance of the material B of the thermal window and this is the outer wall convective resistance. So, this is radiative resistance this is inner convective resistance. So, if I just plug in what all I know that is E dot in minus E dot out before we go to that let us put the overall resistance that is these two resistances are in parallel that is what is this term and this resistance and this resistances are series. So, that is what is L by L A by K A and L B by K B and these two are in series with the net resistance because of convective and radiative resistance inside the oven. So, this is the net resistance. So, if I put that T A that is the air temperature minus T S naught that is the outer wall temperature which is not to exceed 50 degree Celsius is the net resistance equal to outer wall that is H naught into T S naught minus T infinity. What is T S naught? T S naught is this temperature that is this outer wall temperature here essentially convection is taking place. So, if you put that and plug in everything and what is required I need to find L A and I am substituting for L B I have substituted already for L B L B equal to L A by 2. If you see here we have already mentioned L A equal to 2 L B. So, L B equal to L A by 2. So, if I substitute that L A by 2 here if I substitute that and put in all the convective heat transfer coefficients and the radiative heat transfer coefficients and the thermal conductivity I am going to get the thicknesses 41 mm. So, and L A plus L B is going to be 62.7 mm, but there is a one major assumption what we have made here is that ambient air temperature is equal to wall temperature which is not going to happen in real life wall temperature is going to be different from ambient air temperature. So, if that is the case how do I handle this problem? So, that is what essentially is put here. So, if I put for the kitchen wall that is sigma epsilon T wall minus T s I to the power of 4 plus H I. So, you see now I am taking radiation and convection in series equal to this is the radiation inside between the wall and the inner wall temperature that is oven wall temperature and the thermal window temperature T wall to the power of 4 minus T s I to the power of 4 and the convection that is T air to T s I air temperature is going to be high, but definitely air temperature is going to be lesser than T wall that is the oven wall temperature that should be equated to the conductive resistance of the wall and again this conductive resistance we are again equating to the outer wall. Here again we are taking the radiation between the outer wall that is T s O minus T wall O that is T wall O is nothing, but the T ambient that is T infinity this is not T wall O this is T infinity to the power of 4 actually that has this has got shifted here you can see here T wall O equal to T infinity. So, that is T infinity to the power of 4. So, if you simultaneously solve these two equations you will get both T s I and T s O. So, this is how we need to handle just to make our life easy we are assumed that the oven wall temperature and the air temperature same. So, much about this problem. So, we will now move on to what is called as heat generation. So, let us just rewrite I want all of you to write all participants to write the heat diffusion equation in Cartesian coordinates. So, let us write that that is del square T by if assume k is constant del square T by del x squared plus del square T by del y squared plus del square T by del z squared plus q dot upon k equal to rho C p by k that is 1 upon alpha del T by del. So, what we are saying is that we are having 1 D conduction that is temperature is a function of x only and steady state steady state when I say steady state this term is going to vanish and when I say temperature is a function of x only temperature variation with y and temperature variation with z will vanish. So, I am essentially getting notice that I am converting p d e to o d e d square T by d x square plus q dot by k equal to 0 this is again second order differential equation. So, I need two boundary conditions, but the only difference between yesterday's 1 D conduction and today's 1 D conduction is that I have taken heat generation term that is volumetric heat generation I have allowed it to happen. So, let us take a plain slab wall and have heat generation and see how does the temperature distribution vary in this case. So, that is what we are going to do in next few minutes. So, this is the plain slab wall this is the plain slab wall and I am having convective boundary conditions on both the sides that essentially means that the my wall is maintained at T s 1 and T s 2. So, in one case T s 1 is different from T s 2 that means the here the it is hot side and this is the cold side, but I can take both the water temperature both the fluids of the same temperature and same heat transfer coefficient then in that case the wall temperatures on both the sides would be T s. Notice that I have taken origin here at the center x equal to 0 and this side it is going to be minus L and this side it is going to be plus L.  So, let us do that that is we have a plain wall this is the center to start with let me take this as T s 1 and let me take this as T s 2. So, we found that in the last case the symmetric case it was parabolic, but we have not a derived y how it has come out to be parabolic that is what we are going to see now and this is 0 x equal to 0 and this is x equal to minus L and this is x equal to plus L. So, now what is the equation we wrote d square T by dx square plus q dot by k equal to 0 and what are the boundary conditions when x equal to minus L T equal to T s 1 and when x equal to plus L I have T equal to T s 2. So, if what should I do to solve this problem I need to integrate this if I integrate that I am not going to integrate it step by step I will write the equation directly or even we can do that if I integrate that d T by dx equal to q dot upon k into x plus c 1 again if I what is that yeah there is a minus sign please correct me like that. So, T equal to minus q dot by k into x square by 2 plus c 1 x plus c 2. So, I need to utilize these two boundary conditions if I substitute x equal to minus L and then my left hand side of this equation becomes T s 1 and if I substitute x equal to plus L my here it would become T s 2 then I have two equations and two unknowns what are the unknowns c 1 and c 2. So, that is what we have done here. So, if I solve that I get c 1 equal to T s 2 minus T s 1 upon 2 L and c 2 equal to q dot L square by 2 k plus T s 1 plus T s 2 by 2.  So, if I substitute this c 1 and c 2 my equation for temperature would become T of x equal to q dot L square by we can even substitute and c q dot by k x square by 2 plus c 1 is T s 2 minus T s 1 upon 2 L plus c 2 is q dot L square by 2 k plus T s 1 plus T s 2 by 2 something is missing here x is missing. So, now if I rearrange this so that it looks little elegant q dot L square by 2 k if I take it as common between these two terms. So, I would get 1 minus of x by L whole square or x square by L square plus T s 2 minus T s 1 by 2 L into x plus T s 1 plus T s 2 by 2 is it. So, this is the temperature distribution. So, now we will get back and see is that what we got yes. So, this is what we got as the temperature distribution. Now, we have taken a complicated not a complicated a case in which the temperatures on both the walls were different that is T s 1 and T s 2 were different. If T s 1 is equal to T s 2 equal to T s this equation this term will vanish and this will reduce to T s plus T s by 2 that is 2 T s by 2 that is T s. So, T s plus q dot L square by 2 k into 1 minus x square by L square and what is the temperature at the center and that is T of 0 equal to that is q dot L square by 2 k plus T s no to this what is this distribution this is this is parabolic this is parabolic. So, this is precisely what we have plotted earlier when we plotted we did not know that it was parabolic but now we have indeed shown that the temperature distribution in the presence of volumetric heat generation with one dimensional heat transfer the temperature distribution is going to be parabolic is going to be parabolic. So, that is essentially what we have done now if someone asks us how do I relate or how do I calculate the T s from this convective boundary condition that is h and T s how do we do that. So, we can do that now how do we do that. So, that is what should I do I should basically if you see here in this transparency what is that you are doing you are essentially applying energy balance on the outer wall or one of the walls that is let us take this was our wall let me take symmetric boundary condition for the sake of simplicity that is this is T s T s h comma T infinity h comma T infinity if I apply energy balance here what is that minus k d t by d x at x equal to l is equal to at x equal to l is equal to h into T s minus T infinity T s minus T infinity what do I get what do I get what is my temperature distribution if I differentiate my temperature distribution what was my temperature distribution let us go back and see so that we do not remember see this was my temperature distribution. So, if I differentiate that this equation what do I get. So, I get 2 dot l square by 2 k into 1 minus x square by l square T s constant. So, I get what do I get. So, I get q dot l square by minus k into q dot l square by 2 k into minus k into q dot l square by 2 k into minus 2 x at x equal to l square equal to h into T s minus T infinity essentially what I am trying to say is that if you differentiate that temperature distribution and substitute x equal to l you are going to get T s equal to T infinity plus q dot l by h. So, this is this is basically because yesterday professor had taught us that this is the convective boundary condition. So, that convective boundary condition by applying that we have got T s equal to T infinity plus q dot l by h for those guys you are not understood what I have done what I have done is that this d T by d x I have obtained by differentiating this equation and substituting if I differentiate what do I get q dot l square by 2 k into minus 2 x by l square this l square this l square will get cancelled out and minus 2 x becomes minus 2 l 2 2 gets cancelled out. So, I have got minus q dot l by k. So, if I substitute that minus q dot l by k here minus into minus becomes plus k k gets cancelled out. So, I have q dot l. So, q dot l upon h plus T infinity gives me T s that is essentially what I have tried to do in the last few days. So, next is on the same lines we can do the radial system before I do radial system I would like to solve this problem which is there for plane wall then we will approach towards radial system. So, it is a very interesting problem and it is going to tell us something about when to apply resistances and when not to apply resistance analogy we cannot blindly apply resistance analogy anywhere we like. So, that is what this problem is going to tell us. So, the problem is a plane wall is a composite of two materials A and B. So, we have two materials A and B material A is 50 mm this is a typographic mistake this is not 50 meters it is 50 mm and L B is 20 mm and here the wall of material A has volumetric heat generation 1.5 into 10 to the power of 6 watts per meter. So, that means in the material A we have 1.5 into 10 to the power of 6 watts per meter and remember this volumetric heat generation is only in material A not in material B this is the major difference in this problem and thermal conductivity of the material A is 75 seeing that number itself you can say that it is some something like a metal. So, 75 watts per meter Kelvin and L A is 50 mm and material B has no generation and thermal conductivity of material B is 150. Please note this number the thermal conductivity of material B is very high as we go along we will see that this resistance is very less because of high thermal conductivity and the L A sorry this is L B typographic mistake L B is 20 mm and the inner wall surface temperature the inner surface of the material A which is black in color here that is insulated that is this side is insulated. But on the other side of the material that is the one side of the material A is insulated other side of the material A we have material B and for material B to the left of it we have material A and to the right of it it is actually convective boundary condition that is while the outer surface of material B is cooled by water stream T infinity equal to 30 degree Celsius and H equal to 1000 watts per meter squared Kelvin. So, you H you see it is significantly high why it is high because it is water and it is flowing so 1000 it is. So, typically for water H is very high and it is flowing as well so naturally H should be very high 1000 watts per meter meter square meter squared Kelvin this is typo it is not meter Kelvin squared it is meter squared Kelvin and T infinity that is the water temperature is 30 Kelvin. So, here we should not be blindly applying the resistance circuits. So, we need to carefully solve this problem so what is known we know the properties of material A and B and there is volumetric heat generation in A and there is no volumetric heat generation in B and this is insulated and this is convective. Before we solve this problem we need to appreciate one of the major point which we studied just a while ago. If you just see here we have let us take symmetric boundary condition let us forget about asymmetrical boundary condition. If I take symmetrical boundary condition you see what is happening I have convective boundary condition and I have at the origin at the origin what is the thermal gradient what is dT by dx at x equal to 0 even if you solve this you will figure out that because of symmetry itself you do not have to really solve because of symmetry itself you can say that dT by dx is 0 that is the mathematical implication. But what is the physical implication what is the physical implication let us say I have a situation that is there here. Let us say I have a situation where in which this is insulated and this is convective boundary condition still whatever solution we got for this situation is valid isn't it that is even if I have an insulated boundary condition physically and a convective boundary condition on the right of my wall the same temperature distribution is the same temperature distribution is valid is that okay and the center line temperature is also going to be same this is what this is just we have played with the mathematical implication and the physical implication the mathematical implication is that it is symmetric but the physical implication that dT by dx at x equal to 0 is 0 means it is physically insulated okay so that is precisely what we are doing here. So in fact that is what is being written here it is important to note that the plane of the symmetry the temperature gradient is 0 if you differentiate this and put x equal to 0 you are going to get that as 0 or you can easily see that it is because of symmetry you can say that it is 0. So one of the implication is that this solution also applies to plane wall that are perfectly insulated at x equal to 0 and maintained at a constant temperature on the other side at x equal to L that is the physical implication this is what we are going to capitalize in our problem now if you see here in this problem what is that we have done one side is insulated and the other side is constant wall P1 okay. So if I apply that relation here if I apply that so that is how you can see here there is a parabolic temperature distribution in material A linear temperature distribution in material B note this parabolic is because in material A there is heat generation in material B there is no heat generation that is why it is linear and this is the temperature drop in the thermal boundary layer okay. So that is essentially what we are doing here now if I see the if I see what is that I should be doing if I apply what is the energy balance or the what is the heat flux if I see if I make the energy balance at this interface at this interface E dot in to E dot out so what is the what is the heat leaving here what is the heat leaving here it is because of the volumetric heat generation Q dot into heat flux if I have to calculate that would be Q dot into L A Q dot into L A has to be equal to Q dot into L A has to be equal to heat flux please note here one important thing here I cannot apply resistance circuit but here I can apply why I cannot apply heat resistance circuit here because there is volumetric heat generation but here there is no volumetric heat generation so I can apply resistance. So if I apply resistance I will get L B by K B plus the convective resistance that is one upon H should be equal to the heat flux so what is the heat flux Q dot L A equal to heat flux so that should be equal to that is the same heat flux which is going which is going by conduction and convection so the heat flux equal to H into T infinity minus T 2 I do not know T 2 that is what I can compute that is Q dot L A equal to H into T infinity minus T 2 so that is sorry T 2 minus T infinity so that reduces to T 2 equal to T infinity plus Q dot L A by H so I know T infinity 30 Q dot I know L A is 50 mm and H is 1000 you get T 2 as 105 so same heat flux if I apply that is T naught minus T 1 or T 1 minus T 2 equal to we can solve it in multiple ways but we are applying this equation this in a volumetric heat generation case we had derived this that is T naught equal to T 1 plus Q dot L A square by 2 K A we had just derived little while ago so I will compute T 1 from the thermal circuit so T 1 needs to be found I do not know T 1 as of now I know only T 2 how will I get T 1 T 1 will come from net resistance that is Q double dash equal to L B by K B plus 1 by H if I do that and I know the heat flux that is 1.5 into 10 to the power of 6 into 15 into 10 to the power of minus 3 I get T 1 if I put this T 1 I will get my T naught if I put this T 1 and I know all other parameters I will get T naught please note here let us take stock of the numbers what we have got T 2 we have got T naught 5 T 1 we have got 115 see here as you can see that the conductive resistance is much larger than convective resistance if you see here conductive resistance is 150 by 20 mm but convective resistance is 1 by H is 1000 so convective resistance is very less so T 1 to T 2 temperature drop is significantly less compared to that of T 2 to T infinity so what I am trying to say is that you see T 1 is 115 T 2 is 105 in the wall there is a temperature drop of only 10 degree Celsius that is material B wall there is a temperature drop of only 10 degree Celsius but between the outer wall and the water there is a temperature drop of 105 to 30 why because the convective resistance is much lower than the conductive resistance this is the significance that is how the resistances help us in feeling the numbers feeling the numbers so the important point the message what we are going to carry from this problem is that the electrical resistance analogy we started applying only from material B not in material A because in material A there was there was volumetric heat generation so this is the most that is why this problem has been cookable. So having understood how to handle volumetric heat generation on the same lines one can handle radial systems so we have just now till now we have handled volumetric heat generation in plane systems that is the plane wall so similarly we will touch upon radial systems in a radial system if you see that is the cylinder if I take so this is the equation which we have taken yesterday this was the equation we equated that to 0 why because we had neglected the volumetric heat generation now we take volumetric heat generation that means essentially we are saying that the temperature is there in the radial direction and there is volumetric heat generation so that is this cylinder and we have volumetric heat generation and I can either have constant wall maintained or I can take convective boundary condition both mean the same why I say that because I can apply or I can I can balance the heat flux on the wall between convection and conduction and get relation between T s and T infinity through H. So if I differentiate this equation like we did for the last case I am not going to do step by step on the paper I am just going to take you through the steps because I have done that for plane wall so if I differentiate that if I differentiate this sorry integrate this I get r dt dr minus q dot r squared r squared why it has come because I have multiplied this equation throughout by r if I integrate this first term I will get r dt dr and I have r q dot by k that is q dot by k into r squared by 2 that is what is this plus c 1 minus is because I have pushed this from left hand side to the right hand side. Now I will divide this by r dt by dr equal to minus q dot by 2 k into r plus c 1 by r now if I integrate that I get t of r equal to minus q dot by r squared by 2 k already 2 is there so I get 4 k plus c 1 by r that is c 1 log r plus c 2 what are the boundary conditions I am what are the boundary conditions here you can expect that at the center the temperature is going to be symmetric. So that is the symmetric boundary condition dt by dr that is the gradient of the temperature at r equal to 0 is 0 that is at the center and at outer wall that is t at r equal to r naught that is r naught we are taking it as equal to t s that is t s so if I substitute that I am going to get if I substitute this boundary condition in this we can directly see that dt by dr equal to 0 and r equal to 0 so c 1 will tend to become 0 so c 1 is 0 so all that I need to find is c 2 that is for finding c 2 I have to substitute for r as r naught and t at r equal to r naught is t s so c 2 will be equal to t s minus q dot r naught squared upon 4 k so that is what is substituted here. So if I substitute that I will get this c 2 if I substitute that in this equation there is no c 1 anymore so I get t of r equal to t s plus q dot r naught squared by 4 k into 1 minus r squared upon r naught squared again so this is again parabolic you can see that this is again parabolic I am just rearranging this t of r minus t s upon if I find again central line temperature t naught and divide it by t naught minus t s I will get 1 minus r by r naught squared you do not have to worry about this it is just an algebra if you just put r equal to r naught you are going to get that as t s plus q r naught squared by 4 k so if I again divide it by t naught minus t s this is going to vanish that is all we are saying. So if I have to relate t s with t infinity and h if I do the energy balance so I get q dot into volume what is my volume pi d squared by 4 or pi r naught squared into l equal to h into bathing area that is complete cylinder bathing area 2 pi r naught l into t s minus t infinity if I equate this pi pi gets cancelled one r naught vanishes l l gets cancelled out so I am going to end up with t s equal to t infinity plus q dot r by 2 h so basically this is what we have understood in case of volumetric heat generation if I just take a recap of what we have done so the main point what we need to understand is that in this problem wherever volumetric heat generation is there you cannot apply resistance circuit I am telling this again and again because while solving problem usually students tend to make this mistake they think that resistance analogy can be electrical analogy can be applied anywhere and everywhere no everything comes with restrictions so this is the restriction. So we need to appreciate this so now after doing this let us just take couple of problems one more problem I would like to take this is a formulation problem I would not like to take this yeah this problem let us see it is a very interesting problem because there were various questions yesterday on thermal conductivity variation with temperature and everyone wanted a unique answer how does temperature vary so generally we found when we went back and saw the equation when we went back and saw the variations of temperature for various metals generally for metals we are seeing that the thermal conductivity is decreasing with the increase of temperature so but it need not be same for quads we saw that the temperature was increasing so why we do not know that we have to answer out answer little later but now the question is is the temperature distribution in a plane wall always going to be linear may not be so what is that I am trying to do is I am asking a question myself yesterday's till now I have been always saying K is constant now let me relax this assumption and take K equal to K naught plus A t that is K naught is varying with temperature that is that is that is that is the formulation so that is K equal to K naught plus A t in any textbook usually you would see this is a standard problem usually this is the question which is asked so far what we have solved or we have found that it is linear is that if I have a plane wall I have taken linear in which case it would be linear where K equal to K naught that is when A equal to 0 but now let me go back and take a case in which A is positive let me take a case in which A is positive so you will see that for A is positive my temperature distribution is going to be is going to be something like this that is convex and for A negative it is going to be K so why so it is coming from Fourier's law of conduction so the argument is there here so that is when A equal to 0 there is no problem so the question what we are posing is when A is positive it is going to be something like this A is positive A is positive why it is so so if A is positive what will happen K equal to K naught plus A t so what is happening if I differentiate this D K we all know that in a plane wall when heat transfer is taking place from left wall to right wall what is happening to the temperature temperature is decreasing how it is decreasing we do not know how means whether it is decreasing linearly parabolically we do not know that but definitely temperature is decreasing so if I differentiate this K with respect to temperature D K by D t if A is positive this is a mistake D K by D t is not alpha it is A so D K by D t is positive then A is positive so that means what K is what does the D K by D t positive means K is increasing with the increase of temperature or K is decreasing with the decrease of temperature so what will happen K increases with the increase of temperature what does my Fourier law say Q equal to minus K into D t by D x so as K increases this is capital T temperature is decreasing as K x increases that is as I move from left to right of my wall what is happening to my temperature is decreasing so is K because D K by D t is positive so with the decrease in the temperature K is also decreasing but what is constant for a plane wall Q by A has to be constant the heat flux is constant so in order to maintain the same heat flux what should happen might slope that is D K by D t should increase so that is what is happening here so if you see back so D K by D t is increasing D K by D t is sorry D K by D t is decreasing because of the temperature decrease but my Q by A has to be remaining constant in order to keep it constant the only way to compensate it is D t by D x should the slope should increase that is why compared to the slope of the straight line the slope is high here so that is why my nature of the curve is going to be like this for A equal to positive so conversely you can argue out for A equal to negative is that okay so that is how we can understand this is a very important concept so this is just book keeping the slope so if you just take a recap what is happening temperature is decreasing so but the K variation with T is always positive so D K by D t is going to be decreasing so but in order to compensate for this decrease D t by D x has to increase that is the slope of or the variation of the temperature with x has to increase in order to keep my Q by A as constant that is all it is just book keeping okay so this is actually in fact I would think that this is this why I am harping so much on this is because this is usually our PhD interview question so we always ask this question and most of the times people find it very difficult to answer this question so why because we are not used to think this way so I would request all of you all the coordinators in the class spend considerable time in explaining this concept okay so I think with this problem this problem I am skipping because this is there in the tutorial today afternoon we are solving this problem okay so so much about volumetric heat generation so I think we are at the end of the session for next 5 minutes I will just take 3 to 4 questions first question is VNIT Nagpur any question in the plane for a plane P is equal to A plus B x plus C x square the plane for a plane P is equal to A plus B x plus C x square is the math cad method math cad method applied and what is the peculiarity of that math cad what is math cad as far as I know the math cad is just like excel it is just an off software what is this math cad method sir math cad applied for determining the temperature mean or at a particular length of that plane if you want to determine the temperature so in math cad there are certain limitations so I need to know about math cad math cad is something like an excel sheet it is just a software which calculates temperature based on the values what you give A B and C there are no limitations of math cad math cad is limited by our mind so it is just how we give the temperature distribution as A B and C it is going to compute that is all it is okay sir thank you over to you M.A.S. Pillai on well good morning any questions see one of the participants wants to know wants me to re-explain this k variation with temperature so let me just go slow as slow as I can see what we are saying in a linear case k is constant and what does Fourier's law say q equal to minus k A dT dx so there is a linear temperature gradient that is what we found yesterday's derivation and that is this linear temperature variation now what are we saying so and we know that when there is a heat transfer from left wall to the right wall temperature is going to continuously decrease that means T is going to decrease with the increase of x so what will happen to my dk by dt so if A is positive dk by dt equal to A so but my temperature is decreasing so dk by dt is what will happen my dk by dt is positive so as my temperature is decreasing my k is also going to my k is also going to dk by dt is positive as my temperature is decreasing my k is also going to decrease but I have to keep my heat loss rate constant that is q has to be constant because it is given by minus k A dT by dx the only way to compensate this decrease in thermal conductivity with the increase of length is by dt by dx so dt by dx has to go up compare to the case in which k was constant so that is why my distribution temperature distribution is going to be convex for A equal to positive that is upward I hope I have made I think I have made you understand okay I think we are stopping the question and answer session no professor Arun will take over.


Another Akbar episode sound-dampening of the van conversion. Hola everyone, Paul Carlson here, a small workshop guy. What does Akbar stand for? OCVA, that stands for Old Coot Van Adventures. That's a playlist on my YouTube channel where we're going to show the conversion of a Mercedes Sprinter 144 van into a Class B RV. When you get a cargo van, the panels on the side of the walls are going to rattle like crazy and it's going to be very very noisy. So the whole idea here is to put some material up on those panels and to dampen the vibration so that there's less noise. The old Coot, and that would be me, had happened to have four grandsons visiting me on the weekend and so I put them to work. Although if you want to conserve your materials, it's probably not a good idea because it became kind of a random cutting, random sticking approach, but this is not a critical step. You just need to get some of this material inside of each of the panels. It would also be a good idea to do your exterior work first. In other words, we're putting some stuff up here where some windows are going to go and when the windows go in, obviously the panels are going to come out and so I just wasted that material. But in the meantime, I want to drive around in a quieter van. The material that I am using is called NDX, Nancy Victor Exobia, I don't know. And it's designed, you peel off the back of it and you just stick it on the panels and after a while it sticks really, really well. All right. Well, I'll put a link down below and you can check it out yourself over at Amazon. Hey, help out an old coot and give me a like, a comment and a subscription. Be very much appreciated. Adios.


Great. Welcome to the last set news. My name is Rob and today we've got a lot of things to go over so just the thumbnail and title suggests There was an interesting story that came about which talks about what polygon is doing as far as ZK rollups Which are going to roll out pretty soon, which could make Ethereum potentially unstoppable and that's for scaling and also for those pesky fees So we'll take a look at exactly what's going on Also before we do all that we'll take a look at what I call two sides of the same story as I try to give you both of those on this channel So you don't get filled too much with hope him or get downtrodden by all the negativity And then also we'll take a look at clown news, which will feature me which there was a mistake yesterday for the else The Celsius chart that we talked about so we'll take a look at that Also, we'll take a look at the ridiculous fees that are being paid out by Celsius to their employees as I go through chapter 11 And also there's going to be a Twitter spaces with Simon Dixon because chapter 11 bankruptcy has gone through For Celsius he's gonna talk about potentially what his plan is and lastly We'll just talk about how there's going to be an El Paso meetup So if you're an El Paso tonight come on out and meet me. That'll be from 4 to 6 p.m. I'll tell you exactly where it is. So we'll go over all those things but first Let's take a look at the market and actually before we take a look at even the market What I want to show you is two sides of the same story and you can kind of tell what's going on In the media these days, especially with the different stories that are coming out There's a lot of negativity and I will admit I am not the beacon of light of positivity that you that you may have come to expect Because i'm a realist. I know if there's a lot of A lot of things going on in the in the macro environment that is not causing Our market to go up. However, things are looking pretty good And that's positive But I need to tell you that there's always two sides of the same stories this came across the desk And it talks about The cities where rents have risen the most and it talks about how the average rent for a one bedroom apartment in Austin, Texas As more than doubled year over year and it gives a couple of different graphs and charts And it's very interesting. It's very nice to see But if you just read this article it would kind of give you an impression That things are are quite bad and not doing, you know, too great So that of course Is just these sides of the story and if we scroll down here. Whoops scroll down here It'll show us that yeah as far as like the macro Events that are going on House sales are actually going down foreclosures are going up Also interest rates are are increasing as far as for mortgage rates We all know these things and of course, let me take a look at this We're like, man, the sky is falling. Look at that Austin, Texas First of all, I found this crazy that the rent for one bedroom is over $3,000 in Austin, Texas That's a that's the doubled. That's 108 percent increase in jersey sitting in jersey It's 4,400 10% Arizona not too bad 1700 New York, New York fit almost $6,000 for the average rent for a one bedroom apartment That's insane And then it goes salt lake city and just here's the increases and then it goes over some different graphs But I was like, well, isn't there if it's all if it's all going up. Is that the whole entire country? Well, no I really so we they even referenced that they go look this is from Rent.com I took a look real quick. There's the rent report July 2022 Goes over some stuff. Well, that's nice Uh, and then it says here one bedroom city average rent price trends And this is what it was talking about beforehand as far as the increases But on the flip side of that same story is there's some places where it goes down too McKinney, Texas is down 50% St. Louis, Missouri. I used to live around there st. Louis, anaheim Really anaheim california is down Houston, Texas is down. It's been the great city of texas kind of crazy Las vegas is down 12 percent. I was lived there for a couple of years too So when you take a look at these stories take it with a grain of salt and try to find both sides of those same stories So speaking of all these things. How's the market doing? It's doing great. However What goes up must come down and be very cautious and I know It's uh, it's annoying to hear these things, you know, rob What are you gonna tell us everything to go and go to the moon? Well, that's gonna be in a couple years. I think so just calm down And uh, I think that these are the good days. Look bitcoin's up 22. I'm not saying that's bad. I'm saying that's awesome That's great. That's fantastic. That theorems up almost 50 for the week down a little bit in the last 24 hours But hey, I mean 50 that's pretty darn good and everything's up for the week, of course last 24 hours A little bit, uh, a little reduction something to take a look at also even polygon the thing that we're going to talk about today Is down 7% in 24 hours, but again 60 percent for the week and um That's what it is. I know yesterday people were pretty exuberant Hopefully nobody foamed in like crazy because that's crypto and that's the market And it makes me think about this well if our market's doing, you know Sideways a little bit or a little bit of increase. How is the regular market doing? Well It started off gangbusters But then I think people get a little bit spook like is this a real deal. Is this a bear rally is just a bull trap What is this? So you can see right here everything started off pretty good Went up and now here we are again s and p 500 nasdaq same type of thing, although Just about a little bit ago about 45 minutes though a little bit of an increase. So that is fantastic Also, let's take a look at some on-chain things This is oh, of course it signed me out because that's what it always does I gotta talk to those guys. Don't worry. I'm not giving anybody my uh password. It doesn't show up. It's hidden So here's the dashboard for crypto quant my inner outflow. Hey, look at that I didn't notice that actually Let me see this Let me blow this up our miners selling Let's go for the last month. Wow. They are They are selling. I just noticed this, huh? This was on 14th july 1 2 3 4 5 Ah six days ago That's what it looks like for but Yeah, that is interesting There was a big sell-off As the bitcoin price man, the guy should have waited a little bit I think they would have done a lot better But again, nobody can nobody can time the tops and the bottoms just isn't wow That is crazy 14th july there was a huge sell-off And now here we are. Huh, it's weird again. They should have waited a little bit So that's what's going on the miners selling interesting Which could be a latent indicator. I mean, that's why things are going down exchange reserves Same thing same thing take it by volume. Yeah, yeah, great. Here's the thing I want to talk about two things first of all leverage ratio and The market value to the realized value ratio and on june 13th anything above above Let me see. What was it numbers anything above 3.7? Is uh, usually an indicator of a pretty big blow off top which we didn't see until February march 2021 somewhere around here mid april may But lately it's been below 1.0, which is usually indicative of a of a bottom ish I can never time the bottom. Nobody really can do that consistently unless there's somebody with a crystal ball But uh since june 13th, we've been in pretty cheap territory again Like I talk about you have to ask yourself. Is this cheap bitcoin or is this inexpensive bitcoin? I think over the next five to ten years. We might think that 20 000 was pretty darn cheap and we just went above That 1.0 mark the last one was at Uh 1.06 of course, that's because of a rally if it falls down again same thing Probably be a little bit more inexpensive, but this one that Makes me gives me pause Which is estimated leverage ratio And anything above 2.0 is considered extremely high or 0.2. Excuse me We've been doing that since gosh December and just this purple line just keeps going up until we fell like crazy because people got liquidated and wrecked And then here we are again, and we're at man. That's crazy high 0.32 Whereas before the the highest of all time ever was 0.33. First of all, I always get questions about this So let me just say what this is The leverage ratio is the open interest divided by the coins reserve Which shows how much leverage is used by users on average increase in values indicates more investors are taking high leverage risk in the derivative trade in the derivatives, so We could have stuff like uh options and swaps and futures longs and shorts It takes an account everything for derivative trades. That's what it's saying And then if we also take a look over here The definition is estimate leverage ratio defines the ratio of open interest divided by the reserve of an exchange ELR indicates how much leverage is used ELR for a derivative exchange tells how much leverage is used by users on average This information measures trader sentiment whether they take a high risk or a low risk So when I take a look at this Whoops, I take a look at anything over here People are still taking some pretty darn high risks And the next question I have is well, how many different Exchanges do they look at over a crypto quant they look at these Well, they just do the all exchange But they look at binance bit for next bit next buy a bit dairy bit ftx get i o who will be global cracking and okx Is that every single one of them? No, but it's enough to give you a pretty good idea Of how much open interest and leverage play there is so it gives me concern That there's this much leverage still going on and uh, maybe just a bunch of gamblers anyhow That's what we have and then to finish this all up Uh, gotta use ben's website into the cryptoverse Even though we're above that The mvrv of 1.0 you have to remember that if we take a look at log of rhythmic regression We can see that we are still Undervalued fair value should be 1.78 trillion for our market cap 1.78 and we're only at 1.1 Which is this blue mark right down here so you can see We're still a little bit undervalued. Do we have a way to go to go up sure could it go up Tomorrow sure why not could it go down to 14,000 sure why not it's crypto nobody knows So that's it a nutshell for the crypto market and what's going on now. Let's take a look at the big story polygon and this one It came across There was a big announcement four days ago It was like one of those just in sun ones where it's like there's an announcement to an announcement But uh, it really was a pretty good one. This is from uh, ryan white He's a ceo polygon studios and he says we already know polygon is a powerhouse leads far and away in partnerships With the zk evm launch we now can scale with security be carbon neutral And handle the transactions per second or tps the future the future internet will be built on polygon with this feature It's that simple and first of all is like, I don't even know what that is. I have no idea what zk evm. So first of all zk evm is pretty much it's a roll-up And the first the next question by asking some of you don't know I just want to make sure we're all on the same page. What's the zk roll up Well zk roll-ups or zero knowledge roll-ups Similar to optimistic roll-ups doesn't matter They combine a large number of layer two transactions that were executed off-chain And submit them as one transaction onto ethereum So just like bitcoin has a letting network ethereum has polygon layer two solutions So they can do all these different transactions up above not deal with the on-chain type of stuff and just at some point BAM blast them all out there and these are all the transactions Process them instead of paying crazy high fees. So that's what that is So now let's get into What the heck is zk evm and why is this so big? So This is an article just put out a couple hours ago. Matter of fact this morning, I guess And it states besides the merge which everybody's so impressed with This is the second biggest event in terms of technology and the ecosystem in general polygon co-founder Jelich said So zk evm a zero knowledge proof based roll-up, which we just talked about achieves equivalence with the ethereum virtual machine or evm This means that developers can easily deploy applications written in solidity The theorem smart contract language language and take advantage of the ecosystems robust developer tools Just as they do on the ethereum mainnet Right now. I'm not impressed.  Like when I read this, I'm just like, I don't really care about that Where's tell me why this is going to be awesome. So we'll get to that roll-ups Based on zero knowledge proofs have several advantages over the optimistic roles, which are already up and running great Zero knowledge roll-ups combine many layer 2 transactions to one which settle on ethereum as a validity proof While computationally intensive Zero knowledge roll-ups are much faster And this is this this is the comment from polygon sandeep. Not while he says nail it It makes ethereum almost technically or theoretically infinitely scalable and that's what everybody's looking for How much can we scale? How far can we go? How far can we bring these transactions per second up? without having the problems of the issues of price And security or safety It has network effects. It has developers. It has users So, you know, we can take web 3 to the next stage of growth And I got to tell you that sounds pretty good because uh, that is the one of the biggest concerns I had there was well, of course the fees and the second one was how many treats transaction per second Can ethereum actually do well with these layer 2 solutions looks like it's infinite Which is kind of like when we talk about with cardano and hydra So I think that'll be let's let's let them battle it out A closed test net a polygon zk evm should be available within two weeks. So again, this isn't even live yet Test net's coming. So everybody calm down Should be available within two weeks with a public permissionless test net to follow a few weeks later A future configuration of off-chain data will be able to reduce the fees further. Let me see that again A future configuration of off-chain data availability We'll be able to reduce the fees further now. We're talking that sounds good. I'm sick of the eth fees Polygon avail envision seven roll of chains. So this is where it gets A little more technical, but this is if you want to know how this works out Well zk avm is a proper old school roll up Potentially significantly efficiency gains are possible by using an off-chain data availability solution such as polygon avail in a roll up 7 to 80 percent of the cost is attributed to storing eth call data That component can move to avail which is on polygon and would transform zk avm into what's known as volidium Everyone is really looking for lower transaction fees. That would be me as as well if the security can be maintained We will see every roll up At least in his opinion, we'll have a roll-up version and a volidium version. Sure So it sounds like things are going to be better faster cheaper And it's just going to take time This was interesting. I didn't know I didn't really know this polygon is a multi-chain ecosystem Well, I guess it makes sense We believe there will be probably thousands such chains built on top of ethereum And this is not a wall again So what does this all mean? This all means that potentially we could see a reduction fees the merge is coming about And hopefully they hit their timeline. I'm a little still a little bit suspect But that's just me kind of a wet blanket a little pessimist and if it happens, well, great Now if polygon can actually do what it says it's going to do with these What do they call zv I always get this wrong. Well, there's zk roll-ups, but zk avm And they can scale infinitely and they can drop the fees How hard would it be to stop? Ethereum as they move forward because they've got a pretty big First mover advantage. They've got a lot of developers working on it Now the question becomes how can the other ETH killers and and different layer one solutions Will you work themselves out? I don't know who's here to win. I really don't care I'm just here to invest into one of the fastest horses and go from there It doesn't mean I won't stop investing in other ones because I still think there's a lot of room to play And there's a lot of room to grow anyhow Let me what you think about that in the comment section if this makes them truly unstoppable Or if your layer one's going to be the most awesome thing. Sure. Maybe it could be I still got my eyes on Cardano and avalanche and salon and all those ones and I'll probably still have them in my portfolio But we'll see anyhow. That's what's going on with that piece. Let me just think about that now. Let's go into Some clown news and unfortunately I am the clown for this one. So it's a bummer It's a bummer Yesterday I think everybody now realize we've been on colorblind Is this what's going on? so Yesterday we did a little breakdown of The sales see us stay in court as far as they're chapter 11 and the deposit breakdown I Inadvertently mix these two up So you got the earned program custody lending and sell balance and I for some reason I'm still having a hard time looking at this thing sell balance is like 4% I guess I wish they just used numbers a real hard time with colors. I mean the custody program I get and 77% is the earn yesterday. I switched around earn program with sell balance. So my bad And uh, that's that's just one part, but I do remind everybody This is was the interesting part from yesterday's video. First of all, of course, we saw the debt that is there And uh, if anybody's the clown, it's I gotta tell you Celsius is doing a pretty good job of clowning themselves because the key legal questions There was two Are the crypto assets and Celsius possession property of the estate? Meaning the Celsius that you and I put on that on that platform They're saying that's theirs and and we actually take a look at yesterday the terms and conditions And it did say essentially that you gave up we gave up all rights And essentially when it went on the platform Uh, it was now the property of Celsius even though they were lending it out So I know people on twitter were telling me but there's some video of of alex machinsky saying that It's your crypto. I'm like, well, I'm still waiting for those videos So if you got it, uh, hit me up in in twitter and tell me what's that where those are Not just some some some errant twitter some tweets from somebody. I don't care about that Show me the video and uh, that'd be great And I'll put it on this channel And then the next one which is I think the biggest clownish thing is Celsius recover customer withdrawals Or loan liquidations Completed in the 90 days before filing as preferences meaning Uh, remember that video I put on June 12. I told everybody I was like, I'm taking mine off. Maybe you should do Uh, they're saying that they could potentially claw that back. That's crazy. So there's that and then also This is from a friend of the show Aaron Bennett. He's got his own youtube channel. He's checking out Good guy got the there's a lot of great news stuff and whatnot and he says, uh Celsius network wants to pay each employee an average of 30 000 The month after they follow chapter 11. This does not include director An officer payments which an additional three million dollars after losing a billion dollars of our money And uh, he breaks it down the estimated amount of weekly payroll payments to employees not including officers Directors stockholders 3.4 million you divide that by how many employees they have that's 30 000 months per employees Well, let's just say they have 900 employees. That's still 15 grand per month per employee. That's a lot of money That's your money. That's our money going to where to these guys. I don't know what they're doing But uh, that's what's happening. I just found it's quite fascinating That's what's going on and if you want to Hear about what potentially the plan could be moving forward And how you can be a part of having your voices heard come on by in about 45 minutes To simon dixon. He is going to be doing a Uh, what is it? What are these things called twitter spaces? Where uh, it's going to be him And a bankruptcy expert. Maybe that's a lawyer. I'm not for sure and this is going to happen at 12 30 p.m Right now it is 11 46 am where i'm at so in 45 minutes Uh, so meet me over there. I actually let me see look at this, right? Yeah, there's a link in the description in the description called twitter spaces with simon and you click on that and it'll take you Right to the twitter spaces So I am eager to see what is going to be said about simon's plan and what's going on moving forward and also Some uh information. It looks like uh simon might be I'm not going to say it. So I'll let him say it. So just come to the space and just check it out. Anyhow, that's enough for clown news Get that thing off, but uh, that's what's going on and then lastly Uh real quickly another exchange goes down. This is i'm not going to read this whole thing because we're kind of running out of time but Zipmex suspends withdrawals as ceo denies financial troubles. Uh, this is They are located in singapore, I believe Crypt exchange Zipmex has paused withdrawals and his platform is following a combination of circumstances beyond its control Which is kind of weird. Why they're doing that now because the market's going up, right? Here's the here's the quote Ah Under the tie license they zipmex are strictly not allowed to touch customer funds. So that's pretty good, right? Because why Why would they need to do that? However, zipmex has a product on the exchange called zip ups that effectively lets users move funds under the Singapore entity to earn yield Which is the downfall. I think of every exchange now. Look at voyager look at uh Look at Celsius and I wouldn't be surprised if it comes out that they get they gave a loan to three euros capital The source explains that the funds were given to babel to generate the yield about 100 million was lent to babel Oh babel, excuse me, which is now at risk of defaults in june hong kong base asset manager babel finance halted withdrawals Due to unusual liquidity pressures and then the whole article was really just about how coinbase was going to buy Zipmex But then they pulled out for some reason but gave a small allotment And for me, I think this is a pretty big opportunity for coinbase to I don't know branch out if zipmex goes down and they already have license in singapore and east asia Be a pretty good pickup for coinbase. Just thought about it. Anyhow That's Concludes that piece. Let me know which thing about a comment section and then lastly before we get into q&a There's a meetup today. So if you're in the l-passel area and very few of you are I just know that because not a lot of people here. I'll be here Union draft house. This will be today from four to six And they got a lot of good food And I got some beer. I like this. I like this picture that they have up school is good But beer is gooder and that's a that's a pretty good point and after this These last couple of weeks. I think maybe maybe we all could use something like that And I got a ton of beer over there. So I will be drinking not to excess but just so you know It's on the east side not the one on the west side Here's mexico Here's that and then I live somewhere around here. That's what's going on. So look That takes care of today's news if you like today's video Give it a like you don't have to subscribe. It's okay, but a like would go a long way That's the only way that youtube kind of recognizes that i'm Actually alive here and that's it.