 So, now epsilon NTU approach we this is for yeah. So, here as I said this epsilon NTUs are work given because earlier in fact today's world we do not need epsilon NTU approach. I can do with LMTD approach itself, but only thing is that I have to go strip by strip and design my heat exchanger using or predict the exit temperatures using the LMTD approach itself. But at that time when case and London came up with case and London by that matter case and London were the first guys who gave and they have books in fact there is a book by name Shah and London his business was to sit down and derive all Nusselt numbers for all laminar configurations that is Shah and London book. Case and London also sat down and derived epsilon NTU for all possible configurations one can conceive. They sat down and wrote it for us that is what we use as hand books for a design. Case and London have given us this epsilon NTU approach, epsilon equal to actual heat transfer by maximum possible heat transfer we know that the maximum possible heat transfer can be between the maximum possible temperature and the minimum possible temperature. Here there is an issue when I take this for the maximum heat transfer I take what is the m dot Cp I take for this maximum temperature difference minimum. How do you explain them why minimum m dot Cp is taken instead of the maximum correct correct correct that is what I do this because I got stuck one day I could not reach my student the next day I went back and did these calculations you spend time on this transparency this transparency is just to answer the question what I asked you that is why I should not take m dot Cp maximum as opposed to m dot Cp minimum the heat load when you take m dot Cp maximum will be higher will be higher it cannot it is not possible you will get at the inadvertently very high temperatures which is not possible just go through this transparency just go through this transparency you correct that is true for both the fluids that is true for both the fluids why only for m dot Cpc minimum that that if I do it only I will understand no what I mean is you can tell that after you do it but without doing you just do not tell that if you only tell that they will not be able to appreciate that is all my point. So then these are the places where as a reader when I start reading I get stuck most possibly my students also are going to get stuck there only so that is why I am concentrating on those locations only all others I am just going fast this is the complete derivation I am not going to go through this derivation if you just put you are going to get epsilon and NTU is UA m dot Cp already professor has told us that UA NTU is uses the idea of the size of the heat exchanger and effectiveness is a function of ratio of the m dot Cps and the NTU and for all configurations as I said case in London has derived it and given us given us in fact honestly I have not derived other than parallel and counter always I think but I have never done that perhaps we should try that we can perhaps try and show before may be for one of the workshops at least for shell and tube might be slightly difficult but we can still attempt let us attempt let us attempt before main workshop let us see I am going to give this as exercise for you because you are also thorough with heat exchangers let us go one mile ahead than what we had gone earlier okay so any one of these one two three four any one of these four you please try to derive you will not get these derivations anywhere you will not get them one thing is for sure you will only get the relations case and London also does not give you the derivation he will give you the derived thing okay so please let us attempt let us put a assignment for ourselves that let me see who is going to answer me first this shell and tube and then cross flow and unmixed and mixed okay so let us see who will answer me first next let us come to interpretation of these perhaps what I mean last epsilon is a function of specific capacity ratio and NTU how did one come up with this why should it be this there are three non-dimensional parameters right effectiveness CR and NTU right one is something to do with the size one is something to do with the heat transfer rate and another is something to do with the fluid mass flow rate and property how on earth will these three talk to each other or is there any connection what are the what are the dimensions of each of these quantities epsilon dimensionless CR dimensionless NTU is also dimensionless can we think of these as ratios of some temperature differences epsilon is a ratio of temperature differences it is quite straight forward there is no problem C what about C C small C C minimum by C maximum that is also temperature difference only heat load equal to m dot Cp into temperature difference equal to m dot Cp into temperature difference that is also temperature difference what about NTU q dot equal to q dot again UA LMTD is q dot that is also temperature difference everything is a ratio of some temperature difference only that is why these non-dimensional groups have come together okay so now coming back I think we will only spend time on one of the cases and then move because I do not think I need to spend time for all other okay last we will see yeah so actually here also a month you can see here also if I put effectiveness versus NTU so you have parallel flow sitting here counter flow sitting here of course when I am plotting this I have taken C equal to 1 it is a good idea one thing I would like to suggest it is a good idea for the students to ask in the assignment to plot these epsilon versus NTU plots whatever I have put ask them to plot in excel sheet for NTU is varying from 0 to 5 in steps of 0.1 or 0.0 excel will calculate all that he has to do is put this but when he does that he will understand the influence of each parameter at least it will get registered in his mind that okay this is how it is going to be next question is why is it like that okay so now let us come to this question if I take C is equal to 1 here you can see effectiveness is lower for parallel flow heat exchanger it is higher for counter all other heat exchangers are going to be so that is about C equal to 1 now let us take how does for a given heat exchanger how does my for a given heat exchanger this is for parallel flow if I understand one rest all are going to follow the same C minimum by C maximum if it is 1 my effectiveness is less as I go on decreasing that it is going to be maximum what is the meaning of this how do I explain this C minimum by C minimum by C maximum is equal to 1 means what mass flow rates are same mcp is same that is what you mean thermal feedback mcp is same but why should its effectiveness should be lower compared to a case where in which for example this case where in which C minimum was 0.25 times let us not take 0 it is little difficult to visualize we will come to 0 but how do we explain or understand ourselves why this C minimum by C maximum of 0.25 should be greater than 1 physically heat transfer rates heat transfer coefficient you mean when you say heat transfer rates what do you mean you mean heat transfer coefficients or heat transfer have to be same know both sides whatever is lost has to be equal to the other side but exchange whatever is the exchange what is getting exchange we are not answering the question we are only observing it I want the answer no that has to have no that has to have an implication on temperature differences know if my mass flow rates difference between the two fluids is different different large let us say large like point what is happening in the temperature gradient there is going to be large temperature differences you can explain maybe if I am not larger yeah what professor is drawing is if m dots are same for both m dots are same for both maybe it is something like this okay for the other one it will be let us start with the same because it has to be same as this minimum but then it will go on the temperature we can very well feel physically that if the temperature differences are more the heat transfers are better that we all physically feel that is what precisely is happening that is what precisely this is what we need to emphasize in the class this graph has to be that is the extreme case what is this case actually what is this case physically why I should think of infinite mass flow rate can I no no sorry I am not joking I am serious I mean I can think of C minimum being 0 also know C minimum 0 means what that is possible no we are on the same page okay so what I am trying to say is when can I think of C minimum equal to 0 is 0 is 0 literally can I make it 0 yes no no not no fluid stationary fluid I am imagining a fluid C minimum being a still fluid another one is okay that is that okay but I do not think we need because their temperature gradients are going to be much larger so that is why it is much better this is the basic I usually spend lot of time on this graph trying to get the explanations from them because this is where we need to interpret rest all is only plugging in okay so that is it so this is true for any heat exchanger any heat exchanger I would just do it for cross flow and sorry parallel flow that is it and another case you were right I was I just forgot you were right I should imagine a case in which where C maximum is infinite where in which C max can be infinite boiler or condenser so there also I can get the maximum that is why I can explain two phase heat exchanger are compact or better than single phase heat exchanger without even reading about two phase flow okay you see the beauty without getting into two phase flow we did condensation did we know anything about two phase flow when we did condensation I do not need anything what all tools we studied for single phase flow were enough to apply that is why we taught you condensation first then came boiling okay here also you do not have to be knowing how does two phase flow work I do not need wide fraction and all that to explain that can come at the end so this also we need to emphasize okay so the same thing I have put it in point so you can have NTU you can do NTU that is if you want to body why am I writing this equation like this I had written for epsilon now I am writing NTU why am I doing like this that is to apply this is what approach if I write equation in NTU I had studied two methods LMTD approach what was I trying to do in LMTD approach getting surface area on the right hand side of this equation what are all there small C small C is mass flow rates and specific is which I know what is epsilon it is all temperature if I know the temperature and the specific I can get so if I that is what is the greatness of case in London see if NTU is there means you do not have to go to LMTD approach at all you can size your heat exchanger all that I have done is transform the previous equations which were written for epsilon because here we wanted to predict the temperatures for a given size the same equation has been now transformed into NTU so if I have to size my heat exchanger I can so what I am trying to say is that please do not tell the student that when I know this when I know inlet temperatures when I know the mass flow rate LMTD approach only has to be used not true not true both the approaches can be used in both the situations in today's model epsilon NTU is straight forward with the calculator we can do but for LMTD approach we may need the excel sheet you check out the exit temperatures I think okay so with this emphasis I think we are through with our course so of course one point I want to emphasis before I say through with the course pumping power nothing comes free in this world pumping power is a major deterrent it is not enough to increase the heat transfer rates but that comes at a cost so we need to calculate the pumping power we need to calculate the pumping power and then fix the sizes of the pump pumping power always we say okay we can neglect you see in steam power plants we draw no we write what in steam power plants what do we draw blower turbine condenser and a small pump and we always in the class in thermodynamics we say pumping power is negligibly small it is not so in a nuclear power plant I learnt it hard way when I went to Tarapur tap 3 Tarapur nuclear power plant that pump is as big as our mechanical engineering department which is of 100 megawatts mind boggling so point is what we tell in the class is sometimes very very giving a wrong impression okay that why I why I take these examples because pumping power cannot be neglected pumps can be that big size and that high capacity mind boggling mind boggling 30 megawatts imagine and I neglect that in thermodynamics but when I neglect that I should be telling that smart is my point that what is my point what what is the tap 4 plant that is 1000 megawatts compared to 2030 but still 30 matters 30 matters compared to 1000 this has become small that is what we have to basically point is we need to make them feel through numbers I am taking this Lord Kelvin's statement Lord Kelvin came up with the idea of temperature because he believed everything there is a statement I do not recollect exactly the same way what he is what he says is in his statement if you do not know something you will tell in through words if you do not understand you tell through words if you have understood something perfectly well you will tell through numbers that is how it is that is why he is called as Lord Lord ship has come not just like that because of this philosophy because of this philosophy he is the one we who gave us the concept of temperature and how to measure it otherwise there is no heat transfer isn't it that potential that concept of temperature came because of his philosophy of quantifying that is what we need to inculcate when we are teaching also everything we should be trying to teach through number that is what we will attempt in the main workshop a concept introduced will solve a problem concept introduced will solve the problem is that okay so I think with this we will we will come to conclusion we have not completed I always tell this in the class we are not completed we are stopping okay we are not completed there can never be a completion for a course we are we are supposed to only start somewhere midway