Plate Fin Heat Exchanger: Multi-stream - Part 2
You are welcome to this lecture, this is in continuation to our earlier discussion where we were trying to analyse, the plate fin type heat exchanger where multiple streams are handled. And we talked about the fiN temperature profile connecting between the two surfaces or  between the plates at temperature t a and t b said that the temperature profile between the plates when known to us and we have derive some kind of we have obtained some kind of temperature difference of temperature profile Peter x equals to 3y x Omega into the fog x it was of this nature 1 – Omega into e ^ x plus we going to eat the power minuswill also try to find out the amount of heat getting transferred so this is said he and TP we had the temperature profile for this film connecting between tea and TV in the fluid flowing on top of this column in field is of temperature take it off then we have been able to find out the total amount of heat getting transferred as a function I mean like this 2h x theta x into DX and the situation was done over the length 02 well this is Gino and this is the length of the fence so we got the total amount of heat transfer in the adjacent field streams RTA NTB now this is exactly what we are looking for in a circuit multiple threatstream if you look at that particular geometric so if it is a flight 548 stream Peterson just say we have tw0 then we have TW1 then we have teachers do to all these are the wall temperature separating what temperature then we have to do food and TW5 and we have supplied 5% depending on their configurations or maybe you’ll of their encounter current to each other the order it maybe parallel counter combinations so that will bethat’s what exactly we have this is the qt amount of heat getting transferred and that was to get my little as we have it earlier that it would come as ancient 2 l into tighter and tighter so as it is attached to this place at this plate and half of the feed is attached to this place and as you know there is a kind of adiabatic temperature profiling condition prevailing at the middle so this is like this is tatw and TV and they’re actually nothing but twtwtw one in this moment that we have about a TV that is connected byat the meeting that the thing then by I’m in depending on the temperature of the fluid from on top of it we will find that the heat either is flowing from this one to the fluid or threat to the world but there is a minimum at the middle of this thing for Beckenham some kind of a diabetic condition has been set at the middle of it so half of the film is as it attached to this plate and half of the field is attached as it to this plate but it may not be the situation for every case is worse t&t we are not the same so depending on the TV we may find various kind of the configurations where we will find that the extreme arm or the minimum the maximum is lying within the film outside the fence andthis is how you going to take a count of those situations that we want to discuss in the class and we will start with the investor communication again so that they will find that the equation we have already talked about now if you want to look at the maxima or the minimum in the clinic question we have to take care of that equation equation and effective 20 and then we can determine what is the position of the maximum or minimum so we have three types known to us what we do isso we have to text Mum to us what we do is that way differentiated with respect to x and then we regret it 10 so this will lead to the situation that theatre a and 1 – Omega and e ^2 mi is equals to 1 – and that will be a little bit I will find that this is coming nothing but it is about -8 to the power minus the exact location of the experiment that is occurring in terms of this thing connected between the two plates as we have told that this has been taken from the paper by example of prashant and it has been taken from the international journal of heat and mass transfer 39 issue of 1996 otherwise you can also refer to the book of jasher and also this if we had been connectingwe’re trying to find out what is the external that is located depending on the size you can understand that this all and it to the power n and that the show will determine what exactly this x is getting located particularly if we say that is equals to one that is equals to e to the t t y sitaray that’s what is r and that means theta b is equals to theta you will find that this ex is coming exactly at alewife so that means we find thatthat means we have anybody to find attached to this place and I’ll buy to feel attached to this place so if that is so if there is a kind of had a better condition at the middle of the field or anywhere else that think they can I use that you know that exist a kind of a diabetic conditions are at the theatre and we can easily use that heater Africa’s 210 hyperbolic MLB NL that’s the basis of inefficiency provided we know the exact location of that extreme but as we have said that this isbut it is possible only when the store at b are equal but in reality you may find that there are several situations bacteria cannot equals to TV and in those cases we have to go for a different how do I estimate one way of doing I’m in estimating the thing is that we try to find out exactly what is the app to fetch that extra amount is located where it is exactly located and if we look at this diagram are we maybe it may be a situation where you will find that this is like ta ta and designed is it be this is this temperature is TV and the fridge temperature throwing on top of that feeling is that 30 and it’s a minimum is somewhere and this point what's the length is the total lengthand we may try to find out for the position and that will be given by y ^ 2 m x is equals to e to the power m l – all by all minus y to the power minus and from there depending on the temperature and the temperature ratio 30 find the value of m and value of l we would be able to find out the position as well the exam in extremist located so we have it and then he’ll – X2 lens over which we have to calculate the transfer so how do you do that so we will be able to find out to introduce that we should be able to calculated overfind out and this is nothing but you know we have already tried to find out that one earlier and this would become twice x into y into theatre and then ETA is because we have assumed that are not assume that means we have told that to say that is an extreme at this point so that means that if a diabetic plain is fine so we know that we have an adiabatic play more at this point so 26 is the printed where is the fenty the at distance location eggs and what is the temperature difference here up to this point theatre a then purchase the heat transfer coefficient is age and this ETA is taken care of that seemed connected between the wall and the slant this is the idea better condition prevailing at this location so this is AT&t and the central pressure profile we have already known to us and what is the length this entire thing is not active so what is taking care of the plants that we have in NC we have not written it as theatre XL variable-length so here we have put it as theatre as if this entire thing is at the fingers temperature RTA so we are multiplying it with the fin effectiveness of an efficiency rather eat a and x the Air transfer coefficient and this is the length of the fieldstop by that they would be able to calculate him a similarly we would be able to calculate QB and you will find Cuba would be twice l – x into sin 2 theta b and then you have it’ll be so this is what is the amount of he’s getting transferred from the wall to the plate is 2 l – 6 into 8 into 3:30 and it’ll be here we are finding that the remaining the end of the film and minus x is having a low as if there is heat transfer coefficient between the heat and the free and the thing is as if the entire scene is butterfingers temperature of theta b which is not actually the case but this fin efficiency is taking care of that one so that you knowyou will find that there is coming as router bit to HK t&t tire and then we have a hyperbolic inverse minus r / sine hyperbolic mlq would be it would be a lot of us to h by Katy to hkt and then happy today then x into cos hyperbolic ml – 1 / sin hyperbolic wonderfully so this is what is QB and this is Cuba so that gives you the temperature and the heat getting transferred from this plate to the fluent and this plate to the phrase this iswe would be able to find out how many things now as we have that it may not be always the situation that they split the bills with you cannot expect that it will be in this configuration than many other situations like this plate temperature maybe just the wallpaper that says I’m in this is here this is here and maybe at this point so that means this teacher of the fridge temperatures may be better than the wallpaper is so in that case what will happen in the heat will be getting transferred from the wall from the 3 to the 1 so only thing that we need not worry about so far to have to do is that we had to just in this automatically that will be taken into account once we are able to emit onceqbiq it will automatically take into account of this temperature but the situation will really be different I mean all these things depend on that equation where we have said that it was the power m x is equals to e to the power m l – I / 1 – 8 ^ and these are will determine the position of the x and the car is basically nothing but the theatre by theatre ar is such that the Aero theatre a of Italy is such that this location of this x is going the physical boundary of the spirit may lead to a situation that he is no longer the extra mum is or longer existing willyou know it comes to if we put one by cos hyperbolic email you know exactly at one by cos hyperbolic ml when this is the value of hard then you will find that this extreme mum is exactly at this location and when we have values are you know when the value is on less than 1 by cos hyperbolic and then it will indicate I mean look into that situation one-by-one so should we have a situation when we have a say exactly are is equals to 1 by cos hyperbolic ml so at that point the extra mum is located at this point and we will find that exactly at that point the situation will be such that it is continuously from the same to the side and four values are less than one by cos hyperbolic ever even find that this is going beyond the physical boundary of the field so here in this case we will have the same extremum located at this point so is it making any kind of changes in the Phoenix questions are in what does physically mean even find that it is meaning but how is v configuration here in this case the fluid is at a temperature that you know this one is at the temperature now the heat is getting transferred from wallet to the Sprite and also TB is higher than the fray temperature so the heat is getting transferred from this one to the fruit the book the real are getting fluid to this preparation in this configuration now if we look into that humour and humour expression ok and if we look into its configuration I am in his expression and there if we look into a situation where all is less than cos hyperbolic ml under this condition I will find that you know in this configuration 40 will find is that in this situation I will find that SQA increase positive or I mean it is coming from this world to the fluid but this will have a changing values here instead of you know he went from the wall to the same even find that the fear of giving hit the fluid is giving heat to that this is in contrast to the earlier situation and it will lead to a kind of direct heat transfer from this wall to wall and bypassing the flu Street and we often call it as the transfers heat conduction or we have to buy him some in this has to be either taken care of separately or we had to define a fin efficiency to take care of this bypass he transferred this is often also called as by Percy transfer as because the heat is as he bypassing from 122 the other and bypassing the fluid so as it directly this heat is QA is going from the street to the other separating plate so if we look into this situation that may be another situation where there is flint Street is such that this is like this but this is ta and this is at TV and the temperature I mean sorry the intermediate rate which is the flowing flowing the convective fluid flowing over thethat one is equals to 8 ^ -5 – y ^ that’s what we have found for that feeling when we got an external but for this situation where I’m at some point you know this thing temperature profile will have same temperature as the top 30 so so in this case that will postpone to a configuration where we will find that the situation is similar to that 30 ^ 2 m x so at some point theatre I will at some point for this situation where we were talking about say he had this is ta and this is it be and this is why we have cancer do so at some pointin this case this will be e to the power 2 m x and this will lead to the situation in the power n 1 – r / y ^ - ml – are so this is different from the previous situation and this will also corresponding to a different situation which giving rise to a different kind of heat transfer and particularly that will lead to having all the ideal place is also why do we have talked about that when it the physical is the maximum of the minimal lies beyond the physical boundary of the condition called when you know the situation is such that the temperature is in between AT&t be that kind of situation how do I taken into account in real situation which we do not no I mean when there are multiple choicein a relationship because that they will be automatically taken into account of those situations so I know we had estimated the hue and QB now we will look for whether it is sufficient to take account of the heat transferred from the wall to the fluid or from this side to this this is adequate all we have to look for something else which is taking account of the actual acetyltransferases conduction of the bike RC transfer and then we’ll be able to should not be worried about whether it is already taken care or not in the analysis so that you will look in the next class and thank you for your attention.