Design and Simulation of Heat Exchangers – Part 2
 
This lecture is in continuation to our earlier discussion on design and simulation of heat exchangers. Today we are going to talk about apsalon in two method in the last time we had talked about the territory Technic not here we are finding two new x wireless the salon or the effectiveness of the heat exchanger and the other term is the number of transfer limits are in abbreviated form it is there ain’t you supposed to call will look into the definition of each of them and then we’ll look how it is related to the design and simulation of the heat exchangers so basically if we remember that we have only talked about extreme heat transfer where we had a heart fluid and it is separated from the call Floyd by a separating well this is the separating all the thickness of the separating wall maybe delta w and its thermal conductivity Mary kW and we had some heart rate coming in and hot freight moving out school freight moving in or freight moving out so there is heat transferred from the heart to the cold feet this change in the temperature of this house too cold this is becoming colder this gold flake is becoming harder out this change in temperature of the hot fluid that delta kids and the Delta CC basically they’re nothing but the change in enthalpy of the cold fluid and the change in calpe of the heart rate now this change cannot be unlimited or in a sense that this is restricted buy some resistance what we have turned as the operator assistanceand so he did not show me how the heart rate registers said hard 8 is equals to 1 by 888 are at the wall that is built at w by a w care of the wall and resistance offered the convective resistance offered in the cold fluid is a CS so this heat transfer instances will be crushed by this heart rate while transferring heat from the hot plate to the curb weight so in a nutshell what we find that this heat transfer from the house to the cold fluid is limited by something which is known as the overall conduct and see where the overall heat transfer a distance away one by the way that is equals to one life as we have said in the earlier one this is Delta w by a w k w + 1 by hhn28 this is the overall heat transfer resistance of the conduct and you were so now we find that the ratio between the overall conductance and the minimum capacity that’s becoming important or that is what is giving the amount of transfer and it is basically relatingso this is the heat transfer coefficient that is equals to what power metres per Kelvin and this is area in metre square so this overall is work by Calvin and on the other side what we have is seeming that is nothing but the CP of the cold or hot in the minimum fluid x the m dog so this is juul pod Casey Kilby and this is Casey park second so this is cancelling all so overall what we get is what but tell him so basically NTU is are non dimensional number non dimensional sonow is it related to the physical dimension of the heat exchanger not necessarily it is not necessarily related to the physical dimensions of the heat exchanger this has been explained nicely with an example by arkasia and schedule like they had given and example of a gas turbine regenerated the intuos pen but the volume the call volume of the heat exchanger days only point 0.01 metre cube this is corresponding to an interview of 10 so in another case in a chemical headaches chemical plant a Shell and tube heat exchanger may have an interview of one but it may have an overall for volume at 100 m q so this is in contrast that way this is not necessarily that a larger into will correspond to a launcher dimension of the heat exchanger but phonic particular or time for heat exchanger if we find that if you win by Simi ufic mean if this parameter is remaining constant of this is the nearly constant then we can say that this a is directly related to the issue that means for a particular type of heat exchanger if we find that the invoice email is nearly constant so if we increase the until the physical dimension of the heat exchanger I will also increase what is the significance of this one we can have an idea about the if it is so happened that this seeming it will directly controlled by and q but we’ll also find that C-Max that can also have find the CC between the denominator but the other 16 that is also controlling the overall heat transfer coefficient because that one by UAE is related to one by hha a + 1 by a CSE and since okay here in this one he has another dog that is a wall registers we may consider detour sometimes we neglect the star know what you find the ceiling is directly controlling the issue in this relation but the other ones will also have an influence on this overall heat transfer coefficient by controlling this at a time when there is a change in ch that will change the HH and that will entrance change the email and that will in turn have an effect on this overall I meant you know this ain’t you can be an effective means of in the design I mean it’s fine it is related to the effectiveness of the heat exchanger we will find that this is during certain advantage in the design and simulation of the heat exchanger principle we need to look into the definition of the getting transfer if we look again into that heat exchanger configuration will find that the heart rate is changing its temperature from the2tails this is PCA in the contact current configuration this is TC out so the actual heat that is getting transferred or the enthalpy change that we have said already that few can be related as c h t h y – HR what is the maximum heat that can be transferred in this boxes so how to estimate based maximum height transfer this maximum heat transfer we can estimate and this is an ideal situation like it will be of a heat exchanger of infinite length and we have to also keep it in mind that so already we have looked into this heat transfer that that is actually taking place and now will look into the overall I’m in the maximum heat that can be transferred so here we will consider a situation where thethey were choosing this one there is an obvious condition where you know we have the simple condition where did that sissy call Sissy will look into that one that is a simple situation but the more complex situation is with when the heart or the coal-fired capacity are unequal so in case we have this c h greater than CC we find that the hot fluid is coming from t h the 6th in and this is t h o and this this is PC in and this is PC out this is k h a now we find that this one fluid being the minimum capacity fluid of the link to it I meant that will experience the maximum temperature difference like when someone is with he has to suffer most so this fluid Stacy will have the maximum difference in temperature so when we have a Hume that ch is better than c c that means the cold fluid is the minimum capacity fluid and the minimum capacity fluid is experiencing the maximum difference in temperature what we have to keep this money in mind that while finding out the maximum difference in temperature we have to identify the minimum capacity fluid and the minimum capacity fluid is supposed to have the maximum difference in temperature but please remember that this condition is only valid when under certain conditions such as valid and the conditions are libraries that there is no external heating League there is no actual conduction of heat there is in finite amount of heat transfer surface area involved in the process so basically this is an ideal heat exchanger and we’re trying to find out then ideal heat transfer that is taking place and it isthis is the hottest temperature in this process creating that will not be able to post that this PC and will never be able to cross the t a g of another words to see how it can never be more than tha this is possible only in extreme heat exchanger but in case of multiple screen protection job this is the not really the case so we’ll discuss about that later discussing about the multi stem play the latest news on planet x is now if we look at this one so the maximum heat that has been transferred is with the minimum capacity of fluid and what is the maximum difference in temperature this is the maximum difference in temperature of TMAX delete it cncc fluid is the minimum what is the meaning of and experience the maximum and so it will come to the lowest temperature that means it will have the maximum difference in temperature at Max so he also the maximum so that is basically the same in x 18 – documents we have an idea about the heat from the actual heat transfer that is taking place so we can now try to find out thethe first situation that we have considered is siege Reddit NCC that is the fill fluid is the minimum capacity fluid and in that case we can write this is nothing but QQ can be written as the change in the hot plate enthalpy change / this is the maximum entropy that would have been changed so seeming which is seeming the pulse rate is the swimming and THC in – 3C and that is the maximum difference in temperature to 60 Max delta t-maxx the maximum difference in cape Paterson that’s x the ceiling and this is relating to the hot fluid and LPG we can also write this to actually transfer income stop the cool fluid enthalpy change so what will find herein this case this becomes a simple expression excellent Eagles to ecr – pcy / thnm islands pcyc 66th and this ratio is similarly try to find out the effectiveness and order situation so in this case what is the minimum capacity fluid CHS the minimum capacity fluid so if we have to now find out and that he transferred us sorry play forgiveness of this heat exchanger how can we find weekend write it as at Salem is equals to the actual food that is getting transferred what is that actually get that is getting transferred so in terms of ch it will be c h x t h e minus t c e I’m sorry this is th in – is it out / what is the minimum capacity fluid ch so this is nothing but t h inline is TCL so this is cancelling out so this essentially becomes thn – t h / t h in minus tce the we can also write it in town song the cold fluid enthalpy change so that becomes c c x PC out minus tcn / C-Max is q-max is equals to c h and that is equals to th in Linus TC you can also write this work but this will not cancel out so it will remain there so let us look into an expression where we can try to relate this excellent and the entry in an earlier discussion we have seen that in this heat exchanger we have taken on small element of length dlz we can ride with you I mean in terms of the overall heat transfer coefficient or conductance x the difference in temperature in the previous class we have discussed about this there we have obtained and expression well tth – DTC is related to DQ and 1 -but we had an expression like this and from there we obtained this relation now you see this was the relation link about page in the earlier discussion now I’m here we can build a small change now in this case we can assume that ch is the meaning of capacity fluid sorry this is we have taken as CEO so this is the case ca is greater than CC we had discussed in the diary of case and know what is the minimum capacity fluid cc is the meaning of capacity through it if cscc is the minimum capacity fluid we have taken that one out CC we have taken out and that becomes with this change and sign it becomes we know that cement base emax is equals to see you so we can write it as 1 – 3 into into and this negative sign has been taken inside so it is 1 – here so now if we put this value of Delta pl what is Delta t l it is PH of -15 / 18 – PC out so we have this relation we also have this relation about the actual heat transfer and the if slightly manipulate these two and it will take the heat exchanger effectiveness expression Epsilon is equals to hear what iswith the little bit of asthmatic we can get the situation so we’ll try to see what we have now just now we have seen that 1 – CRN 2nq is1 – CRF salon by 1 – exile on so how did we arrive at this configuration so on the lake on the right-hand side we have this expression and on the left-hand side what we had is Ellen off thr/ mine is tca so we will add and subtract the first of all we will be fine these expression but do nominator and the numerator by th in this is not thr ok so what we have to do is that thr – PC in this numerator/ th – PC now with this bag where will hand and subtract key h in and subtract 18 from that expression and found this one we will add and subtract TC in and please see it so this will eventually not change the  expression but now we can combine this confirmation and this will finally come as 1 – CR  by one minus eight.