Design and Simulation of Heat Exchangers – Part 1
 
This talk is about the design and simulation of heat exchangers in particular we want to do the LMTD  approach of the design of heat exchangers by lmtd method. So before going into the details we want to look into the design and simulation, what do we mean by design we want to see it with the example of a counter-current heat exchanger, here this heat exchangers we know what is the fluid streams the process treat stains or the process parameters the inland temperature is it temperature the exit and inlet pressure the floor it’s all these parameters process parameters are known to us and what we want to find out is the geometrical parameters like the length the inner and outer diameter of the tubesso in this counter-current heat exchange what we’re basically trying to find out is the different dimensions are the geometrical geometrical parameters are the dimensions of the heat exchanger and we often call it as sizing problem or the design problem because it is related to the size of the heat exchangers we call it sizing now in contrast to this design are also often we know we try to solve the simulation problem what is simulation in simulation if we take the same heat exchanger example that counter-current heat exchanger in this case we know all the geometrical parameters like the length of the exchange is the diameter outer or inner all these parameters unknown in addition to thatwhen will the sunlight temperature and what we intend to find out is the exact temperature of the hot and cold fluids so this is something related to the rating of the simulation of the heat exchanger we call it as simulation problem now we want to try other similar design of a countercurrent heat exchanger and hear this is an example we want to try it with counter-current heat exchanger where we will resume a simple situation by assuming she asked or the c mean by semantic was 21 when we assume that she recalls 21 if we’ll have it a princess profile shown in the figure what will find the Delta t the temperature differencesince we’re trying to solve the counter interior design problem here the temperature in the inlet and outlet also the park and cold fluids unknown here what is SIA it is basically a ratio between the heat capacity of the heart Floyd and complete this ch on the hot capacity capacity is basically a product of the heart rate specific heat x the mass flow rate of the heart rate and the cold cc or the cold capacity is equals to a product of the specific heat of the concert x the mass flow rate of the current this two ratio is basically insulation the hot and cold fluid is equals to one we have achieved so in that situation only we can expect this kind of temperature profile now in this case this is hot in hot out and TC in NYC art know if we take a small elemental length DL across the length of the heat exchanger we find that this is th and this is TC and will also assume that the internal temp of the wall temperature is tw so this TW is filing from design through descent in addition to this assumption that Sierra cause to one that is the simplest case we are making some more additional exemptions like there is no external fitting like that means this through it all through it is not connected with the environment neither the school so it is connected with the environment the heat is being supplied only from the heart rate to the cold fluid wireless separating the separating wall thickness we’re assuming it to be negligible by saying thatyou’re not assuming anything flowing from this end of the world to the other end only we’re assuming the heat flow from the horse float to the Caulfield that’s right is the assumption actual conduction he is so now what will happen thethe difference between the heart and the 148 – 3w and the associated area with this fluid and the wall or the hot side lateral surface area how much is it that is say if it is a age then we have conceded only DL length of this heat exchanger so if we assume that the heat transferred surface area is only found in distributed over there and tell them we will find thattransportation of the Hartford CT to the heat received from the wall to the Wall Street and the related heat transfer surface area and the heat transfer coefficient corresponding to the current circuitbecomes 888 858 – 3w and on this site TW – 50 and not cold AC and ac equation to find out the wall temperature find this relation do is that we can put this wall temperature and replace it in either of these equations replace thebetween this is nothing but it will be one by one by one by that is nothing is the hot side heat transfer resistance and this is the resistance offered by the corporate sector and this one by one by that is the overall resistance offered by this this can be finally expressed in the form of your way into delta t values delta t is the difference between the two fluids and away is the overall heat transfer coefficient given by the expression if we now go to the next light in summary we can say that the q is given by you waiting and so this is the final outcome we have seen is given by 1 by the way is related to the individual heat transfer resistance is offered by the cold and the heart rate and overall we have this individual mass balance for the heart and pulse rate the scituate mass balance is given by ch&p 18 – DHL simulator for the cold so if we can have these equations as we are trying to solve a design problem we know the hot in let you know the heart out let you know the cold inlet and outlet also so we know essentially the amount of heat getting transferred so in this equation window q we know the Delta t we have a large intestine towe know the mass flow rate in a start we can also find out at because the corresponding mass flow rate is also no NC dot is also known we can also try to find out this eggsy and then we can try to find out the age and ac but this is only one equation that the number of unknowns are many like the length internal diameter outside diameter so in order to find out those numbers we have to get all the decorations and by putting some are the constants like the pressure dropped then the South over all sides but we get other equations and then we can try to find out all this a h and ac so this is the simplest situation when we have a human year equals to one and we have tried to design a simple tube in tube heat exchangers now we may not expect always that ch will be equal to the ccrc are will be equals to one in any situation when ch is greater than cc or it may also happen that ch is less than 50 but means CRI the issues they better than none of it will be less than in case ca is greater than cc will find that the temperature profile is similar to the one shown herewill find that the fluid outlet temperature is almost approaching the heart in Latin on the contrary if we will find that this hot outlet is approaching the cold inlet temperature will look like this industry and to simulate design problem for this situation if we consider a small elemental land and then we can expect that would be a small amount of 8DQ getting transferred from the hot glue it to the curb weight through the separating wall and all this album shows which has been made earlier except cl equals 21 all assumptions are still valid here in this case also and only exception is that we have as mchs.net at NCC in this case what we will find that the heat transfer coefficient on the overall heat transfer between the hot plate to the cold fluid can be related to the overall heat transfer coefficient you and if we assume that the area is distributed uniformly over the entire length then lol x d l and t h – tcts is the hot side temperature is outside temperature rightwhat is the change in temperature within that small and DL DQ is in terms of the corn fluid we can write it but the q is equals to minus ccdtc well this dctc is the change in temperature that is happening in the small elemental length DL in the hole through which we can write this first equation in this form 28 can be written as DQ by ch with the negative sign and DTC can be written as minus d q by CCR to write or Express t or th – DTC this is nothing but the detective over the length ddlc of data cannot be expressed as – DQ if we take this one and this expression I’m in here in this equation if we put we find that dth – DTC this is we have taken from here this we had taken from here and we are able to express Dr delta t is equals to minus DQ in 21 by ch minus one by CeCe nowthis part is that form drdt hdtc is equals to you into a Pioneer place – 3C and one y c h – CC now we’re trying we can all integrated from this l equals 202 l equals to 12 and 1 l equals to zero the corresponding difference in temperature is delta-t that is the cost of data at smaller one and this is delta-t Lodge services because we have assumed t c h greater than CC so we have the Delta tiers smaller on this site and delta-t lunch sorry this is 30 l large on thisnow we help the situation still remaining with us cubic associate into THC in – state route that is the mass balance of the cold fluid and this is the mass balance of the Surrey hospital and the cold fluid this is for the heart rate and this is for the cold fluid this is known if we know there’s one we can take c h in this expression and put it here we can take out CC and put the expression in this one if you do that what you will find it an expression like this we have replaced delta DL so the only question now becomes cubicles to you a delta DL – 30 years / natural log data title tax so if youno because the existing policies unknown we can also find out this log mean temperature difference this queue is known in this equation the longman temperature is known so we can find out the overall heat transfer coefficient which is nothing but one by HHH last one by acac so again as we have discussed earlier once we know this expression we can try to find out the hot side and the cold side panel it is but this maybe it may be necessary that the routing number of iterations now we have discussed about this particular situation ch better than CC and we have seen that q equals to your way into the city of la is it valid for ch less than CC it can be shown that this is also valid for this situation also only thing is that distant that delta-t large is occurring on the side and delta t small is occurring on this side in contrast to the situation other things will remain same the same as it will also be taken care accordingly and the same expression also remains valid for this situation now we want to look for the counter-current already situation we have already look for we have already discussed know if we go for a parallel flow heat exchanger or couldn’t heat exchanger again by the same way ifwe will find that the heat transfer overall heat transfer is given by the way into delta team is 10:30 and in this case we will have this as delta-t large and the difference on this site is delta-t and other things so we can see that counter-current and parallel flow or couldn’t hit it can be expressed by q equals to the heat transfer in these cases can be expressed as cubicles to even 10:30 alarm in fact forto consider that situation so we will find that this relation women’s married now if we go to the next light I mean if we find that there is a cross flow heat exchanger doing things that still we can use this correlation we can use the score delayed I’m in relation to because to identity Ellen but with a small correction factor because in this situation this delta TM or the mean temperature of the lock mean temperature that is not the same in case of class third floor and parallel flow heat exchanger it was taken as one and if we put that relation here in will find that this relation is valid for the counter-current and the current election yet but as how to find out that relation reasons that four different heater senior configuration this has already been calculated for our is and this is related to the it is expressed in terms of r&d two parameters which are related to the to temperature differences here this is t in left Dynasty exist and this is the two side that is 20 – t.i. this is one ratio the other ratio is 30 – 20 / the maximum temperature before death that is t.i. capital 10 – expression has been taken from this graph has been taken from a heat and mass transfer book is changing now this is the correction track and then we can design the crossflow heat exchanger. Thank you