Week 9: Lecture 44: Heat Exchanger fundamentals

[music] [bell] [music] [bell] [music] Hello everyone. uh after having done uh convective heat transfer through pipes that is internal flows we come to the most important application of this phenomena that we have studied in what we call as heat exchanger. Heat exchanger in simple terms is nothing but a geometry or a situation where energy is transfer between two different fluids. That's it. So that is what is a heat exchanger. Now you have heat exchangers in everyday life without even realizing or without even calling them as heat exchangers. So when you have a hot cup of coffee or something you would have seen in uh the movies etc. they will take the coffee from in into a tumbler and then pour it into a a cup and then do this like this. So what is happening is the hot beverage is exchanging heat with the surrounding air. In the process it is becoming cold. That is like the simplest heat exchanger that you can see. That is where you are forcing the fluid to go from one vessel to other. you're forcing it. Another heat exchanger is the normal one where you put a cup of coffee in a saucer, allow it to cool with time by exchanging heat with the surrounding. There is no motion but energy transfer is happening. These are all heat exchanges. But what we are going to see as a part of the course is where heat the fluid is one fluid is flowing through a pipe and the secondary fluid or the second fluid. So this is the first fluid. The second fluid is flowing around the pipe either inside another pipe like this. So this is tube in tube concentric pipe situation where I have fluid one here and fluid two flowing through the annulus part or I just have one fluid second is just outside air. So I have hot water carrying pipe and then the water is losing heat to the ambient air h infinity. So fluid 2. So these are all real life situations that we have seen and [clears throat] we will now I mean we have seen these problems individually. Flow around a cylinder we calculate the heat transfer coefficient. Flow through a pipe we have calculated the heat transfer coefficient. We have introduced the concept of overall heat transfer coefficient. And we also saw two cases for flow through pipes where you have a constant wall heat flux and constant wall temperature. And constant wall temperature case we said one is condensation process. The other is evaporation process. One of them would be like this, the other would be like this. And condenser, evaporator, etc. are all classic heat exchangers. Of course very very specific because in one case the fluid is condensing the second case the fluid is evaporating but heat exchanges in general are where there is an exchange of energy between one fluid and another fluid. So there are various ways and means these geometries have been curated over last several decades to improve the heat transfer coe improve the heat transfer. So Q is equal to H A delta T is my governing equation. We when we have multiple resistances we go to UA delta T some reference delta T. This UA needs to be increased as much as possible so that Q is directly influenced. So the aim of all the heat exchanger designers is to go on increasing this as much as possible. ways and means are tried to improve the uh I mean improve the overall heat transfer coefficient so that the size becomes small. If the if the length or the diameter etc is the size of the heat exchanger is made small the power loss due to pumping is also reduced and the aim is essentially to improve heat transfer reduce pumping power. So this is the aim with which people work. Uh but many times these cannot be separated. So you improve heat transfer, you also have to spend more money on pumping power also. But that's a later on thing. So first we'll go into understanding how heat exchangers are designed, what is the basic governing equations, how they are classified, so on and so forth. Okay. So a device that facilitates exchange of heat between two fluids that are at different temperatures with or without mixing with each other is a heat exchanger. Okay. Right? This is saying clearly without but a heat exchanger is where in your house when you have a gizer where hot water is coming in and you also open the cold water tap to get the water out at an optimal temperature. The fluids are mixing. So that's also a heat exchanger. Convective heat transfer in each fluid. Conduction through the walls separating the two fluids. This is typically a representative diagram of a heat exchanger. You typically would have cold fluid on the outside, hot fluid on the inside. So that all the energy from the hot fluid goes into the cold fluid. But certain applications may have this kind of an arrangement also. Okay. So the overall heat transfer coefficient which accounts for these conduction and convection effects. We know summation of the thermal resistance is equal to 1 / UA. So there are two or I mean two broad methods for calculating or for designing the heat exchanges. So one of them is the log mean temperature difference approach. Other is effectiveness NTU method. We will go into them as as we proceed along the discussion. Log mean temperature difference we have already seen in uh internal flow constant wall temperature case. Essentially the same concept except that there we derived it for one fluid being constant temperature other is increasing or decreasing. Here in heat exchanger both the fluids would be changing the temperature and because we are having locally varying delta t at every instant of at every location we need to go back to the concept of log mean temperature difference. Okay. So what is this log mean temperature difference? uh approach F is a correction factor. So all temperatures are known either given directly or we have uh energy balance to find out those four temperatures. What what is this? Let me explain this to you properly. So if I have fluid in one pipe like this, this is say the hot fluid and you have another fluid which is the cold fluid flowing this way. Please note the arrows that I have drawn. This is a tube in tube heat exchanger. One pipe and another pipe which is surrounding this. Please they are not concentric but I hope you understand that they are supposed to be concentric. It's quite hard to draw here. Uh the second case is where uh the fluid is here. Hot fluid is flowing this way. The cold fluid is also flowing in the same direction. Okay. So, same arrangement but just the direction of fluids have reversed. So, this is called as a parallel flow heat exchanger. Parallel flow means both the fluids are flowing in the same direction. Which means if I plot the temperature distribution along the length of the heat exchanger, the hot fluid would uh hot fluid temperature would go on decreasing. The cold fluid temperature would go on increasing this way. T hot I T hot out. T cold I T cold out. This would be the temperature distribution. And you can see at any given instant this is my delta T. So this M do H CPH M do C CPC would be the mass flow rates and the specific heat of the hot and the cold fluid. And we can write heat loss by hot fluid is heat gained by cold fluid in the incremental distance dx. So m dot cold cp cold cold dt cold is equal to m dot hot cp hot d hot. Heat loss by hot fluid. So as I am flowing here from left to right my temperature would decrease. So final minus initial would give me this one. As I moving here this temperature would increase. So the sign essentially is to take care of the fact that decreasing temperature along increasing length. Now we'll come to this part during the derivation. This is called parallel flow. The other one is where we have the fluids going in the opposite direction and we would call this as counterflow. I will remove this circle because it doesn't serve the purpose of understanding too much. This is called as the counterflow arrangement where the two fluids would be like this. So this is hot fluid inlet, hot fluid outlet, cold fluid inlet, cold fluid outlet. This is called as a counterflow heat exchanger. As you can see very simply, parallel flow heat exchanger. Counterflow heat exchanger. Here the delta t driving temperature difference in case of parall flow is not remaining constant. Delta T is equal to T hot local minus T cold local. This quantity deltat T of X decreases as X increases. That means driving temperature difference decreases. Therefore, dq every incremental length the heat transfer goes on decreasing decreases over each new incremental length. So initially you have a large delta q large delta t. Therefore, very large amount of heat is transferred as I move closer and closer to the exit. The each additional imp uh increase in length delta L that you add is going to be less and less useful as we had seen there. That is what the concept of NTU was. Same concept is going to be used here. Whereas here if you check if you check this every location for example the driving temperature difference would be I'm not saying they're equal but they would be nearly the same nearly equal. Therefore here you would have delta t local which is nothing but t of x minus tc of x. The definition remains the same. dt of x is more uniform throughout along the length of the heat exchanger. Okay. So, parall and counterflow. What other thing we can see here? TCO can never at best can asytotically reach PHO. it will never be equal. Okay. So, asytoically reach this one. Whereas here TCO can become greater than TH. Nothing prevents it. Okay. So this is some this gives you a very good advantage of heat transfer here. Okay, we'll see more of this when we do the derivations etc. So counterflow parallel flow two major types of heat exchanges that is how we have classified them and of course there will be derivation for calculation of log mean temperature difference for both these cases which we will see. Okay. So what I'm what why why did we start this? So if I if I knew [snorts] three temperatures mass flow rate m dot h cph m dot cpc knowing the mass flow rates and the uh at least three temperatures [clears throat] we can calculate the fourth temperature. Therefore, all four temperatures known M.H M dot C known all four temperatures known delta T log mean or log mean temperature difference is known. Therefore Q is equal to U A deltat T log mean can be calculated. Okay. So if Q is known that means everything else should I mean if Q is to be found out everything else should be known that means D L should have be known to calculate Q else if Q is given you will get area from the calcul calculations and then area is equal to pi dl. So you choose a diameter get the length or you you might have a constraint on the length. Choose the choose the length get the diameter whatever be it d and l combination can be obtained. So this is the typical kind of lmtv approach problems where all four temperatures would be known. That's the most important thing because I would be able to calculate the LMTD or log mean temperature difference. How to calculate that? I we will go through it. Der derivation would be done. So the formula for this would be obtained. So you can calculate this and mass flow rate properties are known. Three temperatures should be known. So the fourth can be calculated. Three temperatures known. Therefore calculate fourth one by this kind of energy balance. Okay. So that is LMD approach. The other one where only inlet temperatures of the hot and the cold side are known. Type and size of the heat exchanger is known. We can we can calculate outlet temperature by using the effectiveness NTU method. We'll detail it in the next or the subsequent module. Okay. So this is what I had already told. Two fluids flowing in the same direction, opposite direction. Double pipe heat exchanger. This is what it is. We have drawn this already. This is called as a shell and tube heat exchanger. This would be seen in various industrial application. Shell and tube is nothing but a large cylinder which we call as the shell and inside that there will be an array of tubes which are going to be there. So these tubes will carry one fluid. As you can see here, these these are going to carry one fluid. This is flowing through the pipe. On the outside we have what we call as the shell. So the fluid for the shell comes in from here top. There is what we call as some kind of a baffle which would prevent the flow directly going from left to right. It will force it to go down like a divider on the road. Take a U-turn. Go further. Again, there is a divider. Take so that you uh the the shell fluid interacts with the fluid flowing through the tubes over the entire length rather than bypassing it. The tube fluid on the other hand comes in here and separates into multiple tubes. goes through this comes out gets out of here. So I'll just draw this very very simple diagram. Of course that's a very nice diagram. What I'm going to draw is going to be a little bit [clears throat] difficult. U but I'll try to simplify it for you. So you if I want to check this out, this is this is how a baffle would look. Okay. So this baffle is a part of the geometry. So this is your shell and you have Okay. So Yeah. So this would have completed the cylinder but it's not there throughout. It's there to some location. Um I don't know why it's getting erased but nevertheless this is the baffle and you have a baffle in which there will be holes for these tubes. So these tubes would be going through this and the subsequent bottom tubes also would be there. Uh the one fluid would be flowing through these tubes. Okay. Array of cube tube bundle would be there. Now the shellside fluid. Shellside means one which is flowing inside the shell. This is called as a tube side fluid. The one which is shown in black is the tube side fluid. [snorts] This fluid would come in this way. I have so the baffles would be such that I have one baffle this way, other baffle this way, one baffle this way, other baffle this way. Why? Because I want the flow to do this serpentine manner. The fluid should flow. The shellside fluid should flow in a serpentine manner so that the interaction with the tubes is there for a large amount of area because h a deltat t u a delta t this is the contact area surface area. If it did it if it did not have these baffles, the fluid which is coming in would just find the path of least resistance and go through this way. It will not interact with the tube over a large area. Okay. So let's say this baffle is this one. What I have shown here is AB. This is that baffle AB. It is semicircular plus certain location above. So it's not just extending to half. it usually extends to some height above the diameter. Okay. So this is this is what I have tried to draw here. Okay. Now the [clears throat] fluid which is coming would would have come like this and then it would turn around this and go down this way. came in this way went around this way and [clears throat] in the process there would be heat exchange between the tube and the shellside fluid. This is called as a shell and tube heat exchanger and this is very very practical seen in various industries. Okay. Other one is cross flow heat exchanger where you have fluids crossing each other. Okay. As you can see, you have fluid 2 passing through tubes. Fluid one is flowing through the gap between those sheets. Those sheets separate the fluid one, prevent it from interacting with one one set of fluid from interacting with the next one. Whereas in the subsequent diagram, you see fluid one is completely mixed. Fluid two is alone going through the pipe. So left side diagram is where both fluids are unmixed. In right side diagram, fluid one is completely mixing. There is no difference. All the fluid would be mixing because it is not having these kind of perforations. Fluid two is flowing separately in the pipes. Okay. Multipass and cross flow arrangement. Multipass is where you have the fluid coming in and passing through the shell multiple number of times. So this is a single shell. One cylinder is there and four passes. Four passes because the fluid coming in the tube is going through once coming back going through again and coming out. Four times it is traversing the length of the shell. Therefore it's called four pass. This is one shell and six pass. You can see it is traversing six times. You could have multiple shells. So this is one arrangement. Identical arrangement would be below this where the fluid is not yet finished exchanging the heat. It would go through the tube in the second shell and pass it six times. So it will be two shell and 12 pass like that. So you can have this kind of a arrangement. One shell to pass of course is what is shown here. Okay. Okay. Compact heat exchanger is another classification of heat exchanger where your lung human human lung is the best example of compact heat exchanger where the heat transfer surface area to the volume is very very large. Beta is greater than 700 m²ared per meter cube. Anything which shows this number or greater is called as a compact heat exchanger. Car radiator, gas turbine, human lung. Look at human lung. It is 20,000 m squared per meter cube. So you can exchange heat very very efficiently when you have this quantity to be large. Other types of compact heat exchangers are what you see in your car radiator. So you have a tube and you have these circular fins which are there. What you studied in conduction the annular fin this is what is there. So you have fins to improve the heat transfer area. Gas to liquid or liquid to gas. Low heat transfer in gas. So you have to put fins on that side. You have seen all this. And now we come to heat exchangers which are in tubein tube configuration or pipe inside pipe. So for that we we know this concept of thermal resistance. We have one fluid flowing through the inside pipe other flowing through the annulus. R1 and R2 are the inner and outer radius of the inside pipe. There is a wall thickness given by R2 minus R1. K is the thermal conductivity of the material of the tube. A I is the inside surface area of the tube. A kn is the outside surface area. So AI is 2 pi r1. A is 2 pi r2. Of course l is there 2 pi r1 l 2 pi r2 l. hi is the inside heat transfer coefficient. Ho is the outside fluid heat transfer coefficient. How do you calculate that? We have seen it in internal flows. Reynold's number pantal number nil number H. For the annulus use hydraulic diameter concept. Reynold's number pantal number nil number H. So you know the H or you can calculate the H, you know the dimensions. Therefore you can calculate the conduction resistance also. So the total resistance is in convection resistance inside plus wall resistance plus convection resistance on the outside. 1x h1 a1 or hi a i plus 1x h a kn plus the conduction resistance. So we can write this as sum of the resistances is nothing but 1 / ua. So we will write 1 / ui ai overall heat transfer coefficient based on the inner inside surface area of the tube or overall heat transfer coefficient based on the outside surface area of the tube is nothing but the summation of the thermal resistances. So let's just write that a little bit. U A is nothing but 1 / summation of R thermal and this is nothing but UI A I is equal to U A for that matter any U into that particular area. R thermal is 1 / hi into A I plus log of R outer by R inner divided by 2 pi K wall into L + 1 / H knot K. So this is convective resistance inside, convective resistance outside and this is the R conduction through the wall. All these quantities can be calculated. This this this can be calculated because HI is known. How is HI known? Hi known because we have Nassus number which is known which means because Nassus number is a function of PR parental number correlation is known therefore we can calculate it. Similarly Hnot is known because Nassus number outside is known which means it's a function of PR of the fluid flowing outside everything is known. So you can calculate this and the next step would be of course to go and calculate the log main temperature difference. Please remember U alone doesn't have too much of value. U into A is what physically is important reciprocal of the thermal resistances. Okay. So if I [clears throat] if I put the wall resistance to be zero which is very likely to be the case many times if you think of copper tube or very highly thermal conducting material or very thin wall tube. If the problem says thin wall tube you can neglect the conduction resistance which means 1x u is 1x hi plus 1x ho because both the areas remain the same. And of course you add fins you have to use the fin efficiency there appropriately as you had done before. How to calculate fin efficiencies you know how to calculate those things from conduction chapter. So this is where everything is coming together. As you can see fins are being are coming in conduction resistance, convection heat transfer coefficient calculation, convective resistance concept and then overall heat transfer coefficient which we saw earlier which is nothing but reciprocal of the uh thermal resistances. So all of them are coming together in the s single application on heat exchanges. These are some typical numbers which if you want to design uh a heat exchanger for these applications, these could be typical numbers that you start off with. And you can see steam on the tube side force circulation U is about 1,700. And these are typical handbook numbers ballpark. You can calculate these and use these. And for other heat exchangers like steam turbine condenser, it's of the order of 4,000,500 to 4,000. And you look at evaporators, free convection is extremely low. Okay, these are just been given to you so that you have an idea if you're designing something, you know where to start, what to expect. Okay, last thing before we close this module, fouling. Fouling is essentially where deposition of salts etc happens due to uh prolonged use. If you if you uh many times in households where the water is not soft, it's hard water, [snorts] you know, the the pipe you will start to see reduced flow rate in the pipe with time. Okay? And eventually the uh pipe flow rate will be affected so much that you'll have to replace the pipe. And when you open the uh I mean remove the tap and look at the pipe the pipe would have large amounts of deposits. So if you if this is the circular pipe originally bare pipe now because of uh salt deposit you would see something like this. This is all of course this is highly magnified but this is how the deposits are going to be. So this is what is called as fouling. Fowling is going to affect the resist it's going to increase the resistance because this is a conduction resistance to heat transfer. So this conduction resistance is going to affect the overall resistance. R thermal increases. Therefore, UA will decrease your heat transfer would decrease the uh fouling will cause degradation of the tube in terms of heat transfer with respect to time. Therefore, you need to clean them periodically. That means the plant has to be shut down. You will lose money when because steam generation would stop, power generation would stop. But if you don't clean it, your performance will get affected so much that eventually you'll have to replace the pipe. Cleaning can be done using physical methods. You can also use chemical cleaning. Various types of methods are there for cleaning. Whatever it is, cleaning has to be done periodically so that the resistances that are introduced because of fouling can be mitigated quite significantly. Okay. And these are how fing is taken care of. RF by A. RFI by A I RF KN by A. So these resistances are typically given to you. Distilled water, fuel, oil, steam, refrigerants etc. The fing resistances given to you. Units are similar. You look at the thermal conductivity of these things. They are very very low thermal conductivity material. So whatever is there. So convective resistance on both the hot and cold fluid side, conduction resistance in the wall, fouling on the inside and outside. This would represent the entire set of resistances that you would have. Please remember ai is not equal to a not. If it is a thin wall pipe, it would be the same. Otherwise, it is pi dil and pi d l. Okay. So this is a simple problem we'll do in the next module. Thank you. [bell] [music]