 Yeah, let us get back to business, we are on the last leg, this is slog overs I keep saying, so that is what there is a saying, there is a difference between the hero and an ordinary person is that one who last long in the final phase is the one who is the real hero. So we have to even for winning 2020 or one day match, we have to play well in the slog overs. So that is what we will attempt to do now. So we are into heat exchangers, so I guess most of you or most of us are very familiar and this is the pet word which we routinely use heat exchangers, whether we really use them or not I do not know, but still I guess we all use this, okay. So as I said I will not derive anything on the plane paper, I am going to go reasonably fast because I am sure all of you have gone through LMTD NTU epsilon, but let us focus on more on interpretations, explanations rather than examples, okay. So that is why I am not going to spend time on what are the types of heat exchangers, what are the heat exchanger applications, all that I am not going to spend time at all. So let us get to heat exchangers but one clarification now that one of the persons had asked me, I thought I should emphasize, I usually used to go heat exchangers. Heat exchanger is a device, what is the device which we are worried about, here we are not in this heat exchangers or even in UG heat exchangers whatever we teach, we are not worried about direct mixing, one fluid is not directly going to mix with the other fluid, those are also called as heat exchangers, fortunately or unfortunately, but we are not going to be worried about those heat exchangers, here when we say heat exchanger, we mean here that they are going to be separated, there is no question of mixing with the hot fluid and the cold fluid, okay. So that is what we take up as the heat exchanger, now this is the hot fluid and this is the cold fluid, I have just taken tube in tube, so there are three resistances, you can easily see that, okay, there is convective resistance on the inner side, convective resistance on the outer side and then the conductive resistance, so now there are two approaches, one is the LMTD F approach or the LMTD approach, another one is the epsilon NTU approach. What is known in the LMTD approach? I know the inlet temperatures, outlet temperatures, mass flow rates, what is that I am supposed to do is this size my heat exchanger, so that is what I can do with LMTD approach, in epsilon NTU approach, I have been given the heat exchanger, it is there off the shelf in the market, I have been given the catalog of the heat exchanger, I know my mass flow rates and inlet temperatures, I need to predict what would be the outlet temperature, now my question is, can I do with epsilon NTU approach, can I size my heat exchanger using epsilon NTU approach? Sorry, reverse question I think, the question is, can I predict the outlet temperature using LMTD approach, how many knows, why not, because I am not going to go in a logical fashion, I am going to go in a high entropy way that is fine, why because epsilon LMTD approach means what? We will take up this question after we take analysis of LMTD approach, point is the answer is LMTD approach also can be utilized to predict the temperature, sorry to size the, for a given size to predict the temperature, for a given size to predict the temperature, LMTD approach can also be used, I have to just take the differential element, we will come to that little later, why I am saying this because we should be telling that to the student, it will be iterative, it cannot be in one, in one shot I will not get, I have to do it iterative, but we need to emphasize this to student, they should not be under the impression that it is exclusively epsilon NTU approach only can be used to predict the outlet temperature, we should not be giving that impression for that, because textbooks do not tell all this, it is for us to figure it out, okay, there are various types of heat exchangers, one is counter fluid exchanger, parallel fluid exchanger, double piped exchanger, I am just going to take tube in tube heat exchanger, because I am sure all of us have built tube in tube heat exchanger in our labs, we have enough field, why do we go for tube in tube heat exchanger, what is the typical wattage of tube which I can build it tube in tube heat exchanger or which is what is used typically for single phase if I am asking, I am not getting into two phase at this point of time, we are handling only single phase heat exchanger, typically I will not go about 6 to 10 kilo watts, it is not that this is a standard rule, why because the size of my tube in tube, how do I build my tube in tube heat exchanger in lab, it cannot be one pass, right, it cannot be one pass, one pass means only one tube cannot be there, if I get the length when I calculate the size of the heat exchanger, if the length turns out to be 20 meters, can I build a heat exchanger of 20 meters, how long will be 20 meters, 20 into 3, 60 feet, 60 by 10, 6 storey building, can I lay down 6 storey building, it is not possible, what would I do, I will have to take bends and make multiple passes, it is there here multiple passes, you have to take through multiple passes, you can go through lot of multiple passes, of course that will increase the pressure drop, everything comes with a cost that will increase the pressure drop, in spite of that taking multiple passes, there is a limitation up to which you can hold this tube in tube heat exchanger, then you will go for that is as I said in the handbook or it is not that I said 6 to 10 kilo watt, it is just a gross number, it is not that we cannot build tube in tube heat exchanger, if I have more space I will, I can always go for tube in tube heat exchanger, but I can make my size of the heat exchanger smaller if I go for other configurations, may be shell and tube heat exchanger, so that is why we usually do not go for larger capacities, tube in tube heat exchanger, this is the point we need to emphasize to the students. Now, parallel flow, counter flow all of us know, this is T H, what is this temperature, T H I, this is T H O, T C I, T C O, so here also same thing, T H I, T H I, T H I, T H O, T C I, T C O, so now this is about compact heat exchanger just to say that the area density, that is the heat transfer area, surface area upon heat exchanger volume, these are the typical values for various heat exchangers, for a car radiator this beta is around 1000, whenever this beta is above 700, it is called as, we use the word compact heat exchanger through the steam, so compact heat exchanger whenever the value is above 700, it is typically called as compact heat exchanger, I have just put human lungs because that will give you anything human is going to be highly efficient, highly efficient because nature knows how to optimize things by itself, so it has optimized and the human lungs heat exchanger is having a beta of 20,000, quite highly dense, so that is about the area density and of course there are cross flow heat exchangers, so they can be mixed, unmixed, one shell and two tube pass, two shell, four tube pass, all configuration, shell and tube means I think all of us know, in the present day in Google images, that is what I do when I go to the class, Google images I take the pictures and go and show them the shell and tube heat exchangers, of course not for UG, but perhaps we can do that for UG also, that is what I used to do for heat exchangers, these are plate fin heat exchangers, these are plate fin heat exchangers, that is there are plates in between there are fins, so that is essentially the heat transfer is taking place, the mode of the heat transfer is not only conduction, but also sorry, not only convection, but also conduction because through those fins, through those fins, so now locating those fins, roughening those fins, all that is an issue, it is not out of the world, in today's world I mean people are talking about single phase heat exchangers, single phase nuclear reactors, what is that high temperature gas reactor or nuclear reactor, I do not collect the exact name, but there is no HTGR high temperature gas reactor, gas cooled reactor, so cooling is going to be done not in two phase mode, it is going to be only single phase and there they are contemplating of using plate fin heat exchangers and in this the plate is not going to be straight, but the plate is going to be wavy, why, what is the nature of the flow which would be typically in a plate fin heat exchanger, imagine you consider this, there are two plates, you put so many partitions, the heat partition, the flow has to go through each partition, the flow is someone said laminar, flow is laminar, the only way to augment the heat transfer there is to, we have studied this, to increase the swirl, so I have to generate swirl, that is why this partitioning wall is made as a wavy channel, because it is going to be wavy, so I am going to create swirl or the velocity in the other direction not turbulence, it is going to be laminar only, flow is continuing to be laminar, but I am going to create swirl, that is I am going to make one laminar to talk with the another laminar by creating the velocity in the other direction, so wavy type plate fin exchangers, lot of researchers is going there, lot of research is going there, in fact myself and professor Tulsherma have a student, we have learned from through Bark only, we have a student who is a scientist in DRC who is doing the project on that, so that is there are plenty of applications of heat exchangers and it just came to me I just told, fine. So now coming back to overall heat transfer coefficient, I am not going to spend too much time on application that is it, so now let us see the resistance, because of course we have gone through, I am going to breeze through this, professor has already told this in conduction itself, so we have the convective resistance on the inner side, conductive resistance of the wall and the convective resistance on the outer side and I have as he had told whenever there is a u there has to be an area, so I have u i a i or u naught a naught, it is a good practice to keep this u a together, so you do not have to worry about what is that you are handling, so u is meaningless unless area is specified, we need to mention that because usually people ask what is the overall heat transfer coefficient, it is like asking mangesh choudhary which mangesh, I can have hundreds of mangeshs, but hundreds of choudharies, but which choudhary mangesh, that is what makes mangesh choudhary, so we need to qualify overall heat transfer coefficient whether it is based on inlet area or outlet area, so that is what is this and of course for if I have fins I am going to put the fin efficiency both on the inner side and the outer side, these are the typical heat transfer coefficient, I do not think I need to spend time on this, all that you will realize through this is that for two phase flow heat exchangers you will have higher heat transfer coefficient, of course here we need to spend time on fouling because fouling is the student cannot realize for us for all of us fouling is pretty common because we have been biased because we have heard it so many times, so we know it very well fouling we have to spend time fouling increases resistance to fouling is the sedimentation or because of some chemical reaction some scales are being formed, so the conductive resistance which I was neglecting which was only because of the thickness is going to get worse because of these scales, so how do I get this fouling resistance I have put here RFI and RFO how do I get this, how are those standard values generated, but how does one do an experiment to get that, no not by using used tube it is not possible to get the used tube, you do some accelerated chemical treatment experiments in our own labs, in fact fouling is such an important thing in a power plant I always quote this example I learned this hard way when we had a BHEL we were myself professor around RPV professor Vedula and Kananayar we were involved earlier although we got declutched later on we were having discussions with BHEL Trichy, so when we were designing that supercritical boiler design when we were talks were there a person from a chemical engineer had come for those discussions his job he said that his team's job is to control the pH of the fluids throughout the plant why because if it does not control the pH or maintain acidity or basicity properly it is going to affect my scaling, so that is the importance in real life is scaling, so scaling is taken care in real life in any power plant, any power plant it can be coal base, nuclear base, any power plant scaling is going to be a nightmare if I do not take care of the efficiencies properly I remember one of the steam power plants in one of the handbooks I had read the after 5 years in Russia after 5 years when they did the energy budgeting the pumping power went up by 20 to 25 percent after 5 years why because scaling is negative effect because I have to if I have to keep the same flow rate which otherwise would have had lesser pressure drop because of scaling my pressure drops have gone up how many times I can open a meat exchanger and clean it it is not possible and many a times I cannot reach everywhere if it is a shell and tube it exchanger most of the times I cannot reach every nook and corner and do the descaling it is not possible even though I have done it may not be so efficient here we need to stop for students and emphasis that is why I have written chemical treatment plant pH and if scaling becomes a problem periodic cleaning it is not leaning periodic cleaning has to be done and downtime penalties are there so they do not like to shut down the plant so that is that is what we need to emphasis with the students and coming back to measurement they do scale that is fast rated experiments they they have their own mechanisms of whatever scaling would have occurred in 10 years I will do it in shortest possible time by chemically increasing the concentrations are doing something these are what are called as accelerated experiments okay of course I can get the tube but not always I can afford to get that information so that is how this RFI and RFO whatever we get in the standard table are okay so these are the typical RFIs only I keep spending and tell them that you see this is meter squared Kelvin per meter this per watt this implies that if thermal conductivity is 2.9 it is 0.3 mm thick if it is made of 9 I mean this number will not give me the feel this number only will give me the feel you see if this much is the fouling it can generate it is equivalent to 0.3 mm thickness of 9 stone 9 stone thermal conductivity is quite small 2.9 okay fine so there is a problem I am not going to spend time this is the problem I we just put this because we just want to show yeah through this problem what we try to show is that HI AI HA H0 A0 and initially I take a K here I have taken stainless steel where in which I have taken K of 15 this value has come with 15 although I have not shown this if I change this with copper my K will go up to 400 and the conductive resistance will become one order less here it is 9 into 10 to the power of minus 3 here it is going to be 0.01 into 10 to the power of minus 3 that is the reason why I tell that in refrigeration all condensers evaporators every one are made of copper tubes that is what I emphasize on there okay material selection is a biggest issue in heat exchanger design so why copper tube is so rigorously used is because of this this number calculation will tell me otherwise the resistance is thrown now this resistance is pretty small compared to these 2 okay another thing I think I am going to digress little bit here there is so much we can do here with this this little calculation I can calculate I want to spend time 1 more minute or 5 more minutes on this because we have time I can do measurement of heat transfer coefficient with this equation let us say I make conductive resistance 0 that is it is very less I take a thinness cosplay now I want to measure inner side heat transfer coefficient can I do in this heat exchanger tube and tube only let it be parallel counter it does not matter I have 3 resistances HI based HO based and K based conductive conductive resistance I have made it as thin as possible so it is gone so it is now between HI and HO how can I make this I want to measure the heat transfer coefficient on the inner side okay that is one option basically what he is saying is H0 I am going to increase it incessantly high steam it is little difficult to get steam I would say if I am to measure the heat transfer coefficient on the inner side with air as the flow medium let us say I can use outside what is the other fluid you can easily think of which you can get it in the lab water keep your mass flow rates very high so then the Reynolds numbers are high HOs will be over the order of thousands and HI is of the order of 20s and 30s at the most 100 so then what will happen my UI AI is going to be equal to how do I get Q dot now I guess you are with me now I can get my HI because Q dot I know so this is another way of measuring heat transfer coefficient which you can perhaps try in your own heat exchanger I do not know because both sides usually we use water water but we can build one with water and air and people use this why I am quoting this example because if you want to go back home and do a research you want to try twisted tape or you want to come up with your own configuration new configuration put it on the inner side put the air make the air flow through it and in the outer annulus you make the water flow or if you are handling laminar heat transfer coefficient perhaps you can do this make the water on the inner side make it laminar on the outer side even though it is water in all the heat exchangers which you have to go back home and try this experiment inner side you keep the flow rates very less such that the flow rate is laminar outer side you keep the flow rate so high as much as your pump allows you do not think twice check the mass flow rates check H O A naught make sure that it is very small even if it is not small if you can quantify can you quantify outer heat transfer coefficient if you know the mass flow rates yes or no yes because I know the Dittus-Bolter correlation I can apply Dittus-Bolter correlation I know that it is turbulent make sure that it is turbulent and apply Dittus-Bolter correlation you get H O now you should be getting in the same heat exchanger check it out then now the question is now you will get into trouble what is the Nusselt number you will get some representative Nusselt number it will be neither 3.66 nor 4.36 why because couple of issues it is going through developing region to fully developed because I am going to get one average number one average number I am going to get you will get somewhere between 3. sorry somewhere little higher than 3.66 it is going to be in heat exchanger typical boundary condition nearest boundary condition what is that you would think of constant heat watch or constant wall temperature nearer to constant wall temperature nearer to constant wall temperature not truly constant but it would not Nusselt numbers you cannot expect around 4.36 they have to be 3.66 but because you are traversing through developing region the Nusselt numbers may go up but please go back and try okay why I am saying this because this little equation again yeah why why why imagine let us imagine how can it be constant heat flux how can it be constant heat flux yes even in constant wall temperature case same thing it is we were worried about the heat transfer from fluid to plate does not mean that see what is happening from here to here if I take on the outer wall if I said cold wall side I am going to keep the flow rate very high if very high mass flow rate is there means what would be the temperature difference between m dot c in and m dot c out so that my line of thought is not over you have to be with me to come to cover you so if the mass flow rate is very high and the temperature gradient is very less the temperature difference is what on the outer side very small so it is that is the reason why we are saying in fact when we do the experiment we should take care that my mass flow rates are so high that my temperature differences are negligibly small but that depends on my pump capacity if it is going to be 0.2 hp only if you can replace replacing a pump I do not think in the present day is not a big headache change it to 0.5 hp you will get higher mass flow rate okay so what I am trying to why I am coming up with ideas is I am working around your constraints whatever setups you have what all experiments you can do with your own setups that is what I am trying to do okay fine so then coming back okay now let us come back to traditional LMTDF approach and epsilon NTU approach so first let us take up LMTD approach and typical here before analyzing we make all assumptions this is where we have to spend time steady flow will it will any heat exchanger work under steady flow typically typically in a power plant let us say how many days or how many hours or how many minutes a typical power plant will take to reach steady state couple of hours couple of hours it is going to be so point is and loads are also going to vary it is not going to work work only under one load so my heat exchanger normally is not going to work and is it will take enormous time to reach steady state why do I say this why do I say that heat exchanger is going to take enormous time to reach steady state why do I say this I you have to tell me from transient conduction fundamental principles thermal inertia rho v c p of my heat exchanger heat exchangers are as big as this room or building for a power plant so rho v c p of this building how much it would be building means building size heat exchanger that much fluid it is going to be very very large so this assumption of steady flow is in real life is not right this we need to impress however for the sake of simplicity we are taking it as steady flow another kinetic energy and potential energy changes are neglected is it true is it true in power plant one tube is sitting in third story building another tube is sitting in first story at the ground floor there is a potential head but I am neglecting that and it is going through all sorts of bends it is going through contractions expansion because it has to go through all sorts of connections so there is going to be velocity change there is going to be kinetic energy associated with it in any derivation for that matter assumptions is the place where we need to spend more time than the derivation itself okay all the more important in case of heat exchangers next thermo physical properties constant over the length is it true perhaps it is true if I am handling air but in water or liquids properties are going to be going here so but nevertheless I am going to go ahead and make life simple and say that thermo physical properties are constant but once you do this after doing this you can ask them to change the analysis for varying properties if I take the varying properties what will happen what is that will change my hi and ho I have to consider the variable properties if you closely look when you go back home in the notes for variable properties in the correlations there is a term called mu b by mu wall to the power of 23 in all the correlations that essentially takes care of the variation of the properties so point is thermo physical properties are constant is assumption perhaps in a plate finite exchanger which is taking air as the fluid if it is air as the fluid it is not an out of the world assumption okay no heat loss to the surroundings you have done the experiment so much discussion on q cold plus q hot by 2 we took okay so that is not right because point is there is going to be heat loss there is bound to be heat loss it has to talk to atmosphere I am not outside the world I am inside this world and heat transfer coefficient is constant over the length is this right perhaps not a bad assumption in heat exchangers I would say it is not a such a serious assumption why because heat exchangers are quite lengthy quite lengthy initial heat transfer coefficients are going to be high is this assumption going to be affecting on my heat load will it increase my heat load or decrease my heat load if I designed a heat exchanger let us say my heat exchanger is short where in which half of the length is fully partially developed sorry developing and half is fully developed but I will go ahead and make the design of the heat exchanger and design it for a given heat capacity or I will fix my heat exchanger size and design it and get one load but actually in real that is the design load but real life load will be more or less than this will be more you are telling the same thing but you said what heat transfer coefficients I have taken lower no than the actual so that means I have taken a conservative estimate of the h so my load has to go up that is what you meant in the mind but most of the times that is what my teacher used to say most of the times you will tell opposite than what you thought that is why he used to tell me whenever your teacher asks you a question stop a while stop a while do not answer immediately even if a student ask you a question you should not respond to him the way I respond very fast you should not I am very impulsive it should not be like that you take a while ask him the same question to rephrase again you also rephrase it so that everyone else understand then you respond by that time you would have mentated that do not answer it impulsively mostly when we answer impulsively we are wrong we are exactly telling opposite of what we intended to tell one assumption pressure drop along the length of the heat exchanger what should it be how how will it affect the design here in this design I am not bothered about pumping power I do not care which size pump I am putting I just all that I say that these are the mass flow rate how I get it I do not care it later on eventually I will have to worry about that in this analysis at this point of time what is trying to say is that we are not worried about the pumping so now I think we do the energy balances MCC MCC PC I do the energy balance and I call this as CCC H and I think I can skip this this is the general thing which we draw okay I have taken this from chengal I do the energy balance I do not intend to do this derivation I do not intend to do this derivation because you all would have done n number of times so you do the energy balance basically and all that I need to tell is why is this plus and why is this minus that is all that is all one is gaining one is losing so that is why these things only we have to emphasize more with our students okay so that then they will get trained even when they start studying a textbook on their own what to look for and what not to look for okay so this is DTC DH and then we have an alternate method I equate that I get the temperature difference and I tell that is delta T LMTD this also we have defined already in convective heat transfer this is the parallel flow heat exchanger so we get for parallel flow this one and counter flow this one so similar I usually give counter flow heat exchanger as a exercise I solve it for parallel flow and give it for counter flow and we all know that counter flow LMTD is greater than that of parallel flow LMTD counter flow heat exchanger derivation how many of you have done this please go others please go ahead and try it okay it will not come as simple as this that is why I have put the derivation here in case if you get stuck I have not skipped it I have not skipped it I have given the derivation okay and please go ahead and try and in fact we upload this notes completely the way we are uploading for model in fact the same notes what we are teaching you is the one which we are using for our UG class yeah it is there what I am trying to say is you can share all this with your students my one of my close friend who is in faculty in IIT Madras used to tell this is a fight of knowledge the tools have to be common in war one of the rule is what both the both the guys should have the same weapon so why I keep telling why I take this example because what I am reading to understand something has to be told to my student he can also go back and read maybe we will understand more than what I have understood and he will come back and question me in that discussion I will also learn something that is the reason there is there is there should be that is why we are all worried about open source we should be sharing all the information that is one thing knowledge is one thing which will multiply by sharing okay so our motto in our IIT is Gnanam Paramam Deayam so we need to share only when we share we will learn more why I am taking so many examples because whatever most of the times when I was studying my teacher will not tell where is he taking it from I have to break my head after that course is over somewhere I will realize are you are yes either have had I read that of immediately after he had taught me it would have been so much easier for me to understand that is the reason why I am emphasizing so much don't be secretive about your information what you are assimilating to teach just give him he will make you understand much more than what you have understood believe me our students are much smarter than us I think you all will agree with us no no two ways about it they are all smarter than us they are all smarter than us with that assumption if I start if with that assumption if I start my life is that much easier for that much easier okay anyway I got diagnosed fine so there are lots of problems you can solve that okay this is a standard I think we all give this what will happen I think we will not harp on this you can apply a law special rule and show that this so I think all of us this is a stock question why I don't want to spend time on this and condenser and boiler also professor has told why is LMTD counter flow less than why is LMTD of counter flow higher than the LMTD of parallel for that I just want to put the temperature profile so that that may aid in the thought process aid the thought yes here more or less the temperature gradient is reasonably that's that's that that reasoning that was a very valid point that's what we need to emphasis I will go to I think now it's time to shift to our gears to epsilon NTU and of course there are only one point I would tell before going to epsilon NTU I saw in your data handbook also code and Ram data handbook also what I will do is that textbook I will purchase that code and Ram's handbook so that I can modulate accordingly the notes let us see because most of the things are there in that it's nice actually it's really nice so here we give some correction factors if it is if it is a multi pass and cross flow heat exchanger there are some charts you know these charts do you teach these charts yes so what are these F what is this F actually what is the physical significance of F what is its value going to vary between always in all of these charts it's anywhere between 0 to 1 what does that physically mean I will just tell physical meaning and tell where is this coming from how are these charts generated for that matter experimentally obtained no they are not experimentally obtained analytical solutions ok in fact in heat exchangers course we teach them how to derive that ok do not give the impression that they are experimentally obtained any experimental data cannot be looking so nice all of us agree with that we had enough problems with little little experiment ok so these are all analytically derived when I say analytically derived there are again inbuilt assumptions these results are valid to the extent of the applicability of those assumptions so this is not Bible or Bhagavad Gita or Quran ok this is again valid to the assumptions ok to the extent of the assumptions ok so that that point we need to emphasize and another point I thought ha F is between 0 to 1 what does that mean I am applying it to what you see UAF delta T LMTD for what is the reference I am taking counter flow why that is the best possible heat exchanger any other heat exchanger I build it is going to be not better than counter flow heat exchanger that is why my F is going to be between 0 to 1 this two points we need to emphasize before we blindly apply this chart charts all of us can apply know this do not know that you get that you put this you are going to get the heat transfer coefficients why why you made one statement why are any other heat exchangers poorer in performance than the corresponding counter flow heat exchanger why should it be why counter flow is the best that is that is the ideal thing that is the question no no no what did we say why did we explain parallel and counter flow counter flow is better than parallel on what grounds we told the temperature gradient as my fluid is traversing throughout the heat exchanger the delta T's have to be reasonably constant that cannot be achieved in any other configuration you go back and think in shell and tube heat exchanger cross flow heat exchanger plate fin heat exchanger you cannot achieve that is the reason it is delta T LMTD counter flow is taken as the reference ok these two points we need to emphasize when we tell our students doing calculations they will do it because once we do once we tell them how to apply this relation they will do it so I am not going to tell you how to apply this chart P is known R is known I am not going to tell you all of that ok so with that I guess this is for cross flow there are n number of problems at the end these are all taken from chungal actually I will stop and I have just put the procedure I have just taken the recap I am not going to do that again ok so you can take a recap before going and another thing I want to tell before starting the second you have started today first class you have taken when you go to the next class what do you do with the first thing last class we need to discuss and there our power point helps you cannot again summary is using the board so if you can offer to have power point you flash the power point spend 5 to 10 minutes first because we are sure no student would have read and come that can be taken for sure ok even if someone has read it is good that he will understand it much better and maybe some doubt will crop up in his mind and he will ask he will definitely ask and encourage questions I have been always asking what are the questions what are the questions to the best of my our possibility we have tried to ask answer the questions not that we can answer all the questions but we need to inculcate the habit of asking questions so that we are thinking ok ok let us say excel and to be the exchange how does it consist of there are multiple tubes ok and through the shell it is coming and getting out through the shell and there are baffles ok and it is not going to go through H0 I cannot compute ok I have to go through serpentine passages so there is lot of empiricity in that and definitely because it is not the heat exchange is not as proper as it would have occurred in counter flow it is sorry tube in tube counter flow heat exchange oh no we cannot call any of other heat exchangers as parallel and counter. How many of you are with me when I say shell and tube exchange all of you can imagine shell and tube so there is in cross flow heat in shell and tube heat exchanger is there any counter flow all the time no sometimes my fluid is going up that is why it is somewhere between very rightly told parallel cross counter so but I have taken one case parallel one case counter so any other case has to be in between these two that is how I think ok.