00:00:14.059 --> 00:00:21.310 Hello everyone we were discussing ah finned tube heat exchangers basically we were discussing 00:00:21.310 --> 00:00:28.509 different augmentations techniques and then compact heat exchangers which use augmentation 00:00:28.509 --> 00:00:35.000 ah any suitable augmentation technique to have high rate of heat transfer within a small 00:00:35.000 --> 00:00:44.180 volume. And in that ah fins are extended surfaces are ah techniques for augmenting or enhancing 00:00:44.180 --> 00:00:52.140 the rate of heat transfer and one of the very ah important class of heat exchangers are 00:00:52.140 --> 00:00:57.239 finned tube heat exchangers. So, today we like to see finned tube heat 00:00:57.239 --> 00:01:02.699 exchangers already we have some acquaintance with finned tube heat exchanger, but today 00:01:02.699 --> 00:01:11.050 we will hm ah stress upon some analysis which will be ah the primary step of designing a 00:01:11.050 --> 00:01:20.770 finned tube heat exchanger. So, if we go to the next slide ah fined tube 00:01:20.770 --> 00:01:28.429 heat exchangers are basically cross flow heat exchangers. In most of the cases ah it is 00:01:28.429 --> 00:01:37.789 a cross flow heat exchanger and it is for ah gas liquid heat exchange process. So, liquid 00:01:37.789 --> 00:01:44.851 or liquid vapour mixture will be passing through the tube side very rarely there could be some 00:01:44.851 --> 00:01:52.960 design where it is a gas to gas ah heat exchanger and gas is passing a purely ah hm ah purely 00:01:52.960 --> 00:02:00.229 gases phase or vapour phase without any liquid ah maybe ah allowed to pass through the tube 00:02:00.229 --> 00:02:04.229 side. But that applications are almost rare I mean 00:02:04.229 --> 00:02:10.399 very rare and almost nonexistent. So, we will not consider those kind of application we 00:02:10.399 --> 00:02:16.790 are considering the most common application of finned tube heat exchanger. Where liquid 00:02:16.790 --> 00:02:25.480 will be passing through the tube side and ah outside of the tube will be finned and 00:02:25.480 --> 00:02:34.340 gas will be passing across the finned outside surface of the tube , different designs of 00:02:34.340 --> 00:02:43.580 fins different arrangement of tubes in different design of tubes are possible. So, this some 00:02:43.580 --> 00:02:51.040 of these things have already been discussed. Now the fins they can have different heights 00:02:51.040 --> 00:02:59.810 what we call ah the fin length ah most commonly in case of longitudinal fin incase of radial 00:02:59.810 --> 00:03:06.629 fin or in case of circumferential fin we call it sometimes we call it the height of the 00:03:06.629 --> 00:03:14.430 fin ok. So, because we are considering tubes whether they are ah circular tube or non circular 00:03:14.430 --> 00:03:20.110 tube the fins on this tubes will be mostly circumferential tube. 00:03:20.110 --> 00:03:28.969 So, circumferential tube we do not call the I mean do it we do not ah ah I mean ah call 00:03:28.969 --> 00:03:35.980 it or denote it as the length of the fin, but we call the height of the fin. So, there 00:03:35.980 --> 00:03:44.750 are two classification low fin tubes low fin tubes here the fin heights are small. So, 00:03:44.750 --> 00:03:55.780 if the outer diameter of the ah ah fin sorry outer diameter of the tube is D r is denoted 00:03:55.780 --> 00:04:04.950 by capital D subscript r capital D subscript r and L is the ah length of the fin or height 00:04:04.950 --> 00:04:11.719 of the fin then for low fin tube the range has been given and then for high fin tube 00:04:11.719 --> 00:04:18.530 also the range has been given. So, what we get from there here that low fins 00:04:18.530 --> 00:04:26.490 are of smaller height. So, if they are of smaller height most of the cases they are 00:04:26.490 --> 00:04:32.620 made integral with the fin sorry integral with the tube what does it mean that means, 00:04:32.620 --> 00:04:40.030 the tube material is cut to produce this fin. So, basically one started ones one can start 00:04:40.030 --> 00:04:48.170 with a tube of higher thickness then make small fins on the tube outside surface of 00:04:48.170 --> 00:04:57.139 the tube by machining . So, this is ah ah how the low ah fin tubes are produced high 00:04:57.139 --> 00:05:02.590 fin tubes on the other hand they have got higher length of the tube ah higher length 00:05:02.590 --> 00:05:08.259 of the fins and these fins are separately mounted they are made of separate material, 00:05:08.259 --> 00:05:14.460 they are separately manufactured and then ultimately they are mounted over the outer 00:05:14.460 --> 00:05:19.250 surface of the tube. So, this is the difference between low fin 00:05:19.250 --> 00:05:26.160 tube basically these are integral fin tube fin and the tube are made of same material 00:05:26.160 --> 00:05:33.380 by machining these fins are produced. And high fin tubes this this this fins are separately 00:05:33.380 --> 00:05:41.740 manufactured and then fixed on the outer surface of the tube . Low fin tubes are used in many 00:05:41.740 --> 00:05:47.380 cases ah like condensation etcetera where outside the tube you have to have condensation 00:05:47.380 --> 00:05:52.460 face change heat transfer. So, more than increasing the surface area 00:05:52.460 --> 00:06:01.410 these fins a do ah or rather ah perform some some other duties like they can enhance the 00:06:01.410 --> 00:06:09.410 rate of heat transfer in phase change heat transfer they can take some unique role, then 00:06:09.410 --> 00:06:16.901 low fins are generally integral fin tube integral fins that is what I have mentioned . Now let 00:06:16.901 --> 00:06:22.520 us have some idea regarding the fin tube heat exchanger we are slowly developing this ah 00:06:22.520 --> 00:06:26.479 topic. So, many times I have referred fin tube heat 00:06:26.479 --> 00:06:39.629 exchanger, but even then let me take another ah ah another another opportunity to do give 00:06:39.629 --> 00:06:47.060 some idea regarding fin tube heat exchanger. So, it is like this that if it is a gas liquid 00:06:47.060 --> 00:06:54.419 heat exchanger then it would be good to have the liquid in the tube side so tubular construction 00:06:54.419 --> 00:07:02.400 will be there. So, let us say we have got tubular construction 00:07:02.400 --> 00:07:16.729 this is one tube this is another tube this is the third tube all in a row and then on 00:07:16.729 --> 00:07:35.919 there could be other tubes like this ok. You can understand that there are number of tubes 00:07:35.919 --> 00:07:42.409 like this ah if we see the cross sectional view. So, the cross sectional view will be 00:07:42.409 --> 00:07:49.930 something like this ok and through the tube the fluid is passing. So that means, the fluid 00:07:49.930 --> 00:07:55.889 is passing in this direction in this directions like this and across the tube, so this is 00:07:55.889 --> 00:08:05.620 your liquid some liquid and then across the tube tube then your gas is passing. 00:08:05.620 --> 00:08:13.939 So, this is kind of a ah tube heat exchanger or tubular heat exchanger where only we have 00:08:13.939 --> 00:08:22.610 used bare tubes this this is the fast development of tube tubular heat exchanger for gas liquid 00:08:22.610 --> 00:08:30.550 application and where we have got liquid in the tube side and gas outside the tube and 00:08:30.550 --> 00:08:35.350 in a cross flow arrangement. Now, many cases this kind of the heat exchangers 00:08:35.350 --> 00:08:41.510 are used because of their low cost and because as they do not have any fins etcetera they 00:08:41.510 --> 00:08:47.579 will give very less amount of pressure drop at the same time the tubes can be clean easily. 00:08:47.579 --> 00:08:53.870 So, where we have to handle that gas etcetera maintenance is a problem this kind of heat 00:08:53.870 --> 00:08:59.640 exchangers are to be used. Now, the next thing what we can do for making 00:08:59.640 --> 00:09:04.700 the heat exchanger compact and having higher effectiveness of the heat exchanger we can 00:09:04.700 --> 00:09:13.190 provide some sort of a fin to all the tubes. So, there will be some gap between the fins 00:09:13.190 --> 00:09:19.380 otherwise air cannot pass, so something like this we will provide some gap will be there 00:09:19.380 --> 00:09:27.040 we will show you a good figure later on. So, basically on these this is a tube and 00:09:27.040 --> 00:09:35.589 on this tube we are at regular interval we are providing fins. So, this is kind of one 00:09:35.589 --> 00:09:44.420 fin so this is another fin so at regular interval we are providing fin on the tube. So, this 00:09:44.420 --> 00:09:51.779 is then our heat exchanger becomes your fin tube heat exchanger. So, what are the challenges 00:09:51.779 --> 00:10:00.589 in these ah fin tube heat exchanger analysis. So, any heat exchanger ah designed ah we have 00:10:00.589 --> 00:10:16.850 this basic ah equation that is Q dot is equal to U A into delta T effective or mean. So, 00:10:16.850 --> 00:10:22.050 here in case of this fin tube heat exchanger whatever may be the fin arrangement whatever 00:10:22.050 --> 00:10:28.920 may be the tube arrangement we have to have this kind of basic equation. Suppose we want 00:10:28.920 --> 00:10:36.240 to find out the ah overall sorry we want to find out the amount of heat transfer then 00:10:36.240 --> 00:10:42.579 we have to use this kind of a formula. So, first we have to determine the delta T 00:10:42.579 --> 00:10:49.540 effective or delta T mean depending on the arrangement of the two fluids whether it is 00:10:49.540 --> 00:10:56.500 counter flow, whether it is cross flow, whether it could be cross flow only, but whether it 00:10:56.500 --> 00:11:02.930 is cross counter flow or ah a parallel counter flow kind of a arrangement or whether it is 00:11:02.930 --> 00:11:08.730 a complex kind of arrangement depending on that we have to have delta T effective. 00:11:08.730 --> 00:11:14.079 So, once we have delta T effective from the arrangement which I am not going to discuss 00:11:14.079 --> 00:11:24.200 ah ah in this ah particular section we have to also determine U and A. That means, overall 00:11:24.200 --> 00:11:31.630 heat transfer coefficient and the area we have to heat transfer area we have to calculate 00:11:31.630 --> 00:11:40.220 and you know that U and A are not independent . So, we have to ah the the relationship etcetera 00:11:40.220 --> 00:11:50.339 have been told earlier, so ah here basically we will ah see how to determine U and how 00:11:50.339 --> 00:11:58.510 to determine A. Now, A ah particularly we have to have some 00:11:58.510 --> 00:12:14.269 idea regarding the A on the fin side, so basically ah A fin side . So, these we will discuss 00:12:14.269 --> 00:12:21.910 how to determine a on the fin side and we will also discuss how to determine the overall 00:12:21.910 --> 00:12:26.860 heat transfer coefficient or T. Now, overall heat transfer coefficient or 00:12:26.860 --> 00:12:34.010 U that will depend on basically if we neglect fouling then it will depend on three different 00:12:34.010 --> 00:12:41.630 resistances inside the tube fluid is flowing. So, there will be convictive ah heat transfer 00:12:41.630 --> 00:12:48.540 inside the tube that resistance will come then the tube material that is a ah solid 00:12:48.540 --> 00:12:54.870 barrier a on the path of the heat transfer. So, conduction kind of resistance will come 00:12:54.870 --> 00:13:02.910 and then on the fin side air is passing, so another resistance convective resistance for 00:13:02.910 --> 00:13:08.800 air will come. Now, the third thing third ah resistance is 00:13:08.800 --> 00:13:16.240 more crucial because the fin passages are complex and we will see that we have to use 00:13:16.240 --> 00:13:22.221 different kind of correlations etcetera for that. So, I am giving the principle or the 00:13:22.221 --> 00:13:30.839 philosophy how this design can be done inside the tube the design is not that much difficult. 00:13:30.839 --> 00:13:36.839 Because whether we take circular tube or non circular tube most of the cases we assume 00:13:36.839 --> 00:13:43.730 the flow to be fully developed why because the tube length is so large that the developing 00:13:43.730 --> 00:13:48.230 region is small compare to the fully developed region. 00:13:48.230 --> 00:13:54.399 So, flow will be in most of the cases almost all the cases it will be in the turbulent 00:13:54.399 --> 00:14:00.220 region. So, details kind of correlation will give us the heat transfer and some sort of 00:14:00.220 --> 00:14:06.680 a well known relationship many available relationships are there we can calculate the pressure drop 00:14:06.680 --> 00:14:13.089 for the liquid side. Gas side it is not that easy gas side due 00:14:13.089 --> 00:14:20.339 to the complex geometry it is not not showed easy. And our emphasis of this lecture or 00:14:20.339 --> 00:14:29.130 the coming lecture may be will be on the prediction of gas side or fin side prediction of heat 00:14:29.130 --> 00:14:36.750 transfer if the fin side and prediction operation of the fin side so this will be our emphasis. 00:14:36.750 --> 00:14:47.430 So, with these let me proceed but ah let me tell you ah one thing ah I guess want to share 00:14:47.430 --> 00:14:54.740 with you that you see that ah though time to time I have shown that for a circular tube 00:14:54.740 --> 00:15:02.899 we can have we can have different kind of fins. 00:15:02.899 --> 00:15:11.759 Let us say this is the circular tube we can have a fin like this in this case of course, 00:15:11.759 --> 00:15:21.540 we do not use a single fin number of fin just like a star shape this one is used. So, here 00:15:21.540 --> 00:15:31.570 we can have another fin on this side we can have another fin like 00:15:31.570 --> 00:15:52.290 this and if we see the cross section, so the it will look like this . So, these are longitudinal 00:15:52.290 --> 00:16:03.940 fins provided over a circular tube ok. So, this is one kind of design one can have 00:16:03.940 --> 00:16:11.980 another design one can have that this is a circular tube on the circular tube you are 00:16:11.980 --> 00:16:18.329 having some sort of a disk. So, this is a circular tube and on the circular tube we 00:16:18.329 --> 00:16:26.199 are having this is your fin, so this is disk fin or circumferential fin or radial fin annular 00:16:26.199 --> 00:16:33.149 fin different names are given . This is one kind of a design, but even in 00:16:33.149 --> 00:16:42.829 these design one can have ah the different variation and ah then one can have the continues 00:16:42.829 --> 00:16:51.410 plate fin which is p s by a number of a circular tube. So, let us say this is continues plate 00:16:51.410 --> 00:16:58.060 fin, so mainly there are this three variation, but there could be more variation also for 00:16:58.060 --> 00:17:04.130 circular tube. So, these are kind of different fins fin arrangement what we can have for 00:17:04.130 --> 00:17:10.209 circular tube and all these fins or rather all these arrangement can be used in fin tube 00:17:10.209 --> 00:17:20.870 heat exchanger good let us ah let us go to the next slide huh. 00:17:20.870 --> 00:17:32.840 So, here the geometrical characteristics of circular fin ah and ah circular fin of uniform 00:17:32.840 --> 00:17:37.520 thickness, so that is why it is called rectangular cross section. So, this is this is more commonly 00:17:37.520 --> 00:17:41.500 used and let us see what are the geometrical characteristics 00:17:41.500 --> 00:17:48.800 So, let us say the ah ah the outer diameter of the tube is D r basically it is the root 00:17:48.800 --> 00:17:54.800 diameter of the fin that is why subscript r has been used. And then outer diameter of 00:17:54.800 --> 00:18:01.070 the fin that is D t that is the tip diameter of the fin that is why the subscript t has 00:18:01.070 --> 00:18:09.750 been used W is the width of the fin and S is the inter fin distance. So, similar thing 00:18:09.750 --> 00:18:16.660 will be repeated number of time, so let us say we are considering L length of that tube 00:18:16.660 --> 00:18:22.330 the length of the tube which we are considering that is L and in that L length there will 00:18:22.330 --> 00:18:29.910 be number of ah fins on the outer surface of the tube. 00:18:29.910 --> 00:18:38.310 If we go to the next figure so this is what most of the cases we use if we use individual 00:18:38.310 --> 00:18:45.380 fins then this is in line array. So, in line array you can see that in the in line array 00:18:45.380 --> 00:18:58.450 ah we have got we have got ah two geometrical ah figures sorry geometrical parameter P1 00:18:58.450 --> 00:19:06.420 and P 2 P 1 is the one pitch and P 2 is another pitch 00:19:06.420 --> 00:19:14.580 So, basically the array is defined if it is in line array, so the array is defined by 00:19:14.580 --> 00:19:22.671 two different pitches P 1 and P 2 and in this figure what we can ah understand that ah if 00:19:22.671 --> 00:19:43.770 I give this is basically your D r and this is your D t group diameter and tip diameter. 00:19:43.770 --> 00:19:50.150 Air is flowing through this and air is flowing through the air is flowing through the ah 00:19:50.150 --> 00:19:59.200 ah arrow direction and liquid is flowing normal to the diagram, so this is how is our arrangement. 00:19:59.200 --> 00:20:15.380 Next arrangement if we go next arrangement if we go then next arrangement if we go then 00:20:15.380 --> 00:20:24.810 what we find that ah ah we have got staggered array. So, staggered array ah then for defining 00:20:24.810 --> 00:20:33.520 staggered array we need three dimensions three different pitches P 1 P 2 and P 3. 00:20:33.520 --> 00:20:41.290 So, this three pitches are to be given for defining the array with these the fin tube 00:20:41.290 --> 00:20:48.010 ah heat exchanger geometry these are the geometrical parameter. External diameter of the tube at 00:20:48.010 --> 00:20:55.210 the fin root that is D r outer diameter of the fin Dt height of the fin D f minus D r 00:20:55.210 --> 00:21:01.620 by 2 that is equal to L that is fin length also we can call it width of the fin W space 00:21:01.620 --> 00:21:09.360 between fins that is S length of the tube Lt and ah then number of tubes in a row. 00:21:09.360 --> 00:21:18.510 So, they basically tubes we can think of that they are ah they are hm arranged in some sort 00:21:18.510 --> 00:21:27.030 of ah cubical matrix. So, number of tubes in a row that is n t and number of rows that 00:21:27.030 --> 00:21:34.310 is n r then the total number of tubes will be n t into n r that is capital N. Pitch of 00:21:34.310 --> 00:21:40.290 the tubes in the plane perpendicular to the flow that is P1 pitch of the tubes in the 00:21:40.290 --> 00:21:47.530 direction of flow that is P2 and ah pitch of the tubes on the diagonal plane in staggered 00:21:47.530 --> 00:21:51.050 array only in case of staggered array this will come, so this is P3. 00:21:51.050 --> 00:22:00.020 So, with all these things we can define the geometry of a fin tube heat exchanger and 00:22:00.020 --> 00:22:06.390 another ah dimension should come ah only we are interested here for outside heat transfer, 00:22:06.390 --> 00:22:11.670 so that us why that dimension has not come. So, that is the inner diameter of the tubes 00:22:11.670 --> 00:22:17.170 that should also come to define the geometry completely. So, now you can understand that 00:22:17.170 --> 00:22:22.760 how many geometrical parameters are coming in a fin tube heat exchanger, out of all these 00:22:22.760 --> 00:22:32.390 parameters ah this P3 will not be relevant for ah in line array of use otherwise all 00:22:32.390 --> 00:22:39.650 the parameters are common for any ah kind of geometry of the heat exchanger. 00:22:39.650 --> 00:22:51.660 So, then we we have to make certain calculation ah the outer surface of the tube including 00:22:51.660 --> 00:23:01.000 the fin surface is taking part in heat transfer, basically the fluid stream that is the air 00:23:01.000 --> 00:23:09.490 that is making contact with the outer surface of the tubes. So, total surface area of N 00:23:09.490 --> 00:23:19.630 fin tube of length L is given by this formula ah there is some sort of ah ah inner state 00:23:19.630 --> 00:23:26.401 ah of this formula that is given below, but what I will request you that you should try 00:23:26.401 --> 00:23:31.790 to derived this formula. So, the total area that will be the fin area 00:23:31.790 --> 00:23:43.160 plus un finned tube area, so A f is the fin area A w is the wall area that is un finned 00:23:43.160 --> 00:23:50.820 tube area. So, where the surface area of the fin A f that is dependent on the total number 00:23:50.820 --> 00:24:04.520 of tubes that is capital N ah length of the tube Lt and then this is your this is your 00:24:04.520 --> 00:24:14.710 ah the fin surface ah contribution ah there is a small ah typographical mistake. So, these 00:24:14.710 --> 00:24:20.610 D f this should be this subscript should be Dt this is your tip diameter it should not 00:24:20.610 --> 00:24:27.970 be f it should be t, please ah make a correction ah or note the correction that here it should 00:24:27.970 --> 00:24:35.740 not be D f it should be Dt here also it should be Dt here also it should be Dt and then at 00:24:35.740 --> 00:24:42.700 the tip there is some area should Dt into WS and W already has been explained. 00:24:42.700 --> 00:24:49.630 So, this is the fin area, so basically if I have to explain ah I can explain it like 00:24:49.630 --> 00:25:06.470 this you see the fin is the fin is like this on the surface of the tube. And so it has 00:25:06.470 --> 00:25:15.340 got one surface over here another surface over here and then there is one tip surface 00:25:15.340 --> 00:25:27.030 over here, so ah that is how this thing has come ok. So, ah ah this is how we have calculated 00:25:27.030 --> 00:25:35.740 it and I request you all of you to ah do this exercise, then the surface area of the tubes 00:25:35.740 --> 00:25:43.090 between the fins that is given by this particular formula and then the total tube surface area 00:25:43.090 --> 00:25:51.380 with fins removed. Suppose there is no fin then we have got this is the ah area of the 00:25:51.380 --> 00:26:03.400 bare tube if there is no fins. Let me do one thing let me go back to the some previous 00:26:03.400 --> 00:26:10.550 slide to make things to I will try to make things little bit clear. 00:26:10.550 --> 00:26:21.940 So, here if we see here if we see, so what we what we find that this is the bare area 00:26:21.940 --> 00:26:28.730 of the tube from where heat transfer is taking place and this is the area of the sorry this 00:26:28.730 --> 00:26:38.520 is the area of the this is the bare area from where heat transfer is taking place, this 00:26:38.520 --> 00:26:43.860 is the area of the fin from where heat transfer is taking place this is the area of the fin 00:26:43.860 --> 00:26:50.620 from where heat transfer is taking place. So, we have to calculate all these areas to 00:26:50.620 --> 00:27:16.490 get the heat transfer ok. So, now let us go back all right with these ah with these with 00:27:16.490 --> 00:27:26.800 these we have got the we have got the area of the fin area of the bare tube area of the 00:27:26.800 --> 00:27:33.420 ah tube ah which is not covered by the fin. So, this basic areas we have got I would request 00:27:33.420 --> 00:27:40.610 you to ah ah get these do the calculation yourself and get these expression check this 00:27:40.610 --> 00:27:47.940 expression. Then minimum flow area for most cross flow heat exchanger is in the plane 00:27:47.940 --> 00:27:56.710 perpendicular to the flow direction is given by this particular formula ok n t L t all 00:27:56.710 --> 00:28:03.190 this things are been told earlier. That P 1 1 of the pitch this is pitch normal to the 00:28:03.190 --> 00:28:12.130 direction of flow this is D r root diameter of the fin, W that is the width of the fin 00:28:12.130 --> 00:28:18.730 length that is the length of the fin and all these things this is S the gap between two 00:28:18.730 --> 00:28:22.660 So, this is how we will get the minimum flow 00:28:22.660 --> 00:28:31.860 area, so by these what we have done we have got some idea regarding fin tube heat exchanger 00:28:31.860 --> 00:28:37.890 and we are trying to do some analysis which will enable us ultimately to design fin type 00:28:37.890 --> 00:28:43.640 heat exchanger and here I have told certain things are important that fin side calculations 00:28:43.640 --> 00:28:50.220 are important. So, fin side area we have to calculate fin side heat transfer coefficient 00:28:50.220 --> 00:28:57.010 we have to calculate and ah for that we have to consider the geometry and that is why we 00:28:57.010 --> 00:29:02.590 have consider the geometry and from there we have calculated different areas. 00:29:02.590 --> 00:29:07.900 Thank you so we will continue with this topic in the coming lecture.
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