00:00:00.060 that's moving the chapter to dealing 00:00:02.62900:00:02.639 with heat exchangers so this is a 00:00:05.69000:00:05.700 introduction to heat exchangers there's 00:00:08.33000:00:08.340 a lot of heat exchangers and maybe I 00:00:10.16000:00:10.170 could just go through the whole host of 00:00:12.70900:00:12.719 heat exchangers and different styles of 00:00:15.56000:00:15.570 types will eventually do that but not on 00:00:17.59900:00:17.609 the first day but here's a picture of 00:00:19.97000:00:19.980 one that will analyze today it's a 00:00:22.97000:00:22.980 concentric tube or double wall pipe or 00:00:27.41000:00:27.420 pipe you know it's a pipe inside of a 00:00:29.77900:00:29.789 pipe and the fluid inside the one pipe 00:00:33.11000:00:33.120 runs maybe this way and it doesn't mix 00:00:35.47900:00:35.489 with the fluid that's in the annulus 00:00:37.28000:00:37.290 that may run like this and then go out 00:00:41.56000:00:41.570 this is very similar this is a shell and 00:00:45.38000:00:45.390 tube heat exchangers so you have a shell 00:00:47.47900:00:47.489 side and then you have tubes and the 00:00:49.91000:00:49.920 tubes you can see they come in and 00:00:52.18000:00:52.190 they'll split in this manifold in two 00:00:55.40000:00:55.410 different tubes flow it'll be a u-tube 00:00:58.38900:00:58.399 sometimes they're straight through then 00:01:00.50000:01:00.510 they have a manifold on the backend to 00:01:02.86900:01:02.879 go in a straight run through the other 00:01:04.88000:01:04.890 tubes different designs on shell and 00:01:07.25000:01:07.260 tube heat exchangers and out to go so 00:01:09.77000:01:09.780 fluid on the shell side and a fluid on 00:01:12.74000:01:12.750 the tube side 00:01:13.64000:01:13.650 this is automobile radiator so where are 00:01:17.51000:01:17.520 two fluids the fluid with the liquid in 00:01:21.23000:01:21.240 and out mainly water with some 00:01:24.26000:01:24.270 antifreeze and then the air side goes 00:01:27.26000:01:27.270 across so this is a cross flow heat 00:01:30.20000:01:30.210 exchanger and then you have different 00:01:33.46900:01:33.479 these are plate type heat exchangers 00:01:35.69000:01:35.700 where you can actually these are 00:01:39.14000:01:39.150 designed to take apart easily and 00:01:41.27000:01:41.280 serviced easily and so you'll see a lot 00:01:43.81900:01:43.829 of those there they're compromise 00:01:46.28000:01:46.290 between the best efficiency and the best 00:01:48.46900:01:48.479 service ability and the best reliability 00:01:51.23000:01:51.240 and expandability you could long rods 00:01:55.76000:01:55.770 bolt these together you could take the 00:01:58.13000:01:58.140 apart and expand the heat exchanger if 00:02:00.35000:02:00.360 you needed to increase its area make it 00:02:02.81000:02:02.820 larger all right the fluid flow pattern 00:02:06.46900:02:06.479 I have other illustrations to talk about 00:02:08.69000:02:08.700 the fluid flow patterns in these hate 00:02:10.55000:02:10.560 heat exchangers but not today 00:02:12.77000:02:12.780 so let's go to the simplest heat 00:02:15.66000:02:15.670 exchanger two concentric tube heat 00:02:18.60000:02:18.610 exchanger and think of either parallel 00:02:21.66000:02:21.670 flow or counter flow so normally we'd 00:02:25.26000:02:25.270 sketch it something like this and say 00:02:28.26000:02:28.270 have fluid that's on the hot fluid flows 00:02:32.43000:02:32.440 this way and the cold fluid flows that 00:02:36.51000:02:36.520 way and the hot fluid and the cold fluid 00:02:40.02000:02:40.030 enter on the same side and exit on the 00:02:42.33000:02:42.340 same side hence the flow are parallel 00:02:45.57000:02:45.580 they're parallel you could maybe say 00:02:48.81000:02:48.820 concurrent flow or some other 00:02:50.39000:02:50.400 terminologies to say they're in the same 00:02:52.35000:02:52.360 direction 00:02:53.09000:02:53.100 how about counter flow and we'll have 00:02:57.24000:02:57.250 the hot side come this way and the cold 00:03:01.35000:03:01.360 side go that way and for introductory 00:03:06.15000:03:06.160 purposes think about location a 00:03:10.38000:03:10.390 coordinate system X runs from 0 to L the 00:03:14.52000:03:14.530 length of those that heat exchanger and 00:03:17.61000:03:17.620 we'll plot the temperature on the y axis 00:03:20.28000:03:20.290 and think about the high temperature the 00:03:23.73000:03:23.740 temperature hot coming in as the highest 00:03:26.01000:03:26.020 temperature and the temperature of the 00:03:29.49000:03:29.500 cold coming in would be the low 00:03:31.95000:03:31.960 temperature and what do you think that 00:03:34.77000:03:34.780 temperatures are going to do as it flows 00:03:37.41000:03:37.420 through the heat exchanger you might 00:03:40.14000:03:40.150 expect that the hot fluid to come down 00:03:43.35000:03:43.360 some and exit at a lower temperature 00:03:46.59000:03:46.600 temperature hot out and the cold fluid 00:03:50.76000:03:50.770 could go up some temperature cold out 00:03:56.30000:03:56.310 would it be reasonable for the cold to 00:03:59.88000:03:59.890 somehow come out at a higher temperature 00:04:02.87000:04:02.880 than the hot out no 00:04:10.05000:04:10.060 No so this is not possible true it's 00:04:14.79000:04:14.800 just not possible why is that not 00:04:16.40900:04:16.419 possible well what's happening is is you 00:04:19.53000:04:19.540 discretize this into little D X's and 00:04:22.17000:04:22.180 for every little DX there's a little bit 00:04:24.33000:04:24.340 of heat transfer a little bit of heat 00:04:25.95000:04:25.960 transfer and if you had that case that I 00:04:27.96000:04:27.970 just erased it would be like hold it 00:04:29.67000:04:29.680 heat is coming out of a hot fluid which 00:04:31.74000:04:31.750 is now cooler than the cold fluid and 00:04:33.57000:04:33.580 flowing to the higher temperature cold 00:04:35.97000:04:35.980 fluid that's not gonna work heat 00:04:38.46000:04:38.470 transfer always goes from what's hot to 00:04:40.56000:04:40.570 cold and things like this okay we're not 00:04:44.31000:04:44.320 we don't think of a complicated system 00:04:47.07000:04:47.080 to like air-conditioning system this is 00:04:50.25000:04:50.260 just fluid exposed other fluids 00:04:54.39000:04:54.400 separated by walls so convection and 00:04:56.94000:04:56.950 conduction heat transfer all right when 00:05:00.99000:05:01.000 might we expect if this was the case 00:05:03.84000:05:03.850 right here and I asked you okay change 00:05:06.62900:05:06.639 it up a little bit I start to increase 00:05:11.61000:05:11.620 the mass flow rate of the hot fluid I 00:05:14.15900:05:14.169 really start pumping more hot fluid 00:05:17.07000:05:17.080 through the system how does it change 00:05:19.52900:05:19.539 the red curve does it change the 00:05:22.44000:05:22.450 temperature of the hot coming in if I 00:05:25.20000:05:25.210 increase the mass flow rate of the hot 00:05:27.54000:05:27.550 fluid how does that red curb the 00:05:31.86000:05:31.870 temperature profile of the hot fluid 00:05:35.25000:05:35.260 change as it goes through the heat 00:05:37.20000:05:37.210 exchanger would it be either coming down 00:05:43.29000:05:43.300 steeper or would it be shallower 00:05:48.71000:05:48.720 shallower wouldn't it be shallower and 00:05:51.95000:05:51.960 so the hot out would go up wouldn't it 00:05:56.84000:05:56.850 the hot out okay what about the cold the 00:06:01.11000:06:01.120 same temperature cold in what would the 00:06:04.14000:06:04.150 cold temperature profile do would it 00:06:07.52900:06:07.539 change would the cold outlet go up or 00:06:11.07000:06:11.080 would it go down all I did was I did not 00:06:15.42000:06:15.430 change the mass flow rate of the cold 00:06:17.21900:06:17.229 fluid or the temperature coming into the 00:06:19.08000:06:19.090 cold fluid all I did was increase the 00:06:22.08000:06:22.090 master 00:06:22.57000:06:22.580 right of the hot fluid would be a little 00:06:27.12900:06:27.139 steeper so that the temperature of the 00:06:30.90900:06:30.919 cold out actually went up a little bit 00:06:35.64000:06:35.650 let's vote with your thumbs 00:06:38.10000:06:38.110 so look okay alright so that's right now 00:06:42.36900:06:42.379 you could play the reverse game and say 00:06:44.92000:06:44.930 what happens if I change the mass flow 00:06:47.43900:06:47.449 rate of the cold fluid and make those 00:06:49.42000:06:49.430 sketches I really think that's helpful 00:06:51.36900:06:51.379 let's do the same thing over here for 00:06:53.83000:06:53.840 the counter current this is much more 00:06:56.32000:06:56.330 popular and we'll see why why would you 00:06:58.68900:06:58.699 design a heat exchanger to run in this 00:07:02.29000:07:02.300 type of configuration well let's put the 00:07:05.40900:07:05.419 same type of hot temperature whoops but 00:07:09.04000:07:09.050 here what do I have on let's get 00:07:12.96900:07:12.979 blackened in all right so over here I 00:07:16.54000:07:16.550 have the temperature the hot fluid in 00:07:18.99900:07:19.009 don't I and on this side I have the 00:07:22.74900:07:22.759 temperature cold in so now describe the 00:07:27.51900:07:27.529 temperature profile well you could have 00:07:30.27900:07:30.289 a temperature profile that looks 00:07:31.95900:07:31.969 something like this and something like 00:07:35.68000:07:35.690 that so that the temperature of the hot 00:07:40.20900:07:40.219 out is but well the temperature of the 00:07:43.68900:07:43.699 hot fluid anywhere inside the heat 00:07:45.87900:07:45.889 exchanger is always higher than the 00:07:49.39000:07:49.400 local temperature of the cold fluid 00:07:52.02900:07:52.039 right okay but as sketched what could 00:07:56.68000:07:56.690 happen right here the temperature the 00:07:59.20000:07:59.210 cold out if I did it very accurately he 00:08:06.61000:08:06.620 could actually exceed the temperature of 00:08:09.33900:08:09.349 the hot out couldn't it couldn't 00:08:13.57000:08:13.580 yeah it could let me see 00:08:19.42000:08:19.430 could you in the parallel flow could you 00:08:21.76000:08:21.770 ever get the hot out lower than the cold 00:08:24.99900:08:25.009 out no it's impossible but here it is 00:08:29.29000:08:29.300 possible okay let me ask you a little 00:08:33.37000:08:33.380 bit what happens if I make the same 00:08:36.85000:08:36.860 temperature for the hot in and the same 00:08:40.08900:08:40.099 temperature for the cold in but I make 00:08:42.25000:08:42.260 the heat exchanger longer I increase its 00:08:46.06000:08:46.070 length so it's like I have to say no put 00:08:49.03000:08:49.040 the length over here and here is the 00:08:53.07900:08:53.089 starting temperature temperature hot in 00:08:56.01000:08:56.020 true but will what will the temperature 00:09:00.16000:09:00.170 profile look like compared to the 00:09:02.62000:09:02.630 shorter smaller heat exchanger now I 00:09:05.26000:09:05.270 have a larger heat exchanger don't 00:09:08.19900:09:08.209 change any flow rates the mass flow 00:09:11.98000:09:11.990 rates the same fluid flow rates are the 00:09:14.07900:09:14.089 same what would happen the temperature 00:09:19.06000:09:19.070 difference would decrease right and so 00:09:22.36000:09:22.370 maybe I know this is going to be a 00:09:24.88000:09:24.890 complicated diagram but it made go like 00:09:28.18000:09:28.190 this and the blue may go like this maybe 00:09:36.06000:09:36.070 something like that did it actually 00:09:40.56900:09:40.579 change the slope of the red line let's 00:09:44.35000:09:44.360 say this was the original LED red line 00:09:46.69000:09:46.700 and that's the second case red line that 00:09:49.06000:09:49.070 it changed the slope of the red line 00:09:55.10000:09:55.110 how about this that it changed the slope 00:09:57.25900:09:57.269 of the blue line case one and case two 00:10:05.47000:10:05.480 yeah and if you make it really long you 00:10:08.81000:10:08.820 can see that if we would have just 00:10:10.75000:10:10.760 extrapolated that blue line up maybe we 00:10:13.63900:10:13.649 would got to a ridiculous case okay so 00:10:18.76900:10:18.779 the slopes changed a little bit 00:10:20.96000:10:20.970 didn't they both of them all right what 00:10:27.07900:10:27.089 dictated the slope or there's a lot of 00:10:29.90000:10:29.910 things that dictate to slope but I'm not 00:10:31.57900:10:31.589 going to change the mass flow-rate and 00:10:33.35000:10:33.360 I'm not going to change the specific 00:10:34.88000:10:34.890 heats of either fluid streams for this 00:10:36.59000:10:36.600 introduction right now for this part of 00:10:38.32900:10:38.339 the discussion what what what what makes 00:10:41.72000:10:41.730 it what makes this slope on the red line 00:10:44.26900:10:44.279 and the slope on the blue line it's the 00:10:49.25000:10:49.260 temperature difference between the red 00:10:51.01900:10:51.029 line and the blue line what does the 00:10:52.75900:10:52.769 temp local temperature differs between a 00:10:54.68000:10:54.690 hot fluid and cold fluid and because 00:10:57.35000:10:57.360 that dictates the rate of heat transfer 00:10:59.62000:10:59.630 hence the rate of change of the hot it's 00:11:02.15000:11:02.160 going to go down and the rate of change 00:11:04.22000:11:04.230 of the cold that's going to go up in the 00:11:05.93000:11:05.940 direction of flow that's pretty 00:11:11.18000:11:11.190 complicated concept all right but let's 00:11:14.93000:11:14.940 do this let's go back and play with it 00:11:17.30000:11:17.310 where I have not changing the length but 00:11:20.68900:11:20.699 I had the temperature of the hot fluid 00:11:23.00000:11:23.010 coming in I'm not gonna change that the 00:11:26.12000:11:26.130 temperatures are hot in I'm not gonna 00:11:28.25000:11:28.260 change the cold in I'm not gonna change 00:11:31.63900:11:31.649 anything with the cold fluid but what am 00:11:34.18900:11:34.199 I gonna do to the hot fluid make it go 00:11:37.51900:11:37.529 faster increase mass flow rate of the 00:11:40.79000:11:40.800 hot fluid all right what will the red 00:11:43.81900:11:43.829 curve do 00:11:49.87000:11:49.880 it used to be here the red curve right 00:11:53.80000:11:53.810 it used to be right here will it go up 00:11:57.47000:11:57.480 or will it go down or will the red curve 00:12:00.07900:12:00.089 stay the same so if I increase the mass 00:12:05.38900:12:05.399 flow rate of the hot fluid the red curve 00:12:08.87000:12:08.880 will go up stay the same or go down top 00:12:16.69900:12:16.709 and you're exactly right so that's what 00:12:19.85000:12:19.860 happens to the red curve okay what about 00:12:24.41000:12:24.420 the blue curve it used to be like this 00:12:28.43000:12:28.440 will the blue curve increase you know go 00:12:32.00000:12:32.010 up a little bit steeper or not nothing 00:12:38.21000:12:38.220 in the cold nothing in the cold it'll go 00:12:43.40000:12:43.410 up and why would it go up a little bit 00:12:48.73000:12:48.740 because the delta T is a little greater 00:12:52.22000:12:52.230 to drive that heat transfer hence more 00:12:54.53000:12:54.540 heat is going to get into the cold fluid 00:12:56.09000:12:56.100 I didn't change the temperature of the 00:12:58.93900:12:58.949 hot fluid all I did was change the mass 00:13:00.53000:13:00.540 flow rate of the hot fluid but that was 00:13:04.18900:13:04.199 enough to do it I'm not certain how many 00:13:08.42000:13:08.430 of these I know that they're very 00:13:10.28000:13:10.290 productive and you need to process these 00:13:12.19900:13:12.209 type of questions in your mind I don't I 00:13:14.72000:13:14.730 hope a lot of you are following along 00:13:16.73000:13:16.740 but these could be very tricky did you 00:13:23.81000:13:23.820 that's another good question so that now 00:13:26.55000:13:26.560 we say what taste do I have when I would 00:13:29.19000:13:29.200 expect the slopes to be pretty parallel 00:13:32.81000:13:32.820 for the hot fluid in the cold food under 00:13:35.61000:13:35.620 what conditions would that be somebody 00:13:38.46000:13:38.470 would say well probably when the mass 00:13:40.62000:13:40.630 flow rate of the hot fluid is pretty 00:13:42.63000:13:42.640 close to the mass flow rate of the cold 00:13:44.25000:13:44.260 fluid but it's not just the mass flow 00:13:48.24000:13:48.250 rates it's the mass flow rate times a 00:13:50.85000:13:50.860 specific key to the hot fluid and mass 00:13:53.13000:13:53.140 flow rate times specific heat of the 00:13:54.75000:13:54.760 cold fluid when the product of the mass 00:13:57.33000:13:57.340 flow rates and the specific heats are 00:13:59.94000:13:59.950 the same the slopes will be the same 00:14:04.58000:14:04.590 that's it and so in this heat transfer 00:14:08.10000:14:08.110 literature we introduce a cap C symbol 00:14:11.19000:14:11.200 and the cap C is the mass flow rate 00:14:14.76000:14:14.770 times the specific heat I'm not doing 00:14:17.88000:14:17.890 phase change I'm not doing condensation 00:14:20.25000:14:20.260 or vaporization yet we'll get there but 00:14:23.40000:14:23.410 for introductory purposes it's just 00:14:25.47000:14:25.480 single phase if it's a gas it stays a 00:14:28.11000:14:28.120 gas if it's liquid it stays a liquid so 00:14:31.20000:14:31.210 we have a constant specific heat 00:14:33.53000:14:33.540 neglecting temperature dependent 00:14:35.37000:14:35.380 specific heats and you have the mass 00:14:37.23000:14:37.240 flow rate and you have the heat capacity 00:14:40.17000:14:40.180 rate heat capacity rate all right new 00:14:46.92000:14:46.930 term cap see it's used a lot and heat 00:14:49.20000:14:49.210 exchanger literature and analysis and 00:14:52.02000:14:52.030 methods what are the units both SI as 00:14:56.43000:14:56.440 well as US customary system the units 00:14:58.92000:14:58.930 for the heat capacity rate watts so 00:15:04.07000:15:04.080 let's do it this way I'll scroll down 00:15:07.62000:15:07.630 just a little bit so we have mass flow 00:15:10.29000:15:10.300 rate specific heat let's work over here 00:15:12.75000:15:12.760 in Si so we're gonna have kilograms per 00:15:15.57000:15:15.580 second times kilojoules per kilogram 00:15:20.84000:15:20.850 Kelvin or degree C kilograms cancel 00:15:25.76000:15:25.770 I'll have forget the kilo I'll have 00:15:28.23000:15:28.240 watts per degree C true all right mass 00:15:32.28000:15:32.290 flow rate over in the USCS let's do 00:15:35.70000:15:35.710 power 00:15:36.26900:15:36.279 per minute or pounds per hour pounds per 00:15:39.96000:15:39.970 something second and then specific heat 00:15:43.59000:15:43.600 well that's how many BTUs per pound 00:15:47.96000:15:47.970 degree F bit to use cancel so we'll have 00:15:52.29000:15:52.300 BTUs per minute that's some rate of 00:15:55.07900:15:55.089 transfer divided by degrees F it's 00:15:57.80900:15:57.819 consistent isn't that consistent between 00:16:01.86000:16:01.870 them so they do have a little funny 00:16:03.54000:16:03.550 units 00:16:04.17000:16:04.180 it's a beat to use per minute per degree 00:16:07.71000:16:07.720 F or something like that yes well with 00:16:20.93900:16:20.949 the advent of computers we can account 00:16:23.67000:16:23.680 for their variable temperature dependent 00:16:26.06900:16:26.079 properties as it flows through our 00:16:28.31900:16:28.329 system and so we disparate eyes and you 00:16:30.92900:16:30.939 can really do a good job of analysis but 00:16:33.48000:16:33.490 for introductory purposes it's constant 00:16:36.88900:16:36.899 some fluids are more susceptible their 00:16:40.94900:16:40.959 properties change as a stronger function 00:16:43.17000:16:43.180 of temperature so but we're gonna just 00:16:47.67000:16:47.680 use an average temperature think about 00:16:50.22000:16:50.230 water liquids or something like that 00:16:51.86900:16:51.879 gases so that's an idea if if the flow 00:16:56.18900:16:56.199 rate of the mass flow rate of the hot 00:16:58.29000:16:58.300 fluid increases then the hot fluid curve 00:17:01.13900:17:01.149 becomes flatter if the mass flow rate of 00:17:04.13900:17:04.149 the cold fluid increases it becomes 00:17:07.28900:17:07.299 flatter true that goes down and we 00:17:13.91900:17:13.929 already explored increasing the length 00:17:15.92900:17:15.939 so think about increasing mass flow 00:17:18.63000:17:18.640 rates or increasing heat capacity rates 00:17:21.12000:17:21.130 and then also increasing the area or 00:17:26.42900:17:26.439 length here's two basic questions when 00:17:31.26000:17:31.270 you're doing heat exchanger analysis 00:17:33.72000:17:33.730 just basically the two questions are 00:17:36.02900:17:36.039 you're gonna rate the heat exchanger or 00:17:38.49000:17:38.500 you're gonna size the heat exchanger 00:17:41.19000:17:41.200 you're gonna say for this heat exchanger 00:17:43.26000:17:43.270 here it is think about it right here 00:17:45.18000:17:45.190 here it is plop it down on somebody's 00:17:46.95000:17:46.960 desk or there it is right there in the 00:17:49.23000:17:49.240 shop 00:17:50.27000:17:50.280 what will the rate of heat transfer be 00:17:52.58000:17:52.590 with these two inlet fluids what will Q 00:17:56.45000:17:56.460 be what will the rate of heat rate your 00:18:00.29000:18:00.300 heat exchanger by predicting what it can 00:18:02.48000:18:02.490 transfer that's the first question the 00:18:05.72000:18:05.730 second question is is I know what I need 00:18:08.30000:18:08.310 to transfer in my plan I know I need to 00:18:11.18000:18:11.190 get diz many you know gallons per minute 00:18:13.67000:18:13.680 of this type of substance with this 00:18:16.10000:18:16.110 specific heat from this Inlet 00:18:17.87000:18:17.880 temperature that outlet temperature 00:18:19.67000:18:19.680 basically told me what I need to 00:18:21.62000:18:21.630 transfer the rate of transfer needs to 00:18:24.86000:18:24.870 be accomplished right the next question 00:18:28.52000:18:28.530 is is how big should my heat exchanger 00:18:32.60000:18:32.610 be to accomplish that goal 00:18:35.23000:18:35.240 so you size your heat exchanger so what 00:18:39.08000:18:39.090 you're gonna find is you'll find almost 00:18:40.85000:18:40.860 like version a and version B of 00:18:44.68000:18:44.690 equations in the heat exchanger and 00:18:48.07000:18:48.080 chapter and they're gonna be like oh if 00:18:51.29000:18:51.300 you want to rate it use the version a if 00:18:54.83000:18:54.840 you want to size it version B maybe you 00:18:58.61000:18:58.620 recall that different set of tables in 00:19:00.62000:19:00.630 the heat transfer textbook well there's 00:19:04.01000:19:04.020 two analysis methods that are out there 00:19:07.13000:19:07.140 there's really more many more than just 00:19:09.35000:19:09.360 two but to have survived and are still 00:19:11.48000:19:11.490 in heat transfer textbooks one is called 00:19:14.18000:19:14.190 the log mean temperature difference and 00:19:15.83000:19:15.840 it's presented especially for 00:19:18.92000:19:18.930 informational purposes in this class as 00:19:21.98000:19:21.990 well as in most textbooks some textbooks 00:19:24.47000:19:24.480 have relegated to an appendix and it may 00:19:27.62000:19:27.630 eventually go away but it's the 00:19:30.62000:19:30.630 effectiveness NTU method is the more 00:19:33.20000:19:33.210 predominant method it is more flexible 00:19:35.87000:19:35.880 method but when you get a more flexible 00:19:39.20000:19:39.210 predominant method it's sometimes more 00:19:41.15000:19:41.160 abstract and it's harder to understand 00:19:43.76000:19:43.770 what's going on so in the log mean 00:19:47.21000:19:47.220 temperature difference method you have 00:19:48.83000:19:48.840 the rate of heat transfer is some 00:19:52.48000:19:52.490 overall heat transfer coefficient in the 00:19:55.58000:19:55.590 heat exchanger which you may recall 00:19:58.36000:19:58.370 having to work with in the prerequisite 00:20:01.76000:20:01.770 class the overall heat transfer Co 00:20:03.80000:20:03.810 efficient 00:20:04.15000:20:04.160 a lot of times we have a solid 00:20:08.40000:20:08.410 separating a fluid from a fluid and we 00:20:12.52000:20:12.530 think about having the temperature of 00:20:14.71000:20:14.720 the fluid then we have a little 00:20:15.97000:20:15.980 convective resistance little conduction 00:20:18.22000:20:18.230 resistance and little convection 00:20:19.87000:20:19.880 resistance so we'll have the 1 over H a 00:20:23.29000:20:23.300 on that side the 1 over H a on that side 00:20:26.95000:20:26.960 and an L over ka on that side and we 00:20:29.68000:20:29.690 wrap them all together to get a 1 over 00:20:33.27000:20:33.280 UA which is an overall heat transfer 00:20:36.34000:20:36.350 coefficient has the same units like H 00:20:38.98000:20:38.990 convection coefficient so we have that 00:20:42.46000:20:42.470 big symbol I ran out of room sorry about 00:20:45.07000:20:45.080 it let me scoot this down a little bit 00:20:46.75000:20:46.760 all right so the in the log mean 00:20:49.78000:20:49.790 temperature difference you have the rate 00:20:51.88000:20:51.890 of heat transfer in that heat exchanger 00:20:53.83000:20:53.840 is equal to you the overall heat 00:20:57.16000:20:57.170 transfer coefficient times a that gives 00:20:59.65000:20:59.660 me not only the physical size but the 00:21:01.81000:21:01.820 thermal size of that heat exchanger 00:21:04.74000:21:04.750 times an appropriate temperature 00:21:07.09000:21:07.100 difference the log mean temperature 00:21:09.70000:21:09.710 difference is the appropriate 00:21:12.01000:21:12.020 temperature difference let's go back to 00:21:14.77000:21:14.780 these plots right here 00:21:17.02000:21:17.030 or maybe I'll make a new one so if I had 00:21:20.80000:21:20.810 a heat exchanger and this works for 00:21:23.92000:21:23.930 parallel flow counter flow cross flow 00:21:26.29000:21:26.300 all kinds of heat exchangers you just 00:21:28.12000:21:28.130 put a correction factor in or lookup a 00:21:30.40000:21:30.410 core a table to get one of the 00:21:32.50000:21:32.510 properties let's say the hot let me draw 00:21:35.80000:21:35.810 it like this the hot fluid tea hot in 00:21:39.43000:21:39.440 and what's down here tea cold in the 00:21:44.98000:21:44.990 cold food goes like this the hot fluid 00:21:47.50000:21:47.510 goes like that can you see that this 00:21:50.53000:21:50.540 temperature difference throughout the 00:21:52.72000:21:52.730 heat exchanger is roughly the same 00:21:55.41000:21:55.420 that's the temperature difference that 00:21:58.21000:21:58.220 this log mean would give you it would 00:22:01.09000:22:01.100 give you that value all right but what 00:22:03.82000:22:03.830 happens if the hot did something like 00:22:07.39000:22:07.400 this and the blue did something like 00:22:10.36000:22:10.370 that well what you would see that the 00:22:12.13000:22:12.140 temperature difference over here is less 00:22:14.80000:22:14.810 than the temperature difference in that 00:22:16.39000:22:16.400 part of the heat exchanger 00:22:18.06000:22:18.070 so it's like give me the appropriate 00:22:20.94000:22:20.950 temperature difference that is 00:22:22.90000:22:22.910 throughout the heat exchanger and the 00:22:24.88000:22:24.890 log mean temperature difference does 00:22:26.77000:22:26.780 exactly that not only will it work for 00:22:29.68000:22:29.690 this counter flow but it works for the 00:22:33.25000:22:33.260 more theoretical less practical parallel 00:22:37.09000:22:37.100 flow where you can get some dramatic 00:22:41.22000:22:41.230 differences because what does the 00:22:43.63000:22:43.640 temperature difference look like over 00:22:45.64000:22:45.650 here quite large what's the temperature 00:22:48.16000:22:48.170 difference over there quite small and 00:22:51.33000:22:51.340 it'll work in those cases as well so 00:22:55.21000:22:55.220 what is that log mean temperature 00:22:56.47000:22:56.480 difference well what you do is you say 00:22:58.66000:22:58.670 tell me the temperature difference on 00:23:01.03000:23:01.040 one side it really doesn't matter of 00:23:03.48000:23:03.490 that heat exchange or delta T one 00:23:06.16000:23:06.170 difference between the hot and the cold 00:23:08.17000:23:08.180 on this side tell me the temperature 00:23:11.23000:23:11.24000:23:13.27000:23:13.280 on the other side Delta P two and if 00:23:19.42000:23:19.430 you're a student the first time you see 00:23:21.25000:23:21.260 it you say well maybe I'll just add them 00:23:23.92000:23:23.930 together and divide by two in many cases 00:23:26.65000:23:26.660 you wouldn't be too far off but the 00:23:28.69000:23:28.700 accurate log mean temperature difference 00:23:31.75000:23:31.760 method would be delta T on one side 00:23:34.90000:23:34.910 minus the delta T on the second side 00:23:36.94000:23:36.950 divided by the natural log of the delta 00:23:40.36000:23:40.370 T on one side divided by the delta T on 00:23:42.52000:23:42.530 the second side we're gonna drive that 00:23:46.60000:23:46.610 equation in a minute I'm giving you the 00:23:49.36000:23:49.370 perspective before we get into the 00:23:50.95000:23:50.960 brutal math all right the next method is 00:23:55.00000:23:55.010 the effectiveness NTU method 00:23:57.87000:23:57.880 effectiveness often is the epsilon or 00:24:01.18000:24:01.190 some other Greek symbol for 00:24:02.94000:24:02.950 effectiveness NTU is just like you know 00:24:07.27000:24:07.280 LM TD log mean temperature difference is 00:24:11.01000:24:11.020 NTU is the number of transfer units 00:24:16.23000:24:16.240 number of transfer units so the number 00:24:21.49000:24:21.500 of transfer units is just simply defined 00:24:23.95000:24:23.960 as the you are forgot what was you 00:24:29.30000:24:29.310 the overall heat transfer coefficient it 00:24:33.26000:24:33.270 accounts for the fluid convection 00:24:36.05000:24:36.060 resistance on both sides and the wall 00:24:39.11000:24:39.120 typically conduction through it okay so 00:24:41.98000:24:41.990 you a over see hey cap C Oh what was 00:24:48.50000:24:48.510 that that was a product of mass flow 00:24:50.27000:24:50.280 rate in specific heat what is cap see 00:24:52.76000:24:52.770 the name of it heat capacity right 00:24:57.08000:24:57.090 what are these funny units on it BTUs 00:25:00.11000:25:00.120 per minute degree F or watts per degree 00:25:02.69000:25:02.700 C and it's a product MC so it's the 00:25:06.20000:25:06.210 minimum what seem in the minimum heat 00:25:11.15000:25:11.160 capacity rate well I have two fluids I 00:25:13.58000:25:13.590 have a hot fluid a cold fluid I can 00:25:15.29000:25:15.300 calculate the heat capacity rates of 00:25:17.03000:25:17.040 either one of those and I say which one 00:25:19.22000:25:19.230 is the minimum and that's what is used 00:25:21.11000:25:21.120 in the definition of the number of 00:25:22.70000:25:22.710 transfer units and to use all right what 00:25:26.69000:25:26.700 about the effectiveness well the 00:25:28.94000:25:28.950 effectiveness is of definition Q Wow 00:25:33.29000:25:33.300 what was Q used for what's the name of Q 00:25:37.87000:25:37.880 Q is the the rate of heat transfer 00:25:41.21000:25:41.220 occurring and my heat exchanger it's the 00:25:43.94000:25:43.950 rate of heat transfer what would be the 00:25:45.32000:25:45.330 typical SI unit watt or USCS BTUs per 00:25:53.36000:25:53.370 hour BTUs per minute something it's a 00:25:55.55000:25:55.560 rate of heat transfer right so the 00:25:58.37000:25:58.380 effectiveness is the actual rate of heat 00:26:01.58000:26:01.590 transfer being accomplished in that heat 00:26:03.56000:26:03.570 exchanger divided by M ax I don't I keep 00:26:08.18000:26:08.190 always confused what is ma X stands for 00:26:11.80000:26:11.810 the maximum possible the maximum 00:26:15.77000:26:15.780 possible and it takes a while to figure 00:26:19.25000:26:19.260 this out but the let me give you the 00:26:22.73000:26:22.740 equation then try to explain it the 00:26:24.35000:26:24.360 maximum theoretical possible is if I 00:26:26.51000:26:26.520 have the minimum heat capacity rate 00:26:29.42000:26:29.430 times the maximum delta T ever possible 00:26:33.26000:26:33.270 in this heat exchanger between the two 00:26:35.15000:26:35.160 fluids the most extreme high high 00:26:37.19000:26:37.200 temperature is the hot in is there a 00:26:39.62000:26:39.630 higher temperature anywhere in the 00:26:41.30000:26:41.310 system than the hot in 00:26:43.40000:26:43.410 No and what's the lowest temperature 00:26:46.60000:26:46.610 cold in so I got the most extreme 00:26:50.18000:26:50.190 temperature that's physically being 00:26:52.25000:26:52.260 realized times the minimum heat capacity 00:26:54.83000:26:54.840 rate and that gives you the maximum rate 00:26:58.49000:26:58.500 of heat transfer possible make that heat 00:27:03.11000:27:03.120 exchanger as large as you want without 00:27:08.30000:27:08.310 changing your fluid flow rates because 00:27:10.46000:27:10.470 cement is based on comparing the hot 00:27:13.85000:27:13.860 fluid in the cold fluid heat capacity 00:27:15.80000:27:15.810 rates right 00:27:16.46000:27:16.470 don't go changing seem in think about 00:27:18.50000:27:18.510 conceptually changing the area let the 00:27:21.05000:27:21.060 area go long long long huge long heat 00:27:24.74000:27:24.750 exchanger right if we let the long long 00:27:28.34000:27:28.350 long heat exchanger go with the high 00:27:30.95000:27:30.960 mass flow rate of the hot fluid get rid 00:27:33.92000:27:33.930 of this one here so this is the mass 00:27:37.46000:27:37.470 flow F this is the mass flow rate of the 00:27:41.12000:27:41.130 hot fluid it's very very high it's 00:27:43.58000:27:43.590 nearly flat going across right the 00:27:46.31000:27:46.320 temperature of the hot fluid out so I'm 00:27:48.20000:27:48.210 a little bit less than the temperature 00:27:49.46000:27:49.470 of the hot fluid in and I make this L go 00:27:53.33000:27:53.340 very very long so we put a little how do 00:27:56.84000:27:56.850 they draw that line like this saying 00:27:58.91000:27:58.920 there's a break in it yeah right 00:28:04.45000:28:04.460 something like that it's a break in it 00:28:06.92000:28:06.930 so L is way out there what does the blue 00:28:11.69000:28:11.700 fluid do will it go something like this 00:28:21.16000:28:21.170 where what will the temperature of the 00:28:24.05000:28:24.060 blue fluid do going out I have a 00:28:27.56000:28:27.570 super-long it'll go to T hot in so you 00:28:33.59000:28:33.600 could think about making it super long 00:28:35.48000:28:35.490 and you would have the change in this 00:28:38.18000:28:38.190 case can you tell that the heat capacity 00:28:40.16000:28:40.170 rate of the cold fluid is less than heat 00:28:42.56000:28:42.570 capacity rated the hot fluid we let the 00:28:44.72000:28:44.730 mass flow rate the hot fluid go off to 00:28:46.34000:28:46.350 infinity to achieve this so of course 00:28:48.59000:28:48.600 the coke blue is less 00:28:52.11000:28:52.120 so it's a little tricky there's a lot of 00:28:54.89900:28:54.909 you know what if this what if that but 00:28:57.06000:28:57.070 it's the minimum heat capacity rate 00:28:58.83000:28:58.840 times the maximum temperature difference 00:29:01.20000:29:01.210 anywhere the hot fluid in - the cold 00:29:04.28900:29:04.299 fluid in that's the effectiveness NTU 00:29:06.60000:29:06.610 method that's the more practical popular 00:29:10.11000:29:10.120 implementable quicker method well I 00:29:15.84000:29:15.850 thought about taking a blank page have 00:29:19.47000:29:19.480 my notes and just start the derivation 00:29:22.25000:29:22.260 and then I thought mmm I got that page 00:29:26.97000:29:26.980 that page and that page the cover and I 00:29:32.66900:29:32.679 think you would be asleep by that note 00:29:34.71000:29:34.720 so let me say this it's in every heat 00:29:38.85000:29:38.860 transfer textbook it is and it's in our 00:29:43.62000:29:43.630 book - and the derivation is just what 00:29:46.98000:29:46.990 they do in the book is they say and it 00:29:48.63000:29:48.640 follows such that boom and they have two 00:29:50.94000:29:50.950 lines and the work between those two 00:29:52.76900:29:52.779 lines is about two or three pages of 00:29:54.69000:29:54.700 work so anyway let me do this let me 00:29:57.06000:29:57.070 kind of guide you through this so let's 00:30:00.99000:30:01.000 start out we have to pick something to 00:30:02.82000:30:02.830 analyze concentric tube it's easy 00:30:04.98000:30:04.990 mathematically and easy to illustrate 00:30:07.08000:30:07.090 counter flow because that's the 00:30:09.09000:30:09.100 predominant way the fluids are actually 00:30:11.13000:30:11.140 float through heat exchangers and we 00:30:13.23000:30:13.240 want to derive for the temperature 00:30:15.65900:30:15.669 distribution regardless if the hot 00:30:18.84000:30:18.850 fluids flowing really fast or slow 00:30:21.38000:30:21.390 regardless of the specific heat of the 00:30:24.33000:30:24.340 hot fluid or cold fluid or the heat 00:30:26.46000:30:26.470 capacity rates this is gonna work for 00:30:28.11000:30:28.120 all those cases so you think for a 00:30:31.79900:30:31.809 minute just cut a sketch a case put the 00:30:34.32000:30:34.330 hot in over here the hot out cold in 00:30:36.87000:30:36.880 cold out I didn't try to draw them to 00:30:39.29900:30:39.309 have the same slope here's an expert 00:30:43.11000:30:43.120 question which one of them just by 00:30:46.11000:30:46.120 looking at the plot would have a slight 00:30:48.65900:30:48.669 would have the lowest heat capacity rate 00:30:51.99000:30:52.000 which one would have the highest heat 00:30:53.82000:30:53.830 capacity rate this was a really hard 00:30:55.56000:30:55.570 question it's a product a mass flow rate 00:30:58.86000:30:58.870 times specific heat so which one of them 00:31:01.83000:31:01.840 has the highest C CAP C 00:31:04.96000:31:04.970 the cold the cold does very good the 00:31:09.90900:31:09.919 cold food because it doesn't change as 00:31:11.95000:31:11.960 much in the temperature through the heat 00:31:14.56000:31:14.570 exchanger so it's a larger heat capacity 00:31:17.79900:31:17.809 rate you think about higher mass flow 00:31:20.73900:31:20.749 rate higher mass flow rate specific heat 00:31:22.93000:31:22.940 it's really that thermal property okay 00:31:24.78900:31:24.799 we talked about a we're going to talk 00:31:27.27900:31:27.289 about every little DX so if I'm going to 00:31:30.07000:31:30.080 talk about every little DX and I need 00:31:31.86900:31:31.879 the really the DA that goes with it the 00:31:34.29900:31:34.309 perimeter times the D X makes sense so 00:31:36.24900:31:36.259 even if you don't have a perimeter 00:31:37.33000:31:37.340 introduce a perimeter in a concentric 00:31:39.82000:31:39.830 tube it makes sense to have a perimeter 00:31:41.87900:31:41.889 but we're talk about the amount of heat 00:31:44.68000:31:44.690 the small D Q transferred at every 00:31:48.21900:31:48.229 little DX okay so notice mathematically 00:31:52.77900:31:52.789 what am I writing D H T DX the rate of 00:31:56.73900:31:56.749 change of the hot fluid temperature as I 00:31:59.25900:31:59.269 move in the positive direction of change 00:32:02.10900:32:02.119 of X do you see this what I'm trying to 00:32:04.18000:32:04.190 say right here is guess what it's 00:32:08.01900:32:08.029 positive don't overthink it the fluid is 00:32:12.51900:32:12.529 flowing in the negative x direction but 00:32:15.51900:32:15.529 when I plot the temperature T H is a 00:32:18.58000:32:18.590 function of X the slope is positive 00:32:22.97900:32:22.989 likewise the change of the cold 00:32:26.08000:32:26.090 temperature with respect to X is also 00:32:28.57000:32:28.580 positive they both have a positive and 00:32:30.78900:32:30.799 I'm going to be working in the same X X 00:32:33.36900:32:33.379 goes from 0 to L all right so the heat 00:32:38.04900:32:38.059 capacity rates with the units watts per 00:32:40.29900:32:40.309 degree C or as shown for the cold and 00:32:42.33900:32:42.349 the hot fluid and I look and I say what 00:32:44.88900:32:44.899 is my rate equation to predict what this 00:32:47.61900:32:47.629 term is DQ because that's what controls 00:32:50.46900:32:50.479 how the temperatures change isn't it if 00:32:53.25900:32:53.269 it's I can get a lot of heat transfer 00:32:56.58000:32:56.590 for the same delta T the temperature the 00:33:00.66900:33:00.679 hot in the temperature the cold will 00:33:02.04900:33:02.059 more rapidly change isn't this my rate 00:33:04.71900:33:04.729 equation 00:33:05.37900:33:05.389 it's a u a DT and U is overall heat 00:33:10.11900:33:10.129 transfer coefficient also we know just 00:33:13.50900:33:13.519 if I look only at the cold fluid the 00:33:16.59900:33:16.609 amount of heat into the cold fluid 00:33:18.79000:33:18.800 makes the temperature the cold fluid go 00:33:20.89000:33:20.900 up by what heat capacity rate times the 00:33:25.03000:33:25.040 change in the cold fluid temperature 00:33:27.39000:33:27.400 does this equation look sense makes 00:33:29.95000:33:29.960 sense this one came from our rate 00:33:32.77000:33:32.780 equation it's basically our description 00:33:35.59000:33:35.600 of rates of heat transfer it's a 00:33:37.96000:33:37.970 combination a convection conduction 00:33:39.55000:33:39.560 convection combination of Newton's four 00:33:43.39000:33:43.400 EA's Newton's law what is this second 00:33:47.71000:33:47.720 one it's not Newton's it's not for yays 00:33:50.86000:33:50.870 law what is it you just landed on the 00:33:55.90000:33:55.910 sheet of paper I don't know it looked 00:33:57.61000:33:57.620 good it looked like it was sensible to 00:33:59.38000:33:59.390 write down no no no what's the basis for 00:34:02.68000:34:02.690 it genius 00:34:06.18000:34:06.190 if I give them a little a plus a little 00:34:08.95000:34:08.960 star you know walk around and let 00:34:10.69000:34:10.700 kindergarten put a little star on the 00:34:12.25000:34:12.260 paper that's all you have to do to make 00:34:13.78000:34:13.790 me happy Ben the same thing in thermal 00:34:16.06000:34:16.070 one thermo two heat transfer now thermal 00:34:18.13000:34:18.140 systems design professor the answer to 00:34:22.18000:34:22.190 the question is the first law of 00:34:24.15900:34:24.169 thermodynamics you're right isn't it it 00:34:30.82000:34:30.830 is and guess what 00:34:32.50000:34:32.510 for those that want to show off now 00:34:34.56000:34:34.570 let's take a look at D Q and what its 00:34:37.27000:34:37.280 effect on the hot fluid stream first law 00:34:41.44000:34:41.450 thermodynamics conservation of energy I 00:34:43.60000:34:43.610 transfer it heat in to the system and 00:34:45.88000:34:45.890 there's now going to be increase in the 00:34:48.13000:34:48.140 temperature that flowing fluid all right 00:34:50.11000:34:50.120 we combine now this equation we get rid 00:34:54.52000:34:54.530 of the del Q's we put the rate on both 00:34:56.71000:34:56.720 sides here here now I have two equations 00:35:00.01000:35:00.020 I want to combine them if you never did 00:35:04.87000:35:04.880 this before you will say I don't know 00:35:07.27000:35:07.280 which way you're going well trust me 00:35:09.61000:35:09.620 let's start driving to Houston but I got 00:35:11.71000:35:11.720 to first get on UTSA Boulevard and I got 00:35:14.17000:35:14.180 to get on i-10 and I got a turn here 00:35:16.09000:35:16.100 right it's like somebody else did this 00:35:18.55000:35:18.560 before and so you combine them this way 00:35:21.96000:35:21.970 algebraically it's just algebra and you 00:35:24.19000:35:24.200 get this equation and it's starting to 00:35:27.01000:35:27.020 look like changes in temperature 00:35:30.13000:35:30.140 difference proportional to chain 00:35:32.65000:35:32.660 change in location DX I'm getting a 00:35:35.62000:35:35.630 differential equation and then I recall 00:35:38.58900:35:38.599 at X equal to zero the DTD C is equal to 00:35:42.76000:35:42.770 D H out minus D cold in I could do it 00:35:46.05900:35:46.069 and have done it for the parallel flow 00:35:48.27900:35:48.289 let's do it for the counter flow it's a 00:35:49.96000:35:49.970 little more tricky with the counter flow 00:35:51.37000:35:51.380 conceptually the parallel flow is 00:35:53.14000:35:53.150 probably what most texts do anyway but 00:35:56.26000:35:56.270 you then integrate from X equal to zero 00:35:59.38000:35:59.390 to arbitrary X you know the initial 00:36:02.41000:36:02.420 condition at X equal to zero and you get 00:36:04.96000:36:04.970 this equation look at the temperature 00:36:07.42000:36:07.430 hot minus temperature cold at that 00:36:09.37000:36:09.380 location at that location X in our 00:36:12.19000:36:12.200 counter flow concentric tube heat 00:36:14.62000:36:14.630 exchanger is equal to th out minus T 00:36:18.60900:36:18.619 cold in over at X equal to zero times 00:36:22.51000:36:22.520 and I couldn't fit it on one line the 00:36:24.52000:36:24.530 exponential of 1 over CH minus 1 over C 00:36:27.81900:36:27.829 cold all times u P X it's a function of 00:36:30.76000:36:30.770 X it's an exponential function of X you 00:36:36.06900:36:36.079 can play a game you could explore the 00:36:37.90000:36:37.910 solution this is tricky I'm sorry but 00:36:39.94000:36:39.950 this is just what heat exchanger 00:36:41.44000:36:41.450 analysis is if the heat capacity rate of 00:36:44.28900:36:44.299 the cold fluid is greater than heat 00:36:45.76000:36:45.770 capacity ready to cold hot fluid then 00:36:47.68000:36:47.690 look at it the temperature difference 00:36:49.96000:36:49.970 the local temperature difference equal 00:36:51.57900:36:51.589 to a theta initial at the knot and 00:36:54.22000:36:54.230 coming in X exponent of something that's 00:36:58.02900:36:58.039 positive that's the key positive times X 00:37:01.39000:37:01.400 so what's going to happen to the 00:37:03.22000:37:03.230 temperature differences I move in 00:37:04.93000:37:04.940 increasing X it opens up doesn't it it 00:37:10.05900:37:10.069 opens up and then if you say okay what 00:37:13.56900:37:13.579 about the hot fluid being greater than 00:37:15.64000:37:15.650 the cold fluid then if I look up here 00:37:19.92000:37:19.930 that term is now negative I have e to 00:37:26.31900:37:26.329 the negative X what does that do with 00:37:28.90000:37:28.910 increasing X and theta decreases as I 00:37:32.52900:37:32.539 move it gives me the boat the same that 00:37:35.65000:37:35.660 gives me the right shapes doesn't it in 00:37:38.74000:37:38.750 the limit as C cold and C hot equal each 00:37:42.33900:37:42.349 other I have e to 00:37:44.53900:37:44.549 the 0x it's constant temperature 00:37:49.13000:37:49.140 difference through the heat exchanger I 00:37:52.29900:37:52.309 didn't lose you yet now that we have the 00:37:57.10900:37:57.119 temperature difference anywhere in the 00:38:00.07900:38:00.089 heat exchanger is a function of X we can 00:38:02.08900:38:02.099 derive the log mean temperature method 00:38:05.44900:38:05.459 okay so you just say well don't stop at 00:38:09.16900:38:09.179 X take it all the way to L so if you 00:38:11.98900:38:11.999 evaluate the same equation we had it all 00:38:13.93900:38:13.949 the way to L isn't this the temperature 00:38:15.79900:38:15.809 hot n minus cold out equal to what was 00:38:20.95900:38:20.969 that X equal to 0 times e to the minus 00:38:23.41900:38:23.429 everything here I put P times L that's a 00:38:26.34900:38:26.359 so I have you a I went the whole area 00:38:30.62000:38:30.630 now you just do the algebra and you 00:38:35.23900:38:35.249 recall that the C sub H can be replaced 00:38:38.12000:38:38.130 by Q over the temperature difference of 00:38:41.29900:38:41.309 the temperature change experienced by 00:38:43.27900:38:43.289 the hot fluid as well as the heat 00:38:44.71900:38:44.729 capacity rate of cold is Q divided by 00:38:47.44900:38:47.459 the temperature change of the cold fluid 00:38:49.75900:38:49.769 you put that in you're doing some 00:38:52.40000:38:52.410 algebra and lo and behold you get Q is 00:38:55.78900:38:55.799 equal to UA times a big blob and you 00:39:00.52900:39:00.539 call that the log mean temperature 00:39:02.32900:39:02.339 difference so that big log mean 00:39:06.65000:39:06.660 temperature difference can be read as 00:39:08.35900:39:08.369 talked about the temperature difference 00:39:10.99900:39:11.009 on one side the temperature difference 00:39:13.64000:39:13.650 on the other side and it doesn't matter 00:39:17.12000:39:17.130 which one you put it can be DT 1 minus 00:39:20.50900:39:20.519 DT 2 divided by natural log of V T 1 00:39:23.17900:39:23.189 over DT 2 or DT 2 minus D T 1 does it 00:39:27.03900:39:27.049 these equations it's like hold it which 00:39:29.83900:39:29.849 one is right the one on the left or the 00:39:31.60900:39:31.619 one on the right they're the same how is 00:39:35.23900:39:35.249 that true do this I have the natural log 00:39:37.93900:39:37.949 of a over B how is that related to the 00:39:40.37000:39:40.380 natural log of B over a how is that 00:39:44.74900:39:44.759 related how is the natural log of a over 00:39:47.29900:39:47.309 B related to the natural log of B over a 00:39:51.49000:39:51.500 it's a negative sign and so what happens 00:39:55.67000:39:55.680 is you can flip these in the denominator 00:39:59.26900:39:59.279 just put the negative sign and then you 00:40:02.31900:40:02.329 change up on the top that's all so there 00:40:08.72000:40:08.730 you go that's a log mean temperature 00:40:10.03900:40:10.049 difference it works great if you know 00:40:13.30900:40:13.319 the temperatures of the fluids in and 00:40:15.73000:40:15.740 out it's more challenging it leads to an 00:40:19.27900:40:19.289 iterative solution or approach when you 00:40:22.03900:40:22.049 don't know the outlet temperatures but 00:40:23.87000:40:23.880 you're asked to calculate them you kind 00:40:26.18000:40:26.190 of have to guess what is the outlet 00:40:28.22000:40:28.230 temperatures so that I can get an 00:40:29.56900:40:29.579 estimate of the delta T log mean to get 00:40:31.43000:40:31.440 an estimate acute get an estimate of 00:40:33.17000:40:33.180 outlet temperatures they go back and 00:40:34.81900:40:34.829 correct and it's a leads to an iterative 00:40:37.49000:40:37.500 solution it's not bad it's accurate it's 00:40:41.99000:40:42.000 very accurate the next method is the 00:40:45.82900:40:45.839 effectiveness NTU method we had a brief 00:40:49.09900:40:49.109 introduction well what you can do is you 00:40:52.03900:40:52.049 say okay the genius that thought this up 00:40:54.34900:40:54.359 was truly a genius I don't know who it 00:40:56.32900:40:56.339 was originally somewhere I should 00:40:58.54900:40:58.559 research it right and then we should put 00:41:00.20000:41:00.210 we should replace it and put their name 00:41:01.99000:41:02.000 the Joneses method right and honor Jones 00:41:05.66000:41:05.670 that whoever did it so we we know all of 00:41:10.16000:41:10.170 our heat capacity rates at this point in 00:41:13.78900:41:13.799 the analysis it's easier if you just 00:41:15.79900:41:15.809 pick one to be the dominant heat 00:41:18.04900:41:18.059 capacity right the other would be though 00:41:19.46000:41:19.470 but if you did this twice and you 00:41:21.85900:41:21.869 switched it and said no don't let cold 00:41:23.72000:41:23.730 be the greater than the hot let the hot 00:41:25.73000:41:25.740 be greater than the cold you'll get the 00:41:27.62000:41:27.630 same exact result but it's easier to 00:41:30.79900:41:30.809 just pick one and say this is the 00:41:32.74900:41:32.759 relative difference between them okay so 00:41:34.94000:41:34.950 we're just picking that one so the 00:41:37.24900:41:37.259 effectiveness is Q max Q over Q max so 00:41:41.99000:41:42.000 the minimum in this case in general it's 00:41:44.48000:41:44.490 the minimum of the cold and hot but for 00:41:46.27900:41:46.289 this case it's going to be the hot fluid 00:41:48.58900:41:48.599 is the minimum heat capacity rate hence 00:41:51.44000:41:51.450 the definition of men to use as UA over 00:41:54.04900:41:54.059 si men in this case it would be UA over 00:41:57.01900:41:57.029 CH then we have Q max it's typically in 00:42:02.21000:42:02.220 general seem n times this temperature 00:42:05.18000:42:05.190 difference now it's going to be C H 00:42:06.89000:42:06.900 times that temperature difference and 00:42:09.58900:42:09.599 then the actual rate of heat transfer 00:42:11.41000:42:11.420 unraveling effectiveness will be the 00:42:13.81900:42:13.829 effectiveness times the heat capacity 00:42:16.13000:42:16.140 rate of the hot fluid times the 00:42:17.99000:42:18.000 temperature difference is this exciting 00:42:21.62000:42:21.630 I see one big yawn are we following this 00:42:29.02000:42:29.030 would have been helpful if I would have 00:42:31.30900:42:31.319 pretended that I didn't have my notes 00:42:33.14000:42:33.150 and then press you that I'm able to 00:42:34.67000:42:34.680 drive it would take 20 minutes longer 00:42:37.99000:42:38.000 okay let's slug through professor get 00:42:41.18000:42:41.190 the pill take the pain you know so we 00:42:44.75000:42:44.760 had the hot fluid out as the cold flu 00:42:46.49000:42:46.500 the hot fluid in - that how much heat is 00:42:49.28000:42:49.290 transferred the rate of heat transfer 00:42:50.59900:42:50.609 divided by the CH so the hot fluid out 00:42:56.15000:42:56.160 is equal to what is Q replace it right 00:42:58.97000:42:58.980 here put that in there to see HS cancel 00:43:01.27000:43:01.280 kind of like a little bingo whoo look at 00:43:03.85900:43:03.869 that and we can say well delta T 2 is T 00:43:08.80900:43:08.819 hot out I'm sorry T hot out minus T cold 00:43:12.53000:43:12.540 in and I can replace what is T cold in 00:43:19.45000:43:19.460 right here I just put that into this one 00:43:22.76000:43:22.770 into here do the algebra and I get delta 00:43:25.91000:43:25.920 T 2 on one of the sides is T hot n minus 00:43:29.30000:43:29.310 T cold n times 1 minus epsilon the 00:43:32.32900:43:32.339 effectiveness this what I just did here 00:43:36.55900:43:36.569 needs to be done again focusing on the 00:43:38.96000:43:38.970 cold and you get delta T 1 is equal to T 00:43:43.16000:43:43.170 ha T and minus T cold out without any 00:43:45.29000:43:45.300 effectiveness ok algebra on those now 00:43:50.98000:43:50.990 I'm sorry this one gets delta T 1 after 00:43:54.77000:43:54.780 you substitute for T cold out right here 00:43:59.47000:43:59.480 yet the substitute you get this long 00:44:02.59900:44:02.609 equation for Delta T 1 you recall the 00:44:05.93000:44:05.940 log mean temperature difference stick in 00:44:08.00000:44:08.010 delta T ones delta T 2 delta T 1 delta T 00:44:11.27000:44:11.280 2 they expand you look for things to 00:44:15.05000:44:15.060 cancel you only find that to cancel you 00:44:17.96000:44:17.970 now know that 00:44:19.04000:44:19.050 q is equal to UA log mean temperature 00:44:20.93000:44:20.940 difference so you have the whole log 00:44:25.13000:44:25.140 mean temperature difference put in I 00:44:26.87000:44:26.880 know that Q Max 00:44:28.70000:44:28.710 / C min times T hot n minus T cold in 00:44:33.41000:44:33.420 that all in blue is just multiplied by 00:44:36.17000:44:36.180 unity I just multiplied by 1 that way I 00:44:40.82000:44:40.830 can get the definition of the number of 00:44:44.54000:44:44.550 transfer units I can cancel the 00:44:49.85000:44:49.860 effectiveness times Q Max is equal to Q 00:44:52.85000:44:52.860 so all those three red lines cancel and 00:44:55.01000:44:55.020 these Delta T's one of them set cancel 00:44:57.65000:44:57.660 and here is the final result the number 00:45:00.38000:45:00.390 of transfer units is equal to 1 over 1 00:45:04.31000:45:04.320 minus C R the ratio of heat capacity 00:45:07.31000:45:07.320 rates minimum over maximum times the 00:45:10.10000:45:10.110 natural log 1 minus the effectiveness 00:45:12.32000:45:12.330 ratio of heat capacity rates divided by 00:45:14.75000:45:14.760 1 minus and you put a little star there 00:45:16.94000:45:16.950 and you say we did it so if I'm 00:45:20.75000:45:20.760 interested in knowing if I need the size 00:45:23.54000:45:23.550 that I use that first equation because 00:45:26.06000:45:26.070 NTU the area is embedded in NTU if I 00:45:30.47000:45:30.480 need to size it you can rewrite that 00:45:32.69000:45:32.700 same equation with effectiveness on one 00:45:35.06000:45:35.070 side that's the second equation and then 00:45:38.06000:45:38.070 everything else is on the other side so 00:45:40.19000:45:40.200 if I know the area and I want to know 00:45:42.11000:45:42.120 the actual amount of heat transfer then 00:45:44.51000:45:44.520 I would get the effectiveness and then 00:45:46.28000:45:46.290 use that to get the actual Q so use this 00:45:49.31000:45:49.320 second equation to rate and use the 00:45:53.21000:45:53.220 first equation to size the heat 00:45:55.61000:45:55.620 exchanger they're the same equation 00:45:58.81000:45:58.820 they're the same equation they're 00:46:01.07000:46:01.080 mathematically the same alright do I 00:46:04.73000:46:04.740 have enough time to solve the problem 00:46:07.66000:46:07.670 water enters a counterflow concentric 00:46:11.03000:46:11.040 tube heat exchanger at 150 pound mass 00:46:14.27000:46:14.280 per minute so our heat exchanger is 00:46:18.35000:46:18.360 gonna be like this and I'm gonna divide 00:46:21.20000:46:21.210 it like that let's just do the hot fluid 00:46:24.56000:46:24.570 on one side and we'll put the cold flu 00:46:28.59900:46:28.609 on the other side and the water enters 00:46:32.70900:46:32.719 it's going from sixty degrees to one 00:46:36.37000:46:36.380 hundred and forty is the water the cold 00:46:38.49900:46:38.509 fluid or the hot fluid the temperature 00:46:41.73900:46:41.749 of the cold in is sixty degrees F naught 00:46:46.17900:46:46.189 to C and it goes out temperature cold 00:46:49.02900:46:49.039 out is one hundred and forty degrees F 00:46:51.57900:46:51.589 Troop it's the cold fluid waters the 00:46:53.94900:46:53.959 cold fluid it's so we have the mass flow 00:46:57.42900:46:57.439 rate of the cold fluid is one hundred 00:46:59.41000:46:59.420 and fifty pounds per minute they didn't 00:47:02.76900:47:02.779 tell me the specific heat of water it's 00:47:09.45900:47:09.469 about one pound 00:47:10.39000:47:10.400 BTU per pound degree F that's specific 00:47:13.71900:47:13.729 heat of water you would get that out of 00:47:15.60900:47:15.619 the table and her just remember it 00:47:17.49900:47:17.509 what's doing the heating so the water is 00:47:21.15000:47:21.160 the colder fluid oil is the hot fluid it 00:47:27.03900:47:27.049 comes in temperature hot in of two 00:47:30.69900:47:30.709 hundred and forty degrees F and they 00:47:33.18900:47:33.199 tell you the temperature the hot out is 00:47:35.70900:47:35.719 equal to 80 degrees F notice that the 00:47:40.77900:47:40.789 oil comes out lower temperature than the 00:47:43.02900:47:43.039 water goes out makes sense yeah and the 00:47:50.16900:47:50.179 oil has a specific heat let me put it 00:47:53.04900:47:53.059 over here a specific heat of the hot 00:47:55.98900:47:55.999 fluid is point four eight beat to use 00:47:59.31900:47:59.329 per pound mass degree F the overall heat 00:48:03.66900:48:03.679 transfer coefficient is fifty two point 00:48:05.55900:48:05.569 eight BTU per hour per foot squared 00:48:08.10900:48:08.119 degrees what information did that just 00:48:10.39000:48:10.400 give us their cap you that's right 00:48:13.32900:48:13.339 fifty two point a etc what's the 00:48:18.09900:48:18.109 question 00:48:18.83900:48:18.849 determine the heat transfer area what 00:48:23.55900:48:23.569 are we trying to do are we trying to 00:48:25.50900:48:25.519 rate it or size it size it yeah 00:48:28.80900:48:28.819 determine the heat transfer area we're 00:48:31.15000:48:31.160 gonna use the effectiveness NTU method 00:48:32.97900:48:32.989 how are we going to solve this problem 00:48:39.68000:48:39.690 think in general that I'm going to 00:48:42.35900:48:42.369 eventually get NTU equal to some 00:48:46.17000:48:46.180 function of effectiveness and see our 00:48:49.19000:48:49.200 ratio of heat capacity rates once I get 00:48:52.82900:48:52.839 the number of transfer units then I 00:48:55.10900:48:55.119 recall that the number of transfer units 00:48:57.12000:48:57.130 is UA 00:48:57.80900:48:57.819 over C min and so the area is the number 00:49:01.89000:49:01.900 of transfer units times C min divided by 00:49:06.56900:49:06.579 U so I got to get the number of transfer 00:49:10.01900:49:10.029 units then unravel it it's like it's a 00:49:13.25900:49:13.269 dimensionless ratio isn't it is it NTU 00:49:17.03900:49:17.049 dimensionless it's purely dimensionless 00:49:19.55900:49:19.569 yep so okay well I need to get the 00:49:23.27900:49:23.289 effectiveness well how am I gonna get 00:49:25.47000:49:25.480 the effectiveness well actually can I 00:49:27.93000:49:27.940 calculate Q actual what is the rate of 00:49:30.66000:49:30.670 heat transfer that occurs in this heat 00:49:33.05900:49:33.069 exchanger sure you would say either from 00:49:39.56900:49:39.579 the perspective of the cold fluid which 00:49:42.18000:49:42.190 has a heat capacity rate of 150 beat to 00:49:47.13000:49:47.140 use per minute degree F or the hot fluid 00:49:53.88000:49:53.890 they don't give us a capacity rate of 00:49:56.37000:49:56.380 the hot fluid do they but can they is is 00:49:59.16000:49:59.170 this equal to the cold fluid times the 00:50:01.49900:50:01.509 temperature of the cold out minus 00:50:04.55900:50:04.569 temperature of the cold in its 00:50:10.20000:50:10.210 conservation of energy the cold fluid 00:50:12.29900:50:12.309 underwent this change mass flow rate of 00:50:14.78900:50:14.799 the colds given heat the specific heat 00:50:17.51900:50:17.529 is cold is given so we calculate the Q 00:50:20.09900:50:20.109 and there's 12,000 BTUs per minute 00:50:24.98000:50:24.990 well there's 12,000 BTUs per minute 00:50:28.01900:50:28.029 getting into the water where is it 00:50:29.54900:50:29.559 coming from no oil and if it's coming 00:50:33.18000:50:33.190 from the oil then what we say is what 00:50:35.54900:50:35.559 comes out of the oil goes into the water 00:50:37.92000:50:37.930 so it's 12,000 so the Q is equal to the 00:50:41.40000:50:41.410 C of the hot times the temperature of 00:50:43.74000:50:43.750 the hot n minus temperature of the hot 00:50:46.92000:50:46.930 out true I do a little check I just 00:50:50.03900:50:50.049 calculated the Q 00:50:51.79000:50:51.800 have the two temperatures of the hot 00:50:53.26000:50:53.270 fluid I can get the heat capacity rate 00:50:56.02000:50:56.030 of the hot fluid the heat capacity rate 00:50:58.90000:50:58.910 of the hot fluid is calculated to be 75 00:51:02.85000:51:02.860 BTUs per minute degree F do a quick 00:51:08.02000:51:08.030 comparison which one is the minimum so C 00:51:15.07000:51:15.080 min is of the hot and it's 75 BTU per 00:51:20.58000:51:20.590 minute degree F I'm gonna need this C 00:51:23.92000:51:23.930 sub R what is C sub R the ratio of 00:51:27.40000:51:27.410 minimum to maximum so what's the minimum 00:51:31.09000:51:31.100 75 what's the maximum 150 it comes out 00:51:34.33000:51:34.340 to 0.5 Oh have C sub R is 1/2 00:51:38.71000:51:38.720 okay now I know Q what I really need and 00:51:47.92000:51:47.930 I just calculated C sub R right here and 00:51:51.28000:51:51.290 I if I get the effectiveness then I can 00:51:54.10000:51:54.110 just plug it into my equation to 00:51:55.75000:51:55.760 calculate the number of transfer units 00:51:57.52000:51:57.530 well what equation am I going to plug 00:51:58.90000:51:58.910 into either version a or version B which 00:52:05.26000:52:05.270 equation yeah we're going to be we want 00:52:12.49000:52:12.500 to get n to use so we're gonna stick it 00:52:15.16000:52:15.170 into that second version B I said bees 00:52:18.40000:52:18.410 that that equation right there that's 00:52:21.31000:52:21.320 our roadmap okay so I need to get the 00:52:24.64000:52:24.650 effectiveness but how do I get 00:52:26.26000:52:26.270 defectiveness I need to get the maximum 00:52:28.30000:52:28.310 possible 00:52:28.99000:52:29.000 what is that C min times temperature hot 00:52:32.17000:52:32.180 n minus temperature cold in and so the 00:52:36.64000:52:36.650 maximum rate of heat transfer is 13 500 00:52:42.18000:52:42.190 BTUs per min so the effectiveness is 00:52:47.02000:52:47.030 what I actually get divided by the 00:52:49.69000:52:49.700 maximum it's 12,000 divided by 13 500 it 00:52:55.69000:52:55.700 comes in at 0.8 a 00:53:00.59000:53:00.600 eight-nine 89% close to 90% a little bit 00:53:07.23000:53:07.240 under 90% we know the effectiveness the 00:53:10.92000:53:10.930 NT use we use that equation the NTU is 00:53:13.92000:53:13.930 equal to and I'll just rewrite it 00:53:15.44000:53:15.450 natural log of 1 minus the effectiveness 00:53:19.11000:53:19.120 times the ratio of heat capacity rates 00:53:22.26000:53:22.270 divided by 1 minus effectiveness divided 00:53:24.63000:53:24.640 by 1 minus C sub R when you do that the 00:53:28.32000:53:28.330 number of transfer units comes in at 3.2 00:53:31.46000:53:31.470 1 8 9 00:53:33.95000:53:33.960 are there any units with that not it's 00:53:38.43000:53:38.440 dimensionless but when we unravel it up 00:53:41.94000:53:41.950 here to get the area we'll multiply it 00:53:46.71000:53:46.720 by C min we'll divide by cap you the 00:53:49.56000:53:49.570 overall heat transfer coefficient and we 00:53:51.78000:53:51.790 calculate the area to be 274 square feet 00:53:59.18000:53:59.190 it's a large area does that look good 00:54:04.64000:54:04.650 guess what I like to do we solve a 00:54:06.84000:54:06.850 problem but then we turn it around and 00:54:08.79000:54:08.800 change it up just a little bit and so 00:54:11.82000:54:11.830 I'm ready to ask you for a change so the 00:54:16.53000:54:16.540 same wording up here instead of saying 00:54:20.07000:54:20.080 something about the the sizing it we say 00:54:27.69000:54:27.700 no what's we're going to do is the water 00:54:30.09000:54:30.100 flow rate it's gonna change it used to 00:54:32.97000:54:32.980 be 150 used to be 150 pounds per minute 00:54:36.87000:54:36.880 we're now going to change it to 110 00:54:40.05000:54:40.060 pounds per minute what did the mass flow 00:54:43.08000:54:43.090 rate of the water do went down now right 00:54:50.22000:54:50.230 away the temperature of the water going 00:54:52.86000:54:52.870 out we have to relax the temperature of 00:54:56.01000:54:56.020 the oil going out we have to relax 00:54:58.56000:54:58.570 because hey that we just changed an 00:55:01.29000:55:01.300 input in the real system I change one of 00:55:03.63000:55:03.640 those the mass flow rate of the cold 00:55:05.22000:55:05.230 fluid 00:55:07.57900:55:07.589 the area of the size has not changed so 00:55:10.81900:55:10.829 I'm gonna stay with my area to be 274 00:55:15.04900:55:15.059 foot square 00:55:15.85900:55:15.869 this is really just like you might think 00:55:17.50900:55:17.519 hey I sized that piece of equipment and 00:55:19.67000:55:19.680 you guys in the plant you just changed 00:55:21.79900:55:21.809 the flow rates of course now our outlet 00:55:25.45900:55:25.469 temperatures are different than what I 00:55:26.98900:55:26.999 told you they would be because you 00:55:29.29900:55:29.309 changed my Inlet flow rates you've got 00:55:31.09900:55:31.109 to put it back to where I told you right 00:55:33.40000:55:33.410 something like that you can see this 00:55:35.74900:55:35.759 dialog playing out well before I go 00:55:38.50900:55:38.519 through the brute force calculation of 00:55:40.67000:55:40.680 what is the new exit water temperature 00:55:43.06900:55:43.079 the temperature of the cold fluid outlet 00:55:47.44900:55:47.459 I want to ask you a few questions don't 00:55:51.43900:55:51.449 get psyched out but these are the type 00:55:55.13000:55:55.140 of questions so it's really hard to 00:55:56.74900:55:56.759 answer given that problem just set it up 00:56:00.17000:56:00.180 all we did was same size we got to size 00:56:02.74900:56:02.759 now somebody's reduced the flow rate of 00:56:05.17900:56:05.189 the cold fluid the water through the 00:56:07.13000:56:07.140 system will cue change will the 00:56:11.56900:56:11.579 temperature the cold on the outlet 00:56:13.13000:56:13.140 change will the temperature of the hot 00:56:14.92900:56:14.939 on outlet change will the effectiveness 00:56:17.29900:56:17.309 change will the number transfer units 00:56:19.09900:56:19.109 change and we'll see ratio change you're 00:56:21.43900:56:21.449 getting from very physical to abstract 00:56:23.41900:56:23.429 aren't we let's handle the Q first huh 00:56:29.63000:56:29.640 or which one is easiest the temperature 00:56:32.63000:56:32.640 the cold fluid out is probably the 00:56:34.42900:56:34.439 easiest it used to come in at 60 and go 00:56:39.65000:56:39.660 out at 140 but this was now changed to 00:56:42.79900:56:42.809 one one oh what happens to the outlet 00:56:46.45900:56:46.469 temperature of the cold fluid it was 140 00:56:49.54900:56:49.559 is it going to go up is it going to be 00:56:51.49900:56:51.509 now 150 is it going to go down or is it 00:56:55.60900:56:55.619 going to remain the same the temperature 00:56:57.58900:56:57.599 of the cold fluid on the outlet 00:57:05.01000:57:05.020 you say up up up up all right so let me 00:57:13.51000:57:13.520 see if I have the numbers here it'll go 00:57:19.12000:57:19.130 up to 164 degrees F all right now that 00:57:29.08000:57:29.090 we have that one correctly answered 00:57:30.79000:57:30.800 let's take a look at this one the 00:57:33.04000:57:33.050 temperature the hot fluid on the outlet 00:57:34.84000:57:34.850 it was 80 it was 80 how about if I do 00:57:40.00000:57:40.010 this and so I want to really get 00:57:44.14000:57:44.150 everybody to answer this question so I'm 00:57:46.96000:57:46.970 gonna pause and walk around well maybe 00:57:52.36000:57:52.370 this wasn't the easiest question isn't 00:57:54.28000:57:54.290 this not possibly a little easier let's 00:57:58.60000:57:58.610 go solve this problem so the water went 00:58:04.03000:58:04.040 from 60 to 140 but now it went from 60 00:58:09.46000:58:09.470 to 100 64 degrees F this is the new case 00:58:13.00000:58:13.010 because of the lower flow rate what did 00:58:15.46000:58:15.470 the queue change because isn't Q equal 00:58:21.22000:58:21.230 to the heat capacity rate of the cold 00:58:23.23000:58:23.240 fluid times the temperature change of 00:58:25.12000:58:25.130 the cold fluid and isn't the temperature 00:58:27.07000:58:27.080 change greater than it was before isn't 00:58:30.22000:58:30.230 it also Q is equal to the heat capacity 00:58:34.06000:58:34.070 flow rate at hot fluid times the 00:58:35.59000:58:35.600 temperature change it hot fluid now that 00:58:38.20000:58:38.210 it came in 80 and it used to go out I'm 00:58:42.13000:58:42.140 sorry it came in 240 and it used to go 00:58:45.28000:58:45.290 out 80 it's still coming in 240 so this 00:58:51.04000:58:51.050 has to go lower than 80 did the heat 00:58:55.00000:58:55.010 capacity rate of the cold fluid change 00:58:58.05000:58:58.060 going down so what happened to the 00:59:05.17000:59:05.180 actual Q this went up yeah but this went 00:59:09.52000:59:09.530 down more 00:59:13.34900:59:13.359 and so you almost have to slug through 00:59:15.47900:59:15.489 the numbers instead of getting 12,000 00:59:17.75900:59:17.769 beat to use per minute you only got 11 00:59:20.95900:59:20.969 457b tears per minute and if you only 00:59:26.43000:59:26.440 get 11 500 instead of 1200 for 12,000 00:59:31.04900:59:31.059 what happens here it comes out at 87 00:59:38.66000:59:38.670 degrees F alright alright how about the 00:59:45.56900:59:45.579 effectiveness it used to be almost 90% 00:59:50.53900:59:50.549 well you have to work with these things 00:59:53.00900:59:53.019 and it goes down to about 85% and then 00:59:57.35900:59:57.369 what about the number of transfer units 00:59:59.13000:59:59.140 it was 3.2 - well what's the definition 01:00:02.33901:00:02.349 a number of transfer units you a over C 01:00:06.02901:00:06.039 min did the length of the heat exchange 01:00:08.51901:00:08.529 of change or the area change no that you 01:00:11.72901:00:11.739 change no same you how about the minimum 01:00:14.91001:00:14.920 heat capacity well the minimum was 01:00:16.70901:00:16.719 either from the cold fluid or the hot 01:00:19.94901:00:19.959 fluid the hot fluid last time gave us 01:00:23.03901:00:23.049 the minimum true it was 75 the cold 01:00:26.27901:00:26.289 fluid was 150 but with the new flow rate 01:00:30.05901:00:30.069 it's a hundred and ten which one's the 01:00:34.34901:00:34.359 minimum it's still the hot so guess what 01:00:39.42001:00:39.430 did not change the number of transfer 01:00:44.03901:00:44.049 units did not change and then what about 01:00:48.15001:00:48.160 the ratio of heat capacity rates 01:00:50.09901:00:50.109 it was 0.5 0.5 was the 75 over 150 but 01:00:57.39001:00:57.400 now it's 75 over 1 100 what's happened 01:01:00.68901:01:00.699 to the heat capacity rate nudged up a 01:01:05.69901:01:05.709 little bit hidden it so it increased 01:01:10.24001:01:10.250 here it is on plots because these are 01:01:12.79001:01:12.800 the equations we were using and they're 01:01:14.74001:01:14.750 pretty abstract but here is in a plot we 01:01:19.15001:01:19.160 had the first case in light blue where 01:01:21.31001:01:21.320 it was three point two two for the 01:01:23.29001:01:23.300 number of transfer units and the ratio 01:01:26.11001:01:26.120 of men to maximum was 0.5 so there's the 01:01:29.59001:01:29.600 curve of 0.5 it's right where that blue 01:01:31.93001:01:31.940 dot is we read off defectiveness it's 01:01:35.41001:01:35.420 right around 90% a little bit low lower 01:01:37.66001:01:37.670 than 90% 89% right we changed it what 01:01:42.85001:01:42.860 happened we slowed down the cold fluid 01:01:46.65001:01:46.660 the ratio of heat capacity rates went 1 01:01:50.38001:01:50.390 110 whoops 75 over 1 110 which goes a 01:01:55.96001:01:55.970 little bit higher almost point 7 well 01:01:57.85001:01:57.860 they don't have 0.7 so you interpolate 01:02:00.01001:02:00.020 between the line of 0.5 and point 7 5 so 01:02:03.46001:02:03.470 there's my interpolation for the heat 01:02:06.46001:02:06.470 capacity rate of 0.68 the same number of 01:02:09.85001:02:09.860 transfer units what the defectiveness 01:02:11.56001:02:11.570 dude dropped a little so you can see it 01:02:15.31001:02:15.320 on plots as well as work it out in 01:02:18.40001:02:18.410 equations okay I think I'm done with my 01:02:22.45001:02:22.460 time sorry I didn't slug through that 01:02:24.70001:02:24.710 one numerically but I gave you the 01:02:27.31001:02:27.320 answers did I not so the answer is it's 01:02:32.14001:02:32.150 that's the change that's the change it 01:02:35.74001:02:35.750 goes from 80 to 87 degrees F goes from 01:02:40.39001:02:40.400 89 to 9 85 percent stays the same no 01:02:44.77001:02:44.780 change and this one changes from point 5 01:02:49.63001:02:49.640 to what point six what does I say eight 01:02:53.26001:02:53.270 point six eight point six eight thank 01:02:56.86001:02:56.870 you very much
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