00:00:01.220 we have a shell and tube heat exchanger 00:00:03.83000:00:03.840 that has 20 tubes and each of the tubes 00:00:07.09900:00:07.109 undergo two passes through the shell and 00:00:10.28000:00:10.290 there is one shell pass for the fluid on 00:00:13.31000:00:13.320 the shell side so here's our typical 00:00:16.07000:00:16.080 shell and we're gonna have an end let me 00:00:21.32000:00:21.330 just put an end on it like this and the 00:00:23.72000:00:23.730 inlet end and this is divided and we're 00:00:26.81000:00:26.820 gonna bring some fluid in all right the 00:00:31.18900:00:31.199 hot water comes in 00:00:33.59000:00:33.600 so I'll just color code it red then it 00:00:35.66000:00:35.670 goes into how many tubes twenty tubes 00:00:40.91000:00:40.920 and number of tubes is twenty then it 00:00:44.93000:00:44.940 comes out and goes through twenty tubes 00:00:49.43000:00:49.440 out and collected and goes out okay 00:00:55.02900:00:55.039 there's so there's two passes through 00:00:58.91000:00:58.920 the shell the first pass and then the 00:01:01.27900:01:01.289 second pass through the shell it really 00:01:03.26000:01:03.270 doesn't specify if there's a u-turn here 00:01:05.81000:01:05.820 or if it just mixes as I've shown it 00:01:08.84000:01:08.850 there's no distinction all right and 00:01:13.16000:01:13.170 it's the fluid on the shell comes in 00:01:15.23000:01:15.240 here and it's gonna go out there so it 00:01:18.49900:01:18.509 really only goes through one pass of the 00:01:20.63000:01:20.640 shell yes there's some baffles to 00:01:23.51000:01:23.520 promote the flow going back and forth 00:01:26.84000:01:26.850 across the tubes like that 00:01:33.06900:01:33.079 so the flow goes back and forth on the 00:01:35.74900:01:35.759 shell side across the tubes the length 00:01:38.66000:01:38.670 of each pass is four meters the tube has 00:01:47.56000:01:47.570 15 millimeter inner and an 18 millimeter 00:01:50.63000:01:50.640 outer diameter and hot water at 40 point 00:01:56.17900:01:56.189 four kilograms per second so the mass 00:01:58.76000:01:58.770 flow rate of the hot which is water is 00:02:03.17000:02:03.180 flowing at zero point four Oh killer 00:02:06.53000:02:06.540 grams per second in two entering at 77 00:02:10.96900:02:10.979 so it's flowing in the tubes and it 00:02:13.26000:02:13.270 enters temperature hot in let me try and 00:02:15.84000:02:15.850 sketch this temperature hot in is 77 00:02:19.14000:02:19.150 degrees C and exits the temperature hot 00:02:24.30000:02:24.310 out is 37 degrees C oil is our cooler 00:02:32.04000:02:32.050 fluid it blows in the shell side it the 00:02:36.00000:02:36.010 temperature cold in is 7 degrees C and 00:02:40.59000:02:40.600 the temperature cold out is 37 degrees C 00:02:47.36000:02:47.370 calculate the convection coefficient for 00:02:51.30000:02:51.310 the tube outer surface so first 00:02:54.78000:02:54.790 questions first what symbol and what 00:02:57.99000:02:58.000 expected units for my answer so we want 00:03:02.85000:03:02.860 to calculate an H but it's on the tube 00:03:06.72000:03:06.730 outer surface so any subscripts on that 00:03:09.60000:03:09.610 H H Oh Edie typical unit true okay now 00:03:22.76000:03:22.770 it's going to be a long route to get H 00:03:25.98000:03:25.990 naught but it's embedded in the overall 00:03:30.12000:03:30.130 heat transfer coefficient you and so we 00:03:33.81000:03:33.820 recall the equation one over the overall 00:03:35.91000:03:35.920 heat transfer coefficients equal to one 00:03:37.95000:03:37.960 over the H on the inside area inside 00:03:41.79000:03:41.800 plus one over the H outside area outside 00:03:44.67000:03:44.680 and as long as that area matches you a 00:03:48.03000:03:48.040 lot of times we don't put a eye on you 00:03:51.42000:03:51.430 and a or oo on you na we just match it 00:03:54.75000:03:54.760 as UA that make Wei Zhi makes sense so 00:03:58.89000:03:58.900 we can take into account the slightly 00:04:01.08000:04:01.090 larger outer diameter than the slightly 00:04:04.41000:04:04.420 smaller inner diameter of the tube okay 00:04:08.84000:04:08.850 so if you want to calculate the 00:04:11.13000:04:11.140 convection coefficient on the outer 00:04:13.14000:04:13.150 surface I would calculate UA and H and 00:04:17.88000:04:17.890 the inner surface the areas on the inner 00:04:21.06000:04:21.070 surface those are pretty straightforward 00:04:22.65000:04:22.660 true this would be the PI D 00:04:26.89000:04:26.900 on the inner two L's because there's 00:04:30.15900:04:30.169 back and forth and that's the area for 00:04:33.31000:04:33.320 one tube and how many tubes do we have 00:04:37.71000:04:37.720 20 would that give me the total area 00:04:42.07000:04:42.080 inner and likewise what about the total 00:04:46.42000:04:46.430 area outer PI D outer - ly - L each tube 00:04:54.01000:04:54.020 has two passes and then Y ends of T Y 00:04:58.48000:04:58.490 the number of tubes because there's 00:05:01.60000:05:01.610 twenty of them makes sense all right now 00:05:07.18000:05:07.190 let's let's attack H inner first how am 00:05:12.27900:05:12.289 I going to calculate the convection 00:05:14.37900:05:14.389 coefficient on the inside of the tube 00:05:19.74000:05:19.750 it's forced convection so we're probably 00:05:23.37900:05:23.389 going to check the reynolds numbers see 00:05:25.12000:05:25.130 if it's laminar turbulent that's over 00:05:27.73000:05:27.740 2300 turbulent i'll look for a new sort 00:05:30.64000:05:30.650 correlation the name of the most popular 00:05:33.43000:05:33.440 easiest one especially on exams in this 00:05:35.46900:05:35.479 semester would be the d dis bolter i 00:05:37.24000:05:37.250 will give me the new salt number what's 00:05:39.96900:05:39.979 add the new salt number on the inside i 00:05:41.83000:05:41.840 get the h on the inside true so in order 00:05:46.30000:05:46.310 to get it I need to get fluid properties 00:05:49.52900:05:49.539 so what is the temperature average that 00:05:54.10000:05:54.110 I use to evaluate for the water because 00:05:58.81000:05:58.820 water fluid properties are temperature 00:06:00.79000:06:00.800 dependent it'll be the 77 in 37 add 00:06:07.93000:06:07.940 those two together and divide by 2 00:06:11.87900:06:11.889 that'll be 57 degrees C and when I look 00:06:16.54000:06:16.550 in the table they have it in Kelvin so I 00:06:18.40000:06:18.410 add 273 it's 330 Kelvin and it's a line 00:06:22.00000:06:22.010 in the table and I'm so thankful because 00:06:24.43000:06:24.440 if it's a line in the table do I need to 00:06:26.26000:06:26.270 interpolate no so I could get just read 00:06:29.26000:06:29.270 off the properties what properties are 00:06:31.27000:06:31.280 going to be needed to calculate that 00:06:33.15900:06:33.169 Reynolds number for flow inside of one 00:06:36.07000:06:36.080 tube you can do 00:06:38.92000:06:38.930 give me two favorite equations to 00:06:41.11000:06:41.120 calculate Reynolds number for flow 00:06:42.79000:06:42.800 inside a tube Rho V D / new war true now 00:06:57.70000:06:57.710 somebody says I know the diameter inside 00:07:01.56000:07:01.570 that's easy that was 00:07:04.15000:07:04.160 eight no fifteen millimeters 0.015 meter 00:07:07.71900:07:07.729 I need to get the viscosity of the water 00:07:10.54000:07:10.550 at 330 Kelvin for 89 times 10 to the 00:07:16.54000:07:16.550 minus 6 units of Newton's second per 00:07:20.68000:07:20.690 meter squared and the mass flow rate I 00:07:25.18000:07:25.190 have to think about this a little bit is 00:07:27.46000:07:27.470 it the mass flow rate of the water they 00:07:30.10000:07:30.110 give it to me as point four kilograms 00:07:32.17000:07:32.180 per second but is that through each tube 00:07:35.29000:07:35.300 or just coming into the heat exchanger 00:07:37.65900:07:37.669 and then passing through and separating 00:07:40.36000:07:40.370 and going into twenty different tubes 00:07:42.36000:07:42.370 each it's a total mass flow rate water 00:07:48.15900:07:48.169 flow at 0.4 kilograms per second flows 00:07:51.61000:07:51.620 inside the tubes but it enters at 77 but 00:07:54.87900:07:54.889 it's not I know that you could be 00:07:56.62000:07:56.630 interpreted either way but it's the 00:07:58.77900:07:58.789 total flow for all of them so the MDOT 00:08:01.75000:08:01.760 is going to be 0.40 kilograms per second 00:08:05.05000:08:05.060 divided by the number of tubes from 00:08:06.85000:08:06.860 there's 20 tubes so you divide by 20 00:08:14.15900:08:14.169 point o2 00:08:20.15900:08:20.169 kg/s and when you calculate the Reynolds 00:08:23.08000:08:23.090 number we calculate a Reynolds number 00:08:26.08000:08:26.090 which is 3472 how do I interpret that 00:08:31.62900:08:31.639 Reynolds number barely turbulent but 00:08:35.14000:08:35.150 turbulent nonetheless okay you could 00:08:39.88000:08:39.890 check the entrance region how long will 00:08:42.21900:08:42.229 it have to go before it's fully 00:08:43.60000:08:43.610 developed inside each of those tubes 00:08:47.94000:08:47.950 rule of thumb how long its turbulent 00:08:52.60000:08:52.610 flow tendis ten diameters so so the 00:08:59.35000:08:59.360 length for entrance is around ten 00:09:01.66000:09:01.670 diameters a diameter is point zero one 00:09:04.75000:09:04.760 five so it's a point one five meter 00:09:07.87000:09:07.880 length to be fully developed it's 00:09:10.03000:09:10.040 forward meters long I'm going to neglect 00:09:11.76900:09:11.779 entrance length it's fully developed the 00:09:14.62000:09:14.630 whole lifetime 00:09:15.28000:09:15.290 true so we calculate the new salt number 00:09:19.14000:09:19.150 0.023 00:09:21.00000:09:21.010 Reynolds to the point eight Prandtl to 00:09:23.80000:09:23.810 either the point four or point three you 00:09:26.98000:09:26.990 look at the correlation it's point three 00:09:28.99000:09:29.000 when the fluid inside the tube is being 00:09:31.14000:09:31.150 cooled not heated the hot water is being 00:09:35.59000:09:35.600 cooled as it flows through the tubes so 00:09:39.28000:09:39.290 we use adidas Boelter correlation we 00:09:41.82900:09:41.839 calculate a new salt number which is 00:09:45.64000:09:45.650 twenty two point one the convection 00:09:48.37000:09:48.380 coefficient on the inside new salt times 00:09:51.69900:09:51.709 K divided by D you have to go back and 00:09:55.84000:09:55.850 get the thermal conductivity of water at 00:09:58.87000:09:58.880 three hundred and thirty Kelvin and you 00:10:01.60000:10:01.610 get the H's 956 watts per meter squared 00:10:07.21000:10:07.220 degrees C a lot of work to get H inner 00:10:13.98000:10:13.990 so we finally got this term calculated 00:10:17.17000:10:17.180 we're looking to calculate H dot 00:10:19.59000:10:19.600 everything in this equation I know 00:10:21.73000:10:21.740 except for you a how am I going to 00:10:26.35000:10:26.360 calculate UA 00:10:32.92000:10:32.930 yeah let's go ahead and use the 00:10:35.26900:10:35.279 effectiveness NTU method so I'm gonna 00:10:39.38000:10:39.390 have to make some more room here I'm 00:10:41.84000:10:41.850 sorry can i I'm just gonna have to add 00:10:45.20000:10:45.210 another sheet okay so what I need to do 00:10:48.56000:10:48.570 is I need to find you a to find you a 00:10:52.88000:10:52.890 the pattern is this number of transfer 00:10:55.31000:10:55.320 units as you a over C min hence if I 00:10:58.40000:10:58.410 could get the number of transfer units 00:10:59.90000:10:59.910 then in you a is equal to number of 00:11:02.51000:11:02.520 transfer units times C min right alright 00:11:06.44000:11:06.450 how do I find the number of transfer 00:11:08.30000:11:08.310 units well I'm gonna look for a function 00:11:10.91000:11:10.920 of effectiveness and the ratio of heat 00:11:15.07900:11:15.089 capacity rates well I'll have to 00:11:18.56000:11:18.570 calculate the heat capacity rate of the 00:11:20.81000:11:20.820 cold fluid the capacity rate of cold 00:11:24.35000:11:24.360 fluids mass flow rate of the cold times 00:11:26.21000:11:26.220 specific heat at cold and that comes in 00:11:30.11000:11:30.120 at 22 31 watts per degree C heat 00:11:37.51900:11:37.529 capacity rate of the hot fluid is the 00:11:42.92000:11:42.930 mass flow rate of the hot fluid times 00:11:44.72000:11:44.730 specific heat of the hot fluid let me go 00:11:48.59000:11:48.600 back to my problem the hot fluid was the 00:11:52.28000:11:52.290 water I needed to get the specific heat 00:11:54.80000:11:54.810 at 330 Kelvin what about the oil I 00:11:58.73000:11:58.740 skipped that a little bit didn't I for 00:12:01.25000:12:01.260 the oil the oil you calculate the 00:12:05.48000:12:05.490 average temperature is the temperature 00:12:08.48000:12:08.490 coming in of 7 plus the temp 37 divided 00:12:13.76000:12:13.770 by 2 00:12:14.32900:12:14.339 it comes in average of 22 degrees C 00:12:19.85000:12:19.860 which is 295 Kelvin and so we get the 00:12:24.11000:12:24.120 fluid properties for oil at that 295 so 00:12:28.81900:12:28.829 we can get for the oil the density the 00:12:31.67000:12:31.680 specific heat we can get the SKA s'ti 00:12:34.13000:12:34.140 thermal conductivity Prandtl number 00:12:35.78000:12:35.790 whatever properties we want alright so 00:12:39.67000:12:39.680 that was for the cold fluid to give us 00:12:42.65000:12:42.660 the 00:12:43.78000:12:43.790 heat capacity rate of the of the oil is 00:12:48.77000:12:48.780 2 to 3 1 the heat capacity rate of the 00:12:51.95000:12:51.960 hot fluid 1 6 7 4 so C sub R the ratio 00:12:59.18000:12:59.190 is 0.75 all right so we have this part I 00:13:06.13000:13:06.140 need to get the effectiveness the 00:13:09.46000:13:09.470 effectiveness is the actual Q divided by 00:13:13.10000:13:13.110 Q maximum what is my actual Q the actual 00:13:20.09000:13:20.100 Q is known from the its 60 6944 watts 00:13:28.51000:13:28.520 and the Q max is C min times temperature 00:13:35.24000:13:35.250 hot in - temperature cold in and that 00:13:39.35000:13:39.360 came in 117 152 watts 00:13:45.04000:13:45.050 hence the effectiveness we back 00:13:47.36000:13:47.370 calculate to be 57% so we have now the 00:13:51.56000:13:51.570 effectiveness well I have to go and I 00:13:55.58000:13:55.590 have to find the right correlation for a 00:13:59.42000:13:59.430 head exchanger like this where I have 00:14:01.60000:14:01.610 two two passes one shall pass 00:14:05.90000:14:05.910 I can do it graphically so what did we 00:14:10.76000:14:10.770 just get we had about 57% for the 00:14:15.95000:14:15.960 effectiveness so somewhere along this 00:14:18.02000:14:18.030 line and what did we have for the ratio 00:14:21.26000:14:21.270 C sub R 0.75 is so we can read off the 00:14:28.25000:14:28.260 number of transfer units little less 00:14:30.53000:14:30.540 than one point five one point four three 00:14:33.82000:14:33.830 no I didn't do that with three digits 00:14:36.41000:14:36.420 reading a chart but you can read a chart 00:14:38.42000:14:38.430 and get close or you can go to an 00:14:41.77000:14:41.780 equation shell and tube heat exchanger 00:14:45.71000:14:45.720 one shall pass with two four or multiple 00:14:50.36000:14:50.370 tube passes well we have two tube passes 00:14:52.88000:14:52.890 it's a multi little step you have to 00:14:55.37000:14:55.380 calculate this parameter 00:14:57.07900:14:57.089 if you calculate the parameter a it 00:14:59.11900:14:59.129 comes in to 1.4 when you calculate it 00:15:01.45900:15:01.469 you put it up into this next equation 00:15:03.22900:15:03.239 for the number of transfer units and 00:15:04.99900:15:05.009 there it's one point four three three 00:15:06.97900:15:06.989 four too many digits but there you go so 00:15:10.69900:15:10.709 that's how you would calculate the 00:15:12.16900:15:12.179 number of transfer units one shall pass 00:15:15.61900:15:15.629 to two passes so we calculate this to be 00:15:21.91900:15:21.929 one point four three three four 00:15:25.02900:15:25.039 that goes into here with the C min we 00:15:31.36900:15:31.379 calculate UA to be two hundred and three 00:15:35.44900:15:35.459 nine nine two thousand three hundred 00:15:37.33900:15:37.349 ninety nine watts per degree C or Kelvin 00:15:41.52900:15:41.539 so that's what I needed right here so 00:15:46.12900:15:46.139 now I can go back to the previous slide 00:15:48.87900:15:48.889 2400 watts per degree C so we have one 00:15:53.53900:15:53.549 over two thousand four hundred watts per 00:15:58.18900:15:58.199 Kelvin you have one over H inner nine 00:16:03.52900:16:03.539 fifty-nine you had all that area inner 00:16:07.11900:16:07.129 one over H outer all that area outer I'm 00:16:12.13900:16:12.149 gonna skip over here Hayden I let me 00:16:15.55900:16:15.569 just give you the number seven point 00:16:17.23900:16:17.249 five three nine eight meter squared area 00:16:20.86900:16:20.879 on outside 9.0 four seven eight meters 00:16:25.30900:16:25.319 squared 00:16:25.95900:16:25.969 hence you calculate from this equation 00:16:29.41900:16:29.429 right here the H naught H dot 332 00:16:35.89900:16:35.909 squared degrees C
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