00:00:04.740 --> 00:00:16.109 In this screencast, we're going to look at a concentric, counter-flow heat exchanger, 00:00:16.109 --> 00:00:30.199 which means that the hot fluid (in our case is oil) enters the heat exchanger in a different 00:00:30.199 --> 00:00:39.870 direction, or counter direction, to the cooling fluid (which in this case is water). The water 00:00:39.870 --> 00:00:49.940 will enter the heat exchanger at the other end while the oil will exit it again counter-flow 00:00:49.940 --> 00:00:59.090 to the water. So we're going to do a similar analysis here, finding the length of a heat 00:00:59.090 --> 00:01:07.630 exchanger, as we did with parallel-flow. The only difference again is going to be that 00:01:07.630 --> 00:01:19.850 this heat exchanger is counter-flow. We're still going to use our governing equation, 00:01:19.850 --> 00:01:32.960 q equals U times A times delta T log mean, as we did with parallel-flow. And again we're 00:01:32.960 --> 00:01:45.240 going to rewrite it in terms of our length. If we look at our properties and our equation, 00:01:45.240 --> 00:01:54.560 what we'll see is that everything is exactly the same in a counter-flow heat exchanger 00:01:54.560 --> 00:02:04.299 as it is in a parallel-flow heat exchanger except for one term. And that term is this 00:02:04.299 --> 00:02:16.470 delta T log mean. Delta T log mean is going to be our delta T 1 (which refers to the difference 00:02:16.470 --> 00:02:24.560 in temperature at the entrance of the heat exchanger) minus our delta T 2 (which is the 00:02:24.560 --> 00:02:35.330 delta T at the end of the heat exchanger) divided by the natural log of delta T 1 over 00:02:35.330 --> 00:02:44.720 delta T 2. What's different in this particular heat exchanger is, because the fluids are 00:02:44.720 --> 00:02:52.599 going in the opposite direction, our delta T 1 and our delta T 2 are going to be different 00:02:52.599 --> 00:03:01.209 for a counter-flow versus a parallel-flow. So let's take a look and see what our delta 00:03:01.209 --> 00:03:11.440 T 1 is going to be. And looking at this picture, we can see that our delta T 1 is going to 00:03:11.440 --> 00:03:23.650 equal the temperature of the oil that's entering the system minus the temperature of the water 00:03:23.650 --> 00:03:34.450 that's exiting the system. So that means that our delta T 1 is going to equal 100 degrees 00:03:34.450 --> 00:03:48.530 C minus 50 degrees C, or 50 degrees. Delta T 2 is going to be the temperature of the 00:03:48.530 --> 00:03:58.860 oil exiting the system minus the temperature of the water entering the system. So our delta 00:03:58.860 --> 00:04:12.709 T 2 is going to equal 60 degrees C minus 25 degrees, or 35 degrees C. And now let's find, 00:04:12.709 --> 00:04:24.030 using these, our delta T log mean. So this is going to be delta T 1, which is 50 degrees 00:04:24.030 --> 00:04:35.750 C, minus delta T 2, which is 35 degrees C, all divided by the natural log of 50 degrees 00:04:35.750 --> 00:04:46.720 C divided by 35 degrees C. And when we calculate this, we find that our delta T log mean is 00:04:46.720 --> 00:04:58.460 equal to 42 degrees Celsius. And now let's put in numbers for our length. And for sizing 00:04:58.460 --> 00:05:10.570 a heat exchanger using parallel-flow, we found that our heat transfer rate was 12,786 watts, 00:05:10.570 --> 00:05:23.229 our overall heat transfer coefficient was 38.1 watts per meter squared degrees C, our 00:05:23.229 --> 00:05:35.460 diameter was equal to 0.03 meters, and again our delta T log mean is 42 degrees C. L is 00:05:35.460 --> 00:05:46.270 going to equal our heat transfer rate, divided by our overall heat transfer coefficient times 00:05:46.270 --> 00:05:57.509 pi times this diameter times our delta T log mean. And when we calculate this, we find 00:05:57.509 --> 00:06:10.150 that the needed length for our heat exchanger is 84.8 meters. We compare this for the length 00:06:10.150 --> 00:06:20.979 of a parallel-flow heat exchanger, which is a 110.6 meters. Why is there a difference? 00:06:20.979 --> 00:06:26.940 Well because the delta T, or the difference in temperature, is greater along the tube, 00:06:26.940 --> 00:06:34.250 you need less surface area for the same amount of heat transfer. Therefore, we would need 00:06:34.250 --> 00:06:38.840 a shorter length for the counter-flow heat exchanger.
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