Heat Transfer Questions & Answers | |
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You should assume a 2D problem. Thus, the depth (what you refer to as “width”) is infinite. Thus, you cannot neglect heat transfer on the right side. In fact, this is what you have to find. As for your second question, the answer is within the problem statement (see the stated assumptions). Good questions. 2 points bonus.
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This is a very good analysis, more detailed than I expected. I'll give you right away 2 points bonus for the effort. You determine boundary layer height using the correlation by Khan et al, but this is overkill in this case. There's no need to try to get such a precise boundary layer thickness over a cylinder because this will only be accurate for the cylinders on the first row of the tube bank. For the cylinders part of the second row, it will be off considerably. What you need to do here is an order of magnitude analysis. Simply find approximately the average thermal layer height within the tube bank. You can use the thermal layer height relationship we derived in class over a flat plate of length $L$ and simply set $L$ to a characteristic length (you can try to set $L$ to $\frac{\pi}{2} D \times \frac{1}{2} N_r$ with $N_r$ the number of rows). This will give you a quite good estimate, more than precise enough for an order of magnitude analysis.
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Hm, the last equation you need is within the problem statement.. You have to make sure the water doesn't freeze and turn to ice. 0.5 point bonus.
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This is a very good question, very well researched. But one issue I have with your question is that the 30% error you outline is not the difference between the correlation and the exact solution but rather the difference between the correlation and some average friction factor obtained from lots of experiments of turbulent flows in pipes. An error of 10-30% is not bad at all (and on target) when dealing with turbulent flows. An error of 3-5 times would be considered off. Thus, you can think of Haaland's and Colebook's correlations as being essentially the same: both will yield an error of 30% or so when compared with experiments. 2 points bonus.
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I don't think switching from one shape factor formula to another will make much of a difference — you should get a very similar result. Just make sure that the restrictions are applicable to your case. I'm not sure what $A\gg B$ means exactly. This is highly case dependent. But I would guess at least 5-10 times larger. 1 point bonus.
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$\pi$ |