Heat Transfer Questions & Answers | |
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Well first determined if this is forced or free convective heat transfer. If it's forced, it shouldn't involve a Rayleigh or Grashoff number. If it's free, choose the free convective heat transfer correlation that is the best suited (only choose irregular solid if you can not find a better way). 1 point bonus.
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Whether you use $T_f$ or not is indicated in the instructions accompanying the Nusselt number correlation. If you need to use $T_f$ but don't know $T_s$ to start with, then you need to proceed iteratively: guess a $T_s$, then find $T_f$, then solve the problem and find a new $T_s$ which can be used as the new guess for $T_s$ and repeat as many times as necessary. 1 point bonus.
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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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$\pi$ |