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What is the relationship between time and heat transfer coefficient? Actually are there any at all? What happens to time taken in heat transfer if the coefficient is value is raised or lowered?

All we know is $$Q=hA(T-T_a)$$ which does not include time. Only surface area and temperatures. Let us say a casting takes 40 minutes to cool down to its 95% of the original temperature. Now if the heat transfer coefficient is 5 times higher, what will be the time required? Will it still take 40 minutes to cool down to 95% of the original temperature?

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  • $\begingroup$ @harshit54, good comment. For industrial heat exchangers, the calculation is $Q=UA\Delta T_{lm}$, where U is the overall heat transfer coefficient, A is the heat transfer area, and $\Delta T_{lm}$ is the log mean temperature difference. This equation is "semantically" incorrect, because Q (in the U.S. system of measure) has units of BTU/hr, which is the rate of heat transfer. $\endgroup$ – David White Jan 5 '19 at 1:13
  • $\begingroup$ @harshit54, you may want to post your comment as an answer. $\endgroup$ – David White Jan 5 '19 at 1:17
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Do you know that Q stands for heat transferred per unit time. It's the rate of heat flow. The correct formula for convective heat transfer is

$\dfrac{Q}{t}=h{A(T_2-T_1)}$

where h is the Heat Transfer Coefficient

As you can clearly see even in the Wikipedia page, the Q is mentioned with a dot above it implying the time derivative of the heat transferred or the rate of heat transfer.

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  • $\begingroup$ We are talking about convection, not conduction. I believe the formula you mentioned is Fourier's law of heat conduction. Is it also valid for convection? I am not sure about that. $\endgroup$ – hellomecha Jan 5 '19 at 4:05
  • $\begingroup$ @hellomecha You are right. I misread the question. Sorry about that. Edited the answer. $\endgroup$ – Harshit Joshi Jan 5 '19 at 4:09
  • $\begingroup$ Does the formula hold good for heat transfer rate as well? Not just about the amount of heat transferred? $\endgroup$ – hellomecha Jan 5 '19 at 12:37
  • $\begingroup$ This formula is valid for the heat transfer rate only. $\endgroup$ – Harshit Joshi Jan 5 '19 at 12:57
  • $\begingroup$ @hellomecha I edited the answer again. Please do reply. $\endgroup$ – Harshit Joshi Jan 5 '19 at 18:33

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