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Adrian F

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I remember when I was in the University (mech. engineering), I had an exam on partial differential equations about heat transfer in a cylinder. We had to determine the temperature distribution. I remember the conditions were that the cylinder was insulated in the side area, had a heat source in the bottom face at 9°C and the top face had a heat transfer coefficient that was taken from a digit in the student's ID number. For my particular case, this digit was 0, so I knew that the result was going to be that the cylinder ended up at 9º in all of its volume, or that the limit of the temperature function when t (time) tends to infinity equaled 9, independent of any other parameter.

Now, I don't remember the procedure, but I remember that I assumed that the rate of heat transfer in the radial direction or

**∂u/**was going to be 0 because there's no heat being transfer in that direction and proceded from there. I got the result right: Lim(T) when t tends to infinity = 9 and wrote the reasoning. The teacher gave me all points in the problem because of the reasoning but said that the procedure was wrong.

**∂r**My question is, was I correct in making that assumption? If anyone could maybe solve this problem here, I'd appreciated.This happened 10 years ago, but I never got the answer. It's been bugging me ever since and I forgot about D.E.

Thanks in advance