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A truncated cone 30cm high is made of Aluminum. The dia at the top is 7.5cm, and 12.5cm at the bottom. The lower surface is maintained at 93 deg C, the upper surface at 540 deg C. the other surface is insulated. Assuming 1 dimentional heat flow, calculate the rate of heat transfer in watts.

2. Homework Equations

Conduction equation:

q/a=k(dt/dx)

3. The Attempt at a Solution

I have the k value from a textbook at 204 w/(m C)

Made the assumptions that k is not a function of x or t and that the rest of the cone is perfectly insulated besides the top and the bottom.

That being the case I simply plugged in the values using

q=k*(A1*T1-A2*T2)/x where T1 is the high temperature and T2 is the low temperature. x is the thickness.

I'm not sure if this involves some kind of integration though. I fear I may be oversimplifying the problem.

This question was asked previously in the forum but was unanswered.

Thanks for the help.

K