A spherical shell has inner radii a and outer radii b. The temperatures at the inner and outer surfaces are T2 and T1. The thermal conductivity of the shell material is k. I have to derive an equation for the total heat current through the shell.(adsbygoogle = window.adsbygoogle || []).push({});

The equation for heat current through a rod is H=k*A*DeltaT/L where L is the length of the rod.

For this sperical shell the area which is perpendicular to the flow of the heat is changing with the radius. So I have to integrate the area. Am I right here?

I have tried to integrate the area by doing:

A=integrate(4*pi*r^2) from a to b

But I end up with something far from the right answer, don't want to get into that.

Could anyone please give me a hint to this problem?

Thanks

The right answer is H=4*pi*k*a*b*DeltaT/(b-a)

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# Homework Help: Heat current through a spherical shell

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