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Two thin concentric metallic spherical shells of radii r1 and r2 (r1 < r2) have the gap between them filled with a material of thermal conductivity K. The inner shell is at temperature theta1 and the outer at theta2 (theta1 < theta2). What is the rate of heat flow through the material?

1. 4*pi*K*r1*r2*(theta2 - theta1) / (r2 + r1)
2. 2*pi*K*r1*r2*(theta2 - theta1) / (r2 - r1)
3. 4*pi*K*r1*r2*(theta2 - theta1) / (r2 - r1)
4. pi*K*r1*r2*(theta2 - theta1) / (r2 - r1)

Correct answer: 4*pi*K*r1*r2*(theta2 - theta1) / (r2 - r1)

Solution

For radial conduction between concentric spheres, H = 4*pi*K*r1*r2*(theta2 - theta1)/(r2 - r1).

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