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Two thin metallic spherical shells of radii r1 and r2 (r1 < r2) are placed with their centres coinciding. A material of thermal conductivity K is filled in the space between the shells. The inner shell is maintained at temperature θ1 and the outer shell at temperature θ2 (θ1 < θ2). The rate at which heat flows radially through the material is:-

1. 4πKr1r2(θ2 − θ1)/(r2 − r1)
2. 2πr1r2(θ2 − θ1)/(r2 − r1)
3. K(θ2 − θ1)/(r2 − r1)
4. K(θ2 − θ1)(r2 − r1)/(4πr1r2)

Correct answer: 4πKr1r2(θ2 − θ1)/(r2 − r1)

Solution

For steady radial conduction through a spherical shell, dQ/dt = 4*pi*K*r1*r2*(theta2 - theta1)/(r2 - r1).

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