A composite spherical shell is made up of two materials having thermal conductivities K and 2K respectively as shown in the diagram. The temperature at the innermost surface is maintained at T whereas the temperature at the outermost surface is maintained at 10T. A, B, C and D are four points in the outer material such that AB = BC = CD. The effective thermal resistance between the inner surface of the shell and the outer surface of the shell for the radial heat flow is

Question

A composite spherical shell is made up of two materials having thermal conductivities K and 2K respectively as shown in the diagram. The temperature at the innermost surface is maintained at T whereas the temperature at the outermost surface is maintained at 10T. A, B, C and D are four points in the outer material such that AB = BC = CD. The effective thermal resistance between the inner surface of the shell and the outer surface of the shell for the radial heat flow is, 1 8 π KR, 1 7 π KR, 7 4 8 π KR, 6 4 9 π KR

MARKS App · Accepted Answer

R eff = ∫ R 2 R dx K 4 π x 2 + ∫ 2 R 3 R dx 2 K 4 π x 2 = 1 4 π K - 1 x R 2 R + 1 8 π K - 1 x 2 R 3 R ⇒ R eff = 7 4 8 π KR

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