A spherical shell, with thermal conductivity k, has inner and outer radii of r₁ and r₂, respectively. The inner surface of the shell is subjected to a uniform heat flux of q̇₁, while the outer surface of the shell is exposed to convection heat transfer with a coefficient h and an ambient temperature T_∞. Determine the variation of temperature in the shell wall and show that the outer surface temperature of the shell can be expressed as T(r₂) = (q̇₁/h)(r₁/r₂)² + T_∞.

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91 Spherical container 2 h, T