A spherical container, with an inner radius r₁ = 1 m and an outer radius r₂ = 1.05 m, has its inner surface subjected to a uniform heat flux of q̇₁ = 7 kW/m². The outer surface of the container has a temperature T₂ = 25°C, and the container wall thermal conductivity is k = 1.5 W/m ∙ K. Show that the variation of temperature in the container wall can be expressed as T(r) = (q̇₁r₁²/k)(1/r₂ -/r₂) + T₂ and determine the temperature of the inner surface of the container at r = r₁.

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T₂ n Spherical container 172