Heat Conduction in a Spherical Shell

Consider the above diagram to represent an orange, we are interested in determining the rate of heat transfer through the peel (the peel dimensions are a bit exaggerated!). Heat flow is along radial direction outwards.

Fourier's Law in radial coordinates

Substituting the area of a sphere

Integrating, between r = r₁ and r₂, and T₁ and T₂,

The thermal resistance is expressed as