Heat conduction in a spherical shell (Fig. 11B.4), a spherical shell has inner and outer radii R₁ and R₂. A hole is made in the shell at the North Pole by cutting out the conical segment in the region 0 < θ < θ₁. A similar hole is made at the South Pole by removing the portion (π – θ₁) < θ < π. The surface 0 = 0 is kept at temperature T = T₁, and the surface at 0 = π – θ₁ is held at T = T₂. Find the steady-state temperature distribution, using the heat conduction equation.

Transcribed Image Text:

Hole at top - (at "north pole") Solid Insulated ( surfaces Similar hole at "south pole" (b) (a)