Heat conduction in a spherical shell (Fig 11B 4), a spherical shell has inner and outer radii R 1 and R 2 A hole is made in the shell at the North Pole by cutting out the conical segment in the region 0 1 A similar hole is made at the South Pole by removing the portion ( 1 ) The surface 0 0 is kept at temperature T T 1 , and the surface at 0 1 is held at T T 2 Find the steady state temperature distribution, using the heat conduction equation Hole at top (at north pole ) Solid Insulated ( surfaces Similar hole at south pole (b) (a)

Question: Heat conduction in a spherical shell (Fig. 11B.4), a spherical shell has inner and outer radii R 1 and R 2 . A hole is

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.

Hole at top - (at

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

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