Solve the following:
Q: A hollow sphere with inner and outer radii of R1 and R2, respectively, is covered with a layer of insulation having an outer radius of R3. Derive an expression for the rate of heat transfer through the insulated sphere in terms of the radii, the thermal conductivities, the heat transfer coefficients, and the temperatures of the interior and the surrounding medium of the sphere.
GIVEN
An insulated hollow sphere
Radii
Inner surface of the sphere = R1
Outer surface of the sphere = R2
Outer surface of the insulation = R3
ASSUMPTIONS
Steady state heat transfer
Conduction in the radial direction only
Constant thermal conductivities
