The thermal conductivity of an opaque insulating material is to be determined by lighting a 5-W light bulb inside a hollow sphere made of that material and measuring the surface temperatures. The sphere has inside and outside radii of 0.01 and 0.015 m, respectively, and is suspended in air at 25°C, which is blown over the sphere at a velocity of 5 m/s. The inner and outer surface temperatures of the sphere are measured with thermocouples at steady state and are 90°C and 60°C, respectively.

(a) Write the differential energy balance equation and proper boundary conditions needed to describe steady-state heat transfer through the spherical shell.

(b) Solve your equation to find an expression for the heat transfer rate.

(c) Determine the thermal conductivity of the material.

(d) Determine the convective heat transfer coefficient at the outer surface of the sphere. Note: assume that the thermal conductivity of the material is independent of temperature.