$10$B$.$t$.$ Heat conduction from a sphere to a stagnant fluid. A heated sphere of radius $R$ is sus$-$

pended in a large, motionless body of fluid. It is desired to study the heat conduction in the

fluid surrounding the sphere in the absence of convection.

$($a$)$ Set up the differential equation describing the temperature $T$ in the surrounding fluid as a

function of $r,$ the distance from the center of the sphere. The thermal conductivity $k$ of the

fluid is considered constant.

$($b$)$ Integrate the differential equation and use these boundary conditions to determine the in$-$

tegration constants: at $r=R,T=T_R$ and at $r=,T=T_{}.$