A spherical metal ball of radius r_0 is heated in an oven to a temperature of T_1 throughout and is then taken out of the oven and allowed to cool in ambient air at T[infinity] , by convection and radiation. The emissivity of the outer surface of the cylinder is e, and the temperature of the surrounding surfaces is T_{surr}. The average convection heat transfer coefficient is estimated to be h. Assuming variable thermal conductivity and transient one-dimensional heat transfer, express the mathematical formulation (the differential equation and the boundary and initial conditions) of this heat conduction problem.