A porous solid is in the shape of a hollow sphere and has temperatures of \(T_{\mathrm{i}}\) and \(T_{\mathrm{o}}\) at the radii of \(r_{\mathrm{i}}\) and \(r_{\mathrm{o}}\), respectively. Find an expression for the heat loss from the sphere.

In order to reduce the heat loss, a gas is blown through the porous hollow sphere at a velocity of \(v_{0}\). Derive an expression for the reduction in heat loss from this system.