A long steam pipe has an outer radius of r1 that is kept at a constant temperature T1. the pip is covered with thermal insulation having an outside radius of r2. The outer ambient temperature of the surrounding air is kept constant at T_inf. Find the rate of heat teansfer from theh insulated pipe to the surrounding air. Show that for such a case, the radius of the insulation associated with the maximum energy transfer, the critical radius, can be found as k/h where k is the thermal conductivity of the insulator and h is the convection heat transfer coefficient.