Consider a hollow steel sphere of inside radius r1=10 cm and outside radius of r2=20 cm. The thermal conductivity of the steel is k = 10 W/mK. The inside surface is maintained at a uniform temperature of T1=230 degree C and the outside surface dissipates heat by convection with a heat transfer coefficient of h = 20 W/m2K into air at T infinity = 30 degree C. Determine the thickness of insulation (ki= 0. 5 W/mK) required to reduce the heat loss by 50%.