A pipe with a surface temperature of 250C passes through a room where the air temperature is 30C. Insulation (density = 577 kg/m3, k = 0.2 W/m-C) is to be applied to the pipe and a convection heat transfer coefficient of 4 W/m2-C can be expected to exist at the surface of the bare pipe or the surface of the insulation after it is applied.

Find the critical radius of the insulation;

if the pipe diameter is 5 cm and insulation of the radius found in part (a) is applied to it, find the heat loss from the pipe before and after the insulation is applied;

If the pipe diameter is 12 cm and insulation of the same thickness as that in part (b) is used, find the heat loss before and after the insulation is applied.

Draw a sketch showing heat transfer rate (W/m) as a function of pipe radius (R) for the two configurations above {(b) and (c)}.