a) Derive an expression for the critical insulation radius of a hollow cylinder in terms of the thermal conductivity of the insulating material and the convective heat transfer coefficient outside the insulation.
b) A hollow spherical vessel with an inner diameter (ID) of 19 cm and an outer diameter (OD) of 20 cm contains a hot fluid. The fluid is to be cooled by exposing the vessel to a surrounding cold fluid with an outside film coefficient of 10 W/m²K. If the vessel is to be insulated with a mica sheet (k = 0.5815 W/m K), determine the thickness of the insulation.