Q. Describe the term ‘Critical Insulation thickness'. What is its significance? Derive an expression for the critical insulation radius of a spherical system.

A bar of square cross-section connects two metallic structures. One structure is maintained at a temperature of 200^o C and the other at 50^o C. The bar is 20mm x 20mm in cross section and 100mm long and has a thermal conductivity of 60W/mK. The ambient air is at 20^o C and heat transfer coefficient between the bar and the ambient is 10W/m²K. Derive an expression for the temperature distribution along the bar & calculate the steady state heat flow rate from the bar to the surrounding.