The figure below shows a cross section through an insulated heating pipe which is made from steel (k=45 W/m K) with an inner radius of 150mm and outer radius of 155 mm. The pipe is coated with 100 mm thickness of insulation having thermal conductivity of k = 0.06 W/m K. Air at inlet temperature $$Ti = 60^\circ C$$ flow through the pipe has a value of convective coefficient hi = 35 W/m$$^2$$ K. The outside surface of the pipe is surrounded by air which is at $$15^\circ C$$ and convective heat transfer coefficient on this surface has a value of ho = 10 W/m$$^2$$ K. Find the critical insulation radius?