A cylindrical cable consists of a central metal wire of diameter 10mm surrounded by a layer of insulation 2mm thick. The wire is heated uniformly by an electric current. The outer surface of the insulation is at 50C. The wire will melt if its temperature at any point exceeds 750C. Relevant parameters are: Conductivity of wire kwire = 100 W.m-1.K-1 Conductivity of insulation kins = 0.01 W.m-1.K-1 Assuming that the system is at steady state (a) Calculate the maximum heating rate (in Watts per cubic metre) that can be sustained without the wire melting. Check that your answer is sensible by calculating the rate at which heat is produced per metre of wire. (3 marks) (b) An additional layer of insulation is added, with k = 0.05 W.m-1.K-1 and whose outer surface has a convective coefficient of 5 W.m-2.K-1. Beyond what minimum thickness of this new layer does heat loss from the wire decrease rather than increase as its thickness is increased? Assume constant temperatures of the outer surface of the wire and the surrounding air. Show all working! (3 marks)