Suppose we have a cylindrical wire of copper of radius R and length L encased by a layer of insulation of thickness . The thermal conductivities of the insulation is k. The copper is at temperature T0 and the temperature of the surrounding air is T air < T 0. The measured heat transfer coefficient between the insulation and air is h. (a) Write the differential equation and boundary conditions that describe the temperature profile in the insulation in terms of the quantities listed above. (b) What is the temperature profile and heat flux in the insulation? (c) What is the rate at which heat is transferred to the air from the wire? (d) Is there an optimal thickness that minimizes or maximizes the heat loss? If so, can you explain why this is the case?