A thin electrical heater is inserted between a long circular rod and a concentric tube with inner and outer radii of 20 and 40 mm. The rod (A) has a thermal conductivity of k A = 0.15 W/m. K, while the tube (B) has a thermal conductivity of k B = 1.5 W/m. K and its outer surface is subjected to convection with a fluid of temperature T_∞ = -15°C and heat transfer coefficient 50 W/m² ∙ K. The thermal contact resistance between the cylinder surfaces and the heater is negligible.

(a) Determine the electrical power per unit length of the cylinders (W/m) that is required to maintain the outer surface of cylinder B at 5°C.

(b) What is the temperature at the center of cylinder A?