A long, hollow cylinder is constructed from a material whose thermal conductivity is a function of temperature according to k = 0.15 + 0.0018T, where T is in ºC and k is in W/(m K). The inner and outer radii of the cylinder are 12.5 cm and 25 cm, respectively.

Under steady-state conditions, the temperature at the interior surface of the cylinder is 427ºC and the temperature at the exterior surface is 93ºC. 

(a) Calculate the rate of heat transfer per foot length, taking into account the variation in thermal conductivity with temperature. 

(b) If the heat transfer coefficient on the exterior surface of the cylinder is 17 W/ (m² K) calculate the temperature of the air on the outside of the cylinder.