Consider a circular tube of diameter D and length L, with a mass flow rate of .

(a) For constant heat flux conditions, derive an expression for the ratio of the temperature difference between the tube wall at the tube exit and the inlet temperature, T_s(x = L) – T_m,i, to the total heat transfer rate to the fluid q. Express your result in terms of , L, the local Nusselt number at the tube exit Nu_D(x = L), and relevant fluid properties.
(b) Repeat part (a) for constant surface temperature conditions. Express your result in terms of , L, the average Nusselt number from the tube inlet to
the tube exit Nu_D , and relevant fluid properties.