A fluid flows through a pipe with inside diameter D = 0.12 m and length L = 75 m. The flow rate of the fluid is 0.26 kg/s. The pipe is maintained at a constant surface temperature of Ts and the flow may be considered fully-developed along the entire length. The fluid enters the pipe with mean temperature Tm, i = 320 K, and exits with a mean temperature Tm, o = 435 K.

The average properties of the fluid are: Pr = 75, Thermal conductivity k = 0.55 W/m K, Density p = 1100 kg/m3, Specific heat c = 1850 J/kg K, Absolute viscosity it = 0.0075 N s/m2.

(i) Calculate the surface temperature of the pipe, 'Ts, necessary for this outlet temperature.
(ii) Calculate the total heat transfer
(iii) Plot the mean temperature, T., and Ts as a function of x.