Problem 4 Engine oil at 25 C, with properties p= 865.8 kg/m, Cp = 2035 kJ/kg-K, u = 8.36x10-2 Pa.s and k = 141.3x10-3 W/m-K, flows through a pipe with diameter of 25 mm and flowrate of 0.5 kg/s. The pipe wall is maintained at constant temperature of 100 C. For pipe lengths between 5 and 100 m, give, as a function of pipe length, a graphical representation of: a. Average Nusselt Hint: remember to check if the flow is in the fully developed region or not, b. Outlet temperature, c. Logarithic mean temperature, d. A sketch how the curves will change with increasing mass flow. Hint: Derive an expression for items a, b and c and write tem in Python to plot. For item d, you can just increase and reduce the mass flow by 50 % and plot the new curves with the original ones