Solve the below problem:
Q: Water flows through a thick-walled tube with an inner diameter of 12 mm and a length of 8 m. The tube is immersed in a well-stirred, hot reaction tank maintained at 85°C, and the conduction resistance of the tube wall (based on the inner surface area) is R"cd = 0.002 m2 · K/W. The inlet temperature of the process fluid is Tm,i = 20°C, and the flow rate is 33 kg/h.
(a) Estimate the outlet temperature of the process fluid. Tm,o. Assume, and then justify, fully developed flow and thermal conditions within the tube.
(b) Do you expect Tm,o to increase or decrease if combined thermal and hydrodynamic entry conditions exist within the tube? Estimate the outlet temperature of the water for this condition.