1. An engineer proposes to insert a solid rod of diameter Di into a circular tube of diameter Do to enhance heat transfer from the flowing fluid of temperature Tm to the outer tube wall of temperature Ts,o. Assuming laminar flow, calculate the ratio of the heat flux from the fluid to the outer tube wall with the rod to the heat flux without the rod, qo"/qo",wo, for Di /Do = 0, 0.10, 0.25 and 0.50. The rod is placed concentrically within the tube.

2. An electrical power transformer of diameter 230 mm and height 500 mm dissipates 1000 W. It is desired to maintain its surface temperature at 47°C by supplying ethylene glycol at 24°C through thin-walled tubing of 20-mm diameter welded to the lateral surface of the transformer. All the heat dissipated by the transformer is assumed to be transferred to the ethylene glycol.

Transformer Tubing with coil insert

(a) Determine the outlet temperature of the pharma- ceutical fluid.

(b) It is desired to further reduce the outlet tempera- ture of the pharmaceutical. However, because the cooling process is just one part of an intricate pro- cessing operation, flow rates cannot be changed. A young engineer suggests that the outlet temperature might be reduced by inserting stainless steel coiled springs into the straight sections of the cooler with the notion that the springs will disturb the flow adja-Coolant 230 mm 500 mmS cent to the inner tube wall and, in turn, increase  the heat transfer coefficient at the inner tube wall. A senior engineer asserts that insertion of the springs should double the heat transfer coefficient at the straight inner tube walls. Determine the outlet tem- perature of the pharmaceutical fluid with the springs inserted into the tubes, assuming the senior engineer

Assuming the maximum allowable temperature rise of the coolant to be 6°C, determine the required coolant flow rate, the total length of tubing, and the coil  pitch S between turns of the tubing.