Chapter 8, Problem 8.104P

A bayonet cooler is used to reduce the temperature of a pharmaceutical fluid. The pharmaceutical fluid flows through the cooler, which is fabricated of $\text{l}0-\text{mm}$ diameter, thin—walled tubing with two $\text{25}0-\text{mm}$ —long straight sections and a coil with six and a half turns and a coil diameter of $\text{75 mm}$ . A coolant flows outside the cooler, with a convection coefficient at the outside surface of $\text{h}=\text{ 5}00\text{ W}/{\text{m}}^{\text{2}}\text{ K}$ and a coolant temperature of $\text{2}0°\text{C}$ . Consider the situation where the pharmaceutical fluid enters at $\text{9}0°\text{C}$ with a mass flow rate of $0.00\text{5 kg}/\text{s}$ . The pharmaceutical has the following properties: $\rho =1200\text{Kg}/{\text{m}}^3,\mu =4\times {10}^{-3}\text{N}\cdot {\text{s/m}}^2,c_p=2000\text{J/Kg}\cdot \text{K},k=0.5\text{W/m}\cdot \text{K}$ , and $k=0.5\text{W/m}\cdot \text{K}$ .

(a) Determine the outlet temperature of the pharmaceutical fluid.

(b) It is desired to further reduce the outlet temperature of the pharmaceutical. However, because the cooling process is just one pan of an intricate processing 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 how adjacent 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 temperature of the pharmaceutical fluid with the springs inserted into the tubes, assuming the senior engineer is correct in his assertion.

(c) Would you expect the outlet temperature of the pharmaceutical to depend on whether the springs have a left-hand or right-hand spiral? Why?