Chapter 9, Problem 9.72P

A biological fluid moves at a flow rate of $\stackrel{\dot{}}{m}=0.02\text{kg/s}$ through a coiled, thin-walled, 5-mm-diameter tube submerged in a large water bath maintained at 50°C. The fluid enters the tube at 25°C.

(a) Estimate the length of the tube and the number of coil turns required to provide an exit temperature of $T_{m,o}=38°C$ for the biological fluid. Assume that the water bath is an extensive, quiescent medium, that the coiled tube approximates a horizontal tube, and that the biological fluid has the thermophysical properties of water.

(b) The flow rate through the tube is controlled by a pump that experiences throughput variations of approximately $\pm 10\%$ at any one setting. This condition is of concern to the project engineer because the corresponding variation of the exit temperature of the biological fluid could influence the downstream process. What variation would you expect in $T_{m,o}$ for $\pm 10\%$ a change in $\stackrel{\dot{}}{m}$ ?