Chapter 11, Problem 11.17P

A concentric tube heat exchanger of length L = 2 m isused to thermally process a pharmaceutical productflowing at a mean velocity of $u_{m,c}=0.1\text{ m/s}$ with an inlet temperature of $T_{c,i}=20°C$ . The inner tube ofdiameter $D_i=10$ mm is thin walled, and the exteriorof the outer tube $\left(D_o=20\text{ mm}\right)$ is well insulated.Water flows in the annular region between the tubes ata mean velocity of $u_{m,h}=0.2\text{ m/s}$ with an Inlet temperature of $T_{h,i}=60°C$ . Properties of the pharmaceuticalproduct are $v=10\times {10}^{-6}{\text{ m}}^2\text{/s}$ , $k=0.25\text{ W/m}\cdot \text{K}$ , $\rho =1100{\text{ kg/m}}^3$ , and $c_p=2460\text{ J/kg}\cdot \text{K}$ . Evaluate waterproperties at ${\bar{T}}_h=50°C$ .
(a) Determine the value of the overall heat transfercoefficient U.
(b) Determine the mean outlet temperature of thepharmaceutical product when the exchanger operates in the counterflow mode.
(c) Determine the mean outlet temperature of thepharmaceutical product when the exchanger operates in the parallel-flow mode.