Chapter 8, Problem 8.115P

An experiment is designed to study microscale forced convection. Water at $T_{m,i}=300K$ is to be heated in a straight, circular glass tube with a $50\text{-}\mu m$ inner diameter and a wall thickness of $\text{1 mm}$ . Warm water at $T_{\infty }=350K,V=2m/s$ is in cross flow over the exterior tube surface. The experiment is to be designed to cover the operating range $1\le {\mathrm{Re}}_D\le 2000$ , where ${\mathrm{Re}}_D$ , is the Reynolds number associated with the internal flow.
(a) Determine the tube length L that meets a design requirement that the tube be twice as long as the thermal entrance length associated with the highest Reynolds number of interest. Evaluate water properties at $\text{3}0\text{5 K}$ .
(b) Determine the water outlet temperature $T_{m,o}$ , that is expected to be associated with ${\mathrm{Re}}_D=2000$ . Evaluate the heating water (water in cross flow over the tube) properties at $\text{33}0\text{ K}$ .
(c) Calculate the pressure drop from the entrance to the exit of the tube for ${\mathrm{Re}}_D=2000$ .
(d) Based on the calculated flow rate and pressure drop in the tube, estimate the height of a column of water (at $\text{3}00\text{ K}$ ) needed w supply the necessary pressure at the tube entrance and the time needed to collect 0.1 liter of water. Discuss how the outlet temperature of the water flowing from the tube, $T_{m,o}$ , might be measured.