An experiment is designed to study micro-scale forced convection. Water at Tm,i = 300 K is to be heated in a straight, circular glass tube with a 50-μm inner diameter and a wall thickness of 1 mm. Warm water at T∞ = 350 K, V = 2 m/s is in cross flow over the exterior tube surface. The experiment is to be designed to cover the operating range 1 < ReD < 2000, where ReD 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 305 K.

(b) Determine the water outlet temperature, Tm.o that is expected to be associated with ReD = 2000.

Evaluate the heating water (water in cross flow over the tube) properties at 330 K.

(c) Calculate the pressure drop from the entrance to the exit of the tube for ReD = 2000.

(d) Based on the calculated flow rate and pressure drop in the tube, estimate the height of a column of water (at 300 K) necessary to 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, Tm.o, might be measured.