A system for heating water with an inlet temperature of 25°C to an exiting temperature of 70°C involves passing the water through a thick-walled tube with inner and outer diameters of 25 and 45 mm, respectively. The outer tube surface is well insulated, and the electrical heating within the tube wall provides for a Uniform generation of q̇ = 1.5 × 10⁶ W/m³.
a. For a mass flow rate of water, ṁ = 0.12 kg/s, how long must the tube be to achieve the desired outlet temperature?
b. If the inner surface of the tube at the outlet is T_s = 110°C,
what is the local convective coefficient at this location?