Chapter 11, Problem 11.35P

A counterflow, twin-tube heat exchanger is made bybrazing two circular nickel tubes, each 40 m long,together as shown below. Hot water flows through thesmaller tube of 10-mm diameter and air at atmospheric pressure flows through the larger tube of 30-mm diameter. Both tubes have a wall thickness of 2 mm. The thermal contact conductance per unitlength of the brazed joint is $100\text{ W/m}\cdot \text{K}$ .The massflow rates of the water and air are 0.04 and 0.12 kg/s, respectively. The inlet temperatures of the water andair are 85 and $\text{23}°\text{C}$ , respectively.

Employ the $\epsilon \text{-NTU}$ method to determine the outlet temperature of the air. Hint: Account for the effectsof circumferential conduction in the walls of the tubes by treating them as extended surfaces.