Chapter 8, Problem 8.86P

A double-wall heat exchanger is used to transfer heat between liquids flowing through semicircular copper tubes. Each tube has a wall thickness of $r_i=20$ mm and an inner radius of $\text{r }=\text{ 2}0\text{mm}$ . and good contact is maintained at the plane surfaces by lightly wound straps. The lube outer surfaces are well insulated.

(a) If hot and cold water at mean temperatures of $T_{h,m}=330$ K and $T_{c,m}=290$ K flow through the adjoining tubes $m_h=m_c=0.2$ kg/s, what is the rate of heat transfer per unit length of tube? The wall contact resistance is ${10}^{-5}{\text{m}}^2\cdot \text{K/W}$ . Approximate the properties of both the hot and cold water as $\mu =800\times {10}^{-6}\text{kg/s}\cdot \text{m},k=0.625\text{W/m}\cdot \text{K}$ , and Pr = 5.35. Hint: Heat transfer is enhanced by conduction through the semicircular portions of the tube walls, and each portion may be subdivided into two straight fins with adiabatic tips.

(b) Using the thermal model developed for part (a), determine the heat transfer rate per unit length when the fluids are ethylene glycol. Also, what effect will fabricating the exchanger from an aluminum alloy have on the heat rate? Will increasing the thickness of the tube walls have a beneficial effect’?