Chapter 8, Problem 8.77P

Consider the ground source heat pump of Problem 5.100 under winter conditions for which the liquid isdischarged from the heat pump into high-density polyethylene (using of thickness $t=8\text{mm}$ and thermal conductivity $k=0.47\text{W/m}\cdot \text{K}$ . The tubing is muted through soil that maintains a uniform temperature of approximately 10°C at the tube outer surface. The properties of the fluid may be approximated as those of water.

(a) For a tube inner diameter and flow rate of $D_i=25\text{mm}\text{and}\stackrel{\dot{}}{m}=0.03\text{kg/s}$ and a fluid inlet temperature of $T_{m,i}=0°C$ , determine the tube outlet temperature (heat pump inlet temperature), $T_{m,o}$ , as a function of the tube length L for $10\le L\le 50m$ .
(b) Recommend an appropriate length for the system. How would your recommendation be affected by variations in the liquid flow rate?