Chapter 9, Problem 9.31P

A refrigerator door has a height and width of $H=1\text{m}\text{and}W=0.65\text{}\text{m}$ , respectively, and is situated in a large room for which the air md walls are at $T_{\infty }=T_{\text{sur}}=25°C$ . The door consists of a layer of polystyrene insulation $\left(k=0.03\text{W/m}\cdot \text{K}\right)$ sandwiched between thin sheets of steel $\left(\epsilon =0.6\right)$ and polypropylene. Under normal operating conditions, the inner surface of the door is maintained at a fixed temperature of $T_{s,i}=5°C$ .

(a) Estimate the heat gain through the door for the worst case condition corresponding to no insulation $\left(L=0\right)$ .
(b) Compute and plot the heat gain and the outer surface temperature $T_{s,o}$ as a function of insulation thickness for $0\le L\le 25\text{mm}$ .