Chapter 3, Problem 3.7P

The walls of a refrigerator are typically constructed by sandwiching a layer of insulation between sheet metal panels. Consider a wall made from fiberglass insulation of thermal conductivity $k_i=0.046\text{W/m}\cdot \text{K}$ and thickness $L_i=50\text{mm}$ and steel panels, each of thermal conductivity $k_p=60\text{W/m}\cdot \text{K}$ and thickness $L_p=3\text{mm}\text{.}$ If the wall separates refrigerated air at $T_{\infty ,i}=4°\text{C}$ from ambient air at $T_{\infty ,\rho }=25°\text{C,}$ what is the heat gain per unit surface area? Coefficients associated with natural convection at the inner and outer surfaces may be approximated as $h_i=h_o=5{\text{W/m}}^{\text{2}}\cdot \text{K}\text{.}$