Subtopic: Conduction heat gain through cold room insulation
Question Statement:
A cold storage wall of surface area $A = 25\text{ m}^2$ is insulated with polyurethane foam of thickness $L = 12\text{ cm}$ and thermal conductivity $k = 0.04\text{ W/(m}\,\text{K)}$. If the outer surface temperature is maintained at $35^\circ\text{C}$ and the inner surface at $4^\circ\text{C}$, the steady-state heat ingress through the wall is ________ $\text{W}$ (round off to two decimal places).
Answer Key:
258.33
Step-by-Step Solution & Explanation
From Fourier's 1D steady conduction law:
$q = \frac{k A (T_{out} - T_{in})}{L}$
Given $k = 0.04\text{ W/(m K)}$, $A = 25\text{ m}^2$, $\Delta T = 35 - 4 = 31^\circ\text{C}$, and $L = 0.12\text{ m}$:
$q = \frac{0.04 \times 25 \times 31}{0.12} = \frac{31.00}{0.12} = 258.33\text{ W}$