Discussion
Calculate the rate of heat transfer per unit area through a copper plate 45 mm thick, whose one face is maintained at 350°C and the other face at 50°C. Take thermal conductivity of copper as 370 W/m°C.
Answer: B
The heat flux is \(2.466\ \text{MW/m}^{2}\).
For steady one-dimensional conduction through a plane wall, Fourier's law gives the heat transfer per unit area:
\[ \begin{aligned} q &= \frac{k (T_{1} - T_{2})}{L} \\ &= \frac{370 \times (350 - 50)}{0.045} \\ &= \frac{111{,}000}{0.045} \\ &\approx 2.466 \times 10^{6}\ \text{W/m}^{2} \end{aligned} \]
That is 2.466 MW/m\(^{2}\). The thickness must be in metres: using 45 instead of 0.045 makes the answer a thousand times too small, 0.0025 MW/m\(^{2}\). Copper's high conductivity is why the flux is so large for a 300°C difference.
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