Question

Temperatures at two sides of a 0.4 m thick copper plate are 1000 and 500 °C. Assuming steady state, one-dimensional conductive heat transfer through the wall and ignoring end-effects, the magnitude of the heat flux through the wall is ............... × 10$^5$ W m$^{-2$ (in integer).} Given: Thermal conductivity of copper = 400 W m$^{-1}$ K$^{-1}$

Hint:

In one-dimensional steady conduction problems, always apply Fourier's law directly. Ensure that the temperature difference is in Kelvin or Celsius consistently since only the difference matters.

Answer 1

Step 1: Recall Fourier's law of conduction.
\[ q = k \frac{\Delta T}{L} \] where $q$ = heat flux, $k$ = thermal conductivity, $\Delta T$ = temperature difference, $L$ = thickness. Step 2: Substitute values.
\[ q = 400 \times \frac{(1000 - 500)}{0.4} \] \[ q = 400 \times \frac{500}{0.4} = 400 \times 1250 \] \[ q = 500000 \, W m^{-2} \] Final Answer: \[ \boxed{5 \times 10^5 \, W m^{-2}} \]