## Brick Wall

A 100 mm thick brick plane wall with a surface area of 1m by 1m has a measured temperature of 200°C on one side, and 77°C on the other. If the thermal conductivity is 69 W/m∙°C, what is the heat transfer?

Hint
Fourier’s Law of Conduction:
$$\dot{Q}=kA\frac{dT}{dx}$$$where $$\dot{Q}$$ is the rate of heat transfer, $$k$$ is the thermal conductivity, $$A$$ is the surface area perpendicular to the direction of heat transfer, $$dT$$ is the change in temperature, and $$dx$$ is the distance. Hint 2 Solve for $$\dot{Q}$$ . No need to convert units to Kelvin. Fourier’s Law of Conduction: $$\dot{Q}=kA\frac{dT}{dx}$$$
where $$\dot{Q}$$ is the rate of heat transfer, $$k$$ is the thermal conductivity, $$A$$ is the surface area perpendicular to the direction of heat transfer, $$dT$$ is the change in temperature, and $$dx$$ is the distance.
$$\dot{Q}=69\frac{W}{m\cdot ^{\circ}C}(1m\times 1m)\frac{(200^{\circ}C-77^{\circ}C)}{0.1m}=(69W)(1)\frac{123}{0.1}=85\:kW$$\$
85 kW