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 in kW?
Expand 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
Time Analysis
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