Heating Distance
A brick plane wall has a measured temperature of 300°C on one side and 125°C on the other. If the thermal conductivity is 50 W/m∙°C and the heat transfer rate is 100 kW, what is the wall’s thickness in meters? Assume the surface area perpendicular to the direction of heat transfer is 2 m^2.
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
$$dx$$
. 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.
$$$100,000W=50\frac{W}{m\cdot ^{\circ}C}\times 2m^2 \times \frac{(300^{\circ}C-125^{\circ}C)}{x}$$$
Solving for thickness:
$$$2,000= 2m \times \frac{175}{x}$$$
$$$x= \frac{2m \times 175}{2,000}=\frac{350m}{2,000}=0.175\:m$$$
0.175 m
Time Analysis
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