## 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**

**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**

**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