Heat loss by conduction through a plane wall

A brick wall 200 mm thick and 20 m² in area (k = 0.72 W/m·K) has a 25 K temperature difference across it. Assuming steady one-dimensional conduction, find the heat loss and the wall's thermal resistance.

Given

Solution

1. 1.Fourier's law for a plane wall
   $$q=\frac{kA\Delta T}{L}$$
   $$q=1800\mathrm{W}$$
2. 2.Thermal resistance of the wall
   $$R_{th}=\frac{L}{kA}$$
   $$R_{th}=0.0139K/W$$

Worked in ProveCalc

Units carry through every line: W/(m·K) times m² times K over m comes out in watts, and the resistance in K/W, with no conversion step to get wrong.

The results above were evaluated by ProveCalc's compute engine (SymPy and Pint), the same engine the desktop app runs on your machine.

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