Thermal conduction Fourier's law

QuickField simulation example

Problem type
Plane-parallel problem of steady-state heat transfer.

Geometry

Given
The temperature at the wall surfaces: T1= 20°C, T2= 60°C;
Thermal conductivity of the wall material λ = 0.4 W/K*m
Wall thickness d = 1 cm.
Wall surface area S = 100 cm².

Task
Determine the heat flux passing through the flat wall and compare with the analytic solution.

Solution
According to Fourier's law*, the heat flux in a flat wall is directed from the hot surface to the cold one and is calculated using the thermal conductivity of the wall, its thickness and area, and the temperature difference:
Φ = λ * (T2-T1)/d * S.

*Wikipedia: Fourier's law

Result
Analytic solution: Φ = 0.4 * (60-20)/0.01 * 100e-4 = 16 W.
Picture of a thermal field in QuickField, vectors show the directions of the heat flow

• Video: Thermal conduction Fourier's law. Watch on YouTube
  
• Download simulation files (files may be viewed using any QuickField Edition).