Heat Conduction Calculator (Fourier's Law)
Work out the steady-state heat flow through a flat wall using Fourier's law of conduction. Enter the material's thermal conductivity, the wall area, the temperature difference across it, and its thickness to get both the total heat flow rate and the heat flux.
Enter Values
How to use this calculator
- Enter the thermal conductivity k of the wall material in W/m.K (e.g. 0.04 for typical insulation).
- Enter the wall area A in square metres and the temperature difference dT across the wall in kelvin (a difference in kelvin equals a difference in degrees Celsius).
- Enter the wall thickness L in metres and read off the heat flow rate Q and heat flux q.
How it works
Fourier's law for one-dimensional steady-state conduction gives Q = k * A * dT / L, where k is thermal conductivity, A is the cross-sectional area normal to heat flow, dT is the temperature difference across the layer and L is its thickness. The heat flux q is the heat flow per unit area, q = Q / A = k * dT / L. The result assumes the temperatures are constant in time and conductivity does not vary with temperature.
Worked example
Worked example. For fibreglass insulation with k = 0.04 W/m.K, area A = 10 m2, a temperature difference dT = 20 K and thickness L = 0.1 m: Q = 0.04 * 10 * 20 / 0.1 = 80 W, and q = 80 / 10 = 8 W/m2.
Common mistakes
- Using a thickness in millimetres or centimetres instead of metres — L must be in metres.
- Confusing conductivity k (W/m.K) with the U-value or heat transfer coefficient (W/m2.K); they are different quantities.
- Entering absolute temperatures instead of the temperature difference across the wall.
Frequently asked questions
Do I use kelvin or degrees Celsius for the temperature difference?
Either works, because a difference of 1 K equals a difference of 1 degC. Only the difference matters, not the absolute temperature.
Does this handle several layers or surface air films?
No. This models a single homogeneous layer with fixed surface temperatures. For multiple layers or convective films, use the thermal resistance or overall heat transfer coefficient calculators.
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- Thermal Resistance Calculator
- Overall Heat Transfer Coefficient Calculator
- Convective Heat Transfer Calculator
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Tip: Enter any known values to calculate the remaining results.
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