Why is T a straight line inside each layer?

With no internal sources and steady 1D conduction in a uniform material, the heat equation reduces to d²T/dx² = 0, so T is linear in x. Different slopes appear in different layers because k and thickness change the thermal resistance.

Does this U-value match my wall certificate?

No. Real envelopes include surface resistances, air gaps, moisture, and 2D/3D bridges. The simulator isolates bulk conduction in three slabs with ideal interfaces.

What if T_right is hotter than T_left?

Then q″ is negative: heat flows from right to left. The arrow and displayed flux magnitude reflect that sign convention.

Multilayer Wall Conduction

Three layers in series: R″ = L/k, q″ and U; T(x) sketch and preset plaster/brick/wool.

About this model

This lab applies Fourier’s law in steady, one-dimensional conduction through three homogeneous layers in series. In each slab, temperature varies linearly with thickness. Per unit area, layer resistance is R″ = L/k (L in metres, k in W/(m·K)). Total resistance adds: R″_tot = Σ R″_i, heat flux q″ = (T_left − T_right) / R″_tot, and U = 1/R″_tot. The drawing shows a color gradient by temperature, a T(x) polyline at interfaces, and an arrow for q″ from hot to cold. A one-click preset loads plaster / brick / mineral wool thicknesses and conductivities as a teaching example, not a certified U-value for a real building.

Who it's for: Introductory heat transfer and building-science intuition; complements the 2D heat-transfer playground.

Key terms

Fourier conduction
thermal resistance R″
U-value
series layers
heat flux q″
thermal conductivity k

How it works

Steady one-dimensional conduction through three layers in series: temperature is linear in each slab, and the heat flux q″ = (T_left − T_right) / Σ(L/k) per unit area. Compare thermal resistance of plaster, masonry, and insulation.

Frequently asked questions

Why is T a straight line inside each layer?: With no internal sources and steady 1D conduction in a uniform material, the heat equation reduces to d²T/dx² = 0, so T is linear in x. Different slopes appear in different layers because k and thickness change the thermal resistance.
Does this U-value match my wall certificate?: No. Real envelopes include surface resistances, air gaps, moisture, and 2D/3D bridges. The simulator isolates bulk conduction in three slabs with ideal interfaces.
What if T_right is hotter than T_left?: Then q″ is negative: heat flows from right to left. The arrow and displayed flux magnitude reflect that sign convention.

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