CONDUCTION
q = ΔT/(L₁/k₁+L₂/k₂) — R-values add in series. Ohm’s law for heat, drawn.
Use the simulation above to change the variables and play through the guided stages. The explanation below describes the default starting values; the simulation updates its explanation as you experiment.
Setup
A two-layer wall separates unequal face temperatures. Heat flows left to right, and the question is how the temperature drop divides across the layers.
Series R
Fourier’s law says heat flux is conductivity times the temperature gradient. Each layer behaves like a resistor for heat, with resistance R equal to thickness over conductivity, and layers in series simply add their resistances — exactly like resistors in a circuit. The same heat flux is forced through both.
Solve
Add the resistances, divide the total temperature difference by them, and out comes the heat flux in watts per square metre. The temperature drop across each layer is that flux times the layer’s own resistance — so the high-resistance layer eats the lion’s share of the drop, and the interface temperature is the hot face minus the first layer’s portion.
The gradient
The temperature profile is linear inside each layer and continuous at the seam. Its slope reverses when the boundary temperatures reverse, while the higher-resistance layer always takes the larger magnitude of temperature drop.
Audit
The same flux crosses both layers to a part in a trillion, the two temperature drops add back exactly to the total difference, and each drop equals flux times resistance. Series thermal resistance is Ohm’s law for heat — the identical arithmetic that runs the voltage divider two wings over.