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Thermal resistance in series

Each layer a wall is built from has its own thermal resistance, exactly like electrical resistors in a circuit. The resistances add in series to find the total resistance, and the heat flow is the same through every layer at steady state, even though the temperature drop differs between them.

R = \dfrac{L}{kA}

thermal resistance, plane layer

R_{tot} = \sum R_i

layers in series

\dot Q = \dfrac{\Delta T}{R_{tot}}

total heat flow

Symbols

$R$	thermal resistance	K/W
$R_{tot}$	total resistance	K/W

Example

Two layers have $R_1 = 0.5$ K/W and $R_2 = 1.5$ K/W. $R_{tot} = 2.0$ K/W. With $\Delta T = 40$ K, $\dot Q = 40/2.0 = 20$ W.

Add resistances in series exactly like electrical resistors:

R_{tot} = \sum L_i/(k_iA)

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← Fourier's law · Cylindrical thermal resistance →

Part of Heat Transfer: Conduction.