# Fourier′s Law

Empirical relationship between the conduction rate in a material and the temperature gradient in the direction of energy flow.

for unidirectional conduction

Where

q_{x} = heat flux in positive x direction [Wm-2]

dT/dx = negative temperature gradient [Km^{-1}]

k = thermal conductivity [Wm^{-1}K^{-1}]

the heat flow rate at steady state can be written:

Where

q = heat flow [W]

ΔT = temperature difference [K]

k = thermal conductivity [Wm^{-1}K^{-1}]

A = area normal to the direction of heat flow [m^{2}]

d = distance in direction of heat flow [m]

**See also: **Fourier, Baron Jean Baptiste Joseph, Heat Flow Rate, Thermal Conduction, Thermal Conductivity.

**Subjects: ** Thermodynamics