Fourier’s Law of Heat Conduction

The law of heat conduction is also known as Fourier’s law. Fourier’s law states that

“the time rate of heat transfer through a material is proportional to the negative gradient in the temperature and to the area.”

Fourier’s equation of heat conduction:

Q = -kA(dT/dx)


‘Q’ is the heat flow rate by conduction (W·m−2)
‘k’ is the thermal conductivity of body material (W·m−1·K−1)
‘A’ is the cross-sectional area normal to direction of heat flow (m2) and
‘dT/dx’ is the temperature gradient (K·m−1).

§  Negative sign in Fourier’s equation indicates that the heat flow is in the direction of negative gradient temperature and that serves to make heat flow positive.

§  Thermal conductivity ‘k’ is one of the transport properties. Other are the viscosity associated with the transport of momentum, diffusion coefficient associated with the transport of mass.

§  Thermal conductivity ‘k’ provides an indication of the rate at which heat energy is transferred through a medium by conduction process.

Assumptions of Fourier equation:

§  Steady state heat conduction.

§  One directional heat flow.

§  Bounding surfaces are isothermal in character that is constant and uniform temperatures are maintained at the two faces.

§  Isotropic and homogeneous material and thermal conductivity ‘k’ is constant.

§  Constant temperature gradient and linear temperature profile.

§  No internal heat generation.

Features of Fourier equation:

§  Fourier equation is valid for all matter solid, liquid or gas.

§  The vector expression indicating that heat flow rate is normal to an isotherm and is in the direction of decreasing temperature.

§  It cannot be derived from first principle.

§  It helps to define the transport property ‘k’.

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