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Fourier’s Law of Heat Conduction

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)
Where,
‘Q’ is the heat flow rate by conduction (W)
‘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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