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Fourier’s Law of Heat Conduction

Fourier’s Law of Heat Conduction

by ProGATE Andheri

Posted on August 13, 2016 at 10:07 AM

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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)
‘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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