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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All Comments

  • pls help me show full working of how to determine fourier’s equation of heat conduction in isotropic medium

    david Nov 20, 2015 5:27 pm Reply
  • How to find the critical thickness of a insulation if the convective heat transfer co-efficient between the insulating surface and air is 25 W/m^2K.A wire of 6mm diameter with 2 mm thick insulation is used(K=0.11 W/mK).And also want to find the percentage of change in the heat transfer rate if the critical radius is used.Can you please solve this problem with all the steps i can understand?

    Sten Lukose May 1, 2016 12:09 pm Reply

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