As discussed in another article, heat conduction is heat transfer from particle to particle inside one medium or several connected mediums without any movement from its particle. How can we quantify the heat transferred by this method? Quantification might be needed if we want to install new heat insulation for our hot water piping or replacing our building insulation. At least, we can check roughly how thick the insulation we need.

Heat Conduction Equation

In general, basic equation for conduction is as following:

heat transferred = driving force / resistance

However, J.B.J. Fourier, at 1882, heat transferred through heat conduction method will be proportional to:

  1. The temperature difference between both side of the medium.
  2. Heat transfer area of the medium.
  3. Thermal conductivity of the medium.

And in opposite correlation with the thickness of the medium. Mathematically, it can be expressed as:

Q = k . A . ΔT / L


  • Q    = heat transfer rate, W (= J/s)
  • L    = thickness, m
  • A    = heat transfer area, m2
  • ΔT    = temperature difference, oC
  • k    = thermal conductivity, W.m/(m2.oC)

Thermal Conductivity Variation

Each substance has different thermal conductivity value. Solid material might be a good heat conductor or a good isolator. Generally, metals are good conductor (k > 8.6 W/(m.K)). While non-metallic solids are usually bad conductor (k < 2.6 W/(m.K)). In some cases, organic solid can be a good conductor, as for example carbon nanotubes. Gaseous (k < 0.17 W/(m.K)) and liquid (k < 0.69 W/(m.K)) phase substance is generally bad conductor and even neglected in conduction calculation. Due to this property, porous solid is also bad conductor since the material is not a continuous body and the pores are filled with gas which is a bad conductor.

Thermal conductivity can be varied due to its material nature, its form (porosity, bulk, homogeneous solid), and temperature. The temperature will generally affect thermal conductivity of homogeneous solid in linear correlation. And for gas, the thermal conductivity will be affected in the proportion of square root of absolute temperature. For liquid, the temperature does not affect thermal conductivity significantly.

Categories: Heat Transfer

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