6. Thermal Conductivity Variation with T

  • Thermal conductivity of fluids increases with the increase in temperature. The exception is water, which exhibits increasing \(k\) up to about 150oC and decreasing \(k\) thereafter. Water has the highest thermal conductivity of all liquids except for liquid metals.

  • Thermal conductivity of solids (in general) decreases with the increase in temperature.

  • The thermal conductivity of a material, in general, varies with temperature. An average value for the thermal conductivity is used when the variation is mild.

  • When the variation of thermal conductivity conductivity with temperature \(k(T)\) is known, the average value of the thermal conductivity in the temperature range between \(T_1\) and \(T_2\) can be determined from \[k_{\text{avg}} = \frac{ \int_{T_1}^{T_2}k(T)dT}{T_2-T_1}  \]

  • The variation in thermal conductivity of a material can often be approximated as a linear function and expressed as \[k(T) = k_o(1+\beta T)\] where \(\beta\) is the temperature coefficient of thermal conductivity.