The Transient Hot-Wire Technique: A Numerical Approach

The measurement of the thermal conductivity of a fluid by means of the transient hot-wire technique so far has made use of an analytical solution of the energy conservation equation for an ideal model, coupled with a set of approximate analytical corrections to account for small departures from the model. For this solution to be valid, constraints were always imposed on the experimental conditions and the construction of the apparatus, resulting in an inability to measure the thermal conductivity of high-thermal diffusivity fluids. In this paper, the set of energy conservation equations describing the transient hot-wire apparatus is solved using the numerical finite-element method. Because no approximate solutions are involved, this provides a much more general treatment of the heat transfer processes taking part in the real experiment, removing all the aforementioned constraints. In the case of the measurement of the thermal conductivity of liquids (fluids with low thermal-diffusivity values), the numerical solution fully agrees with the existing analytical solution. In the case of the measurement of the thermal conductivity of gases, the present solution allows the extension of the application of the transient hot-wire technique to experimental conditions where the value of the thermal diffusivity of the fluid is high