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 sol
ution 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 constructio
n of the apparatus, resulting in an inability to measure the thermal c
onductivity of high-thermal diffusivity fluids. In this paper, the set
of energy conservation equations describing the transient hot-wire ap
paratus is solved using the numerical finite-element method. Because n
o approximate solutions are involved, this provides a much more genera
l treatment of the heat transfer processes taking part in the real exp
eriment, removing all the aforementioned constraints. In the case of t
he 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 t
he thermal conductivity of gases, the present solution allows the exte
nsion of the application of the transient hot-wire technique to experi
mental conditions where the value of the thermal diffusivity of the fl
uid is high.