Rendering the transient hot wire experimental method for thermal conductivity estimation to two-phase systems-theoretical leading order results

The transient hot wire experimental method for estimating the thermal conductivity of fluids and solids is well established as the most accurate, reliable, and robust technique. It essentially relies on a simple analytical formula derived from the solution of the heat conduction from a line heat source embedded in the target medium. This simple and elegant analytical formulation was derived for uniform and homogeneous fluids or solids. Its extension to two-phase or composite systems, while in practical application, does not have any theoretical basis, and it is by no means obvious that the latter may be applied without corrections to such heterogeneous systems. When it is actually applied as for single-phase systems, it is clearly incorrect. This paper presents preliminary results at the leading order (in the sense of an expansion of the solution in powers of time, applicable to short time scales, consistent with the validity of the transient hot wire method), which render the transient hot wire method to two-phase and composite systems. While these leading order approximations extend the applicability of the same analytical formula to two-phase systems, they also produce additional conditions that need to be fulfilled for such an application to provide reliable experimental results.