An integral approach to the inverse estimation of temperature-dependent thermal conductivity without internal measurements

An integral approach is developed to estimate temperature-dependent thermal conductivity without internal measurements. It is assumed that the thermal conductivity can be expressed as a linear function. Hence, the present inverse heat conduction problem is converted to a parameter estimation problem that determines the unknown coefficients of the thermal conductivity function. In a one-dimensional heat conduction domain with heated and insulated walls, the spatial temperature distribution is modeled as a third-order function of position, whose four coefficients are determined from the heat fluxes and the temperatures at both ends at each measurement. Several examples are successfully introduced to verify the present approach. The proposed approach may also be useful to make sufficiently accurate initial guesses for the inverse heat conduction problem to determine the thermal conductivity having an arbitrary function form.