Non-iterative estimation of temperature-dependent thermal conductivity without internal measurements

In this work a direct integration method is proposed to estimate temperature-dependent thermal conductivity in a one-dimensional heat conduction domain without internal measurements. By approximating the spatial temperature distribution in the domain as a third-order polynomial of position and by integrating the heat conduction equation over the spatial and temporal domain, the present method estimates the thermal conductivity directly. Also, this method does not require any prior information on the functional form of the thermal conductivity. Some illustrative examples are examined to verify the proposed approach. The proposed approach may also be useful to make sufficiently accurate initial guesses for sophisticated algorithms usually based on iterative refinement scheme.