Estimation of temperature-dependent thermal conductivity with a simple integral approach

Abstract

We present an integral approach to estimate temperature-dependent thermal conductivity in a transient non-linear heat conduction medium. It is assumed that the thermal conductivity is a monotonic function of the temperature and it can be expressed as a piecewise linear function. Hence, the present inverse heat conduction problem is converted to a parameter identification problem determining the unknown coefficients of the thermal conductivity function that is approximated to be piecewise linear. The spatial temperature distribution required for the integral approach is modeled as a third-order function of position in a one-dimensional heat conduction domain with heated and insulated walls. Four coefficients of the approximated temperature distribution are determined from the heat fluxes imposed and the temperatures measured at both ends at each measurement. Hence, the proposed algorithm does not require any internal measurements. Numerical experiments are successfully introduced to verify the present approach. The proposed method may also be useful to make sufficiently accurate initial guesses for the inverse heat conduction problem to determine the thermal conductivity having an arbitrary functional form