A simple direct estimation of temperature-dependent thermal conductivity with kirchhoff transformation

A direct method is proposed to estimate the temperature-dependent thermal conductivity without internal measurements. In the proposed method, the steady-state nonlinear heat conduction equation is transformed into the Laplace equation via the Kirchhoff transformation. The thermal conductivity is modeled as a linear combination of known functions with unknown coefficients, which are directly determined from the imposed heat flux and measured temperatures at the boundary. Several inverse heat conduction problems are successfully introduced to confirm the validity of the proposed method.