Non-iteration estimation of thermal conductivity using finite volume method

The finite volume approach is developed for the inverse estimation of thermal conductivity in one-dimensional domain. The differential governing equation of heat conduction is converted to a system of linear equations in matrix form using the temperature data and heat generation at the discrete grid points as well as surface heat flux. The unknown thermal conductivities are obtained by solving the system equations directly. The features of the present method are that no prior information about the functional form of the thermal conductivity is required and no iterations in the calculation process are needed. The accuracy and robust of the present method are verified by comparing examples of inverse estimation of spatially and temperature-dependent thermal conductivities with the exact solutions.