Inverse determination of thermal conductivity in two-dimensional domains using finite-difference technique

This paper presents a second-order finite-difference procedure for the inverse determination of thermal conductivity in two-dimensional (2D) domains using the available transient temperature data at discrete grid points. Two kinds of 2D domains are considered-square and cylindrical. The present procedure can predict constant, spatial and temperature dependent thermal conductivities. The estimated thermal conductivity is verified by comparing with a known constant conductivity material (steel). For 2D square domains, the results have also been tested against five benchmark solutions for 1D domain in which thermal conductivities are either constant or linear/non-linear functions of space and temperature by forcing a 2D domain to behave like a 1D domain. The close agreement between the current results and the exact solutions confirms accuracy and effectiveness of the proposed finite-difference technique which does not require a priori knowledge of the functional form for the thermal conductivity.