Inverse determination of thermal conductivity by differential quadrature method

The differential quadrature method (DQM) is employed to inverse determination of thermal conductivity in one-dimensional slab. Several examples including spatially dependent and temperature dependent thermal conductivities are solved to illustrate the accuracy and efficiency of the DQM. The advantages of this approach are that no a priori assumption is made on the functional form of the estimates, and that the estimated thermal conductivity can be obtained directly in the calculating process. Of interest are the effects of the number of the measurement points and magnitude of measurement errors on the accuracy of the estimations. Comparisons are made between the estimated thermal conductivities and exact forms, and the agreement is found out to be generally good. Numerical results demonstrate that the DQM is effective and stable in treating this type of problem.