Solution of non-linear inverse heat conduction problems using the method of lines

Two space marching methods for solving the one-dimensional nonlinear invers e heat conduction problems are presented. The temperature-dependent thermal properties and the boundary condition on the accessible part of the bounda ry of the body are known. Additional temperature measurements in time are t aken with a sensor located in an arbitrary position within the solid, and t he objective is to determine the surface temperature and heat flux on the r emaining part of the unspecified boundary. The methods have the advantage t hat time derivatives are not replaced by finite differences and the good ac curacy of the method results from an appropriate approximation of the first time derivative using smoothing polynomials. The extension of the first me thod presented in this study to higher dimensions inverse heat conduction p roblems is straightforward.