Restoration of the heat transfer coefficient from boundary measurements using the Sinc method

In this paper, the restoration of the time-dependent heat transfer coefficient in the inverse heat conduction problems from some standard or non-standard boundary measurements is investigated. Depending on additional information, the inverse problems can be transformed into an equivalent set of integral equations with convolution kernels. By using an explicit procedure on the basis of Sinc-function properties, the resulting integral equations are replaced by a system of nonlinear algebraic equations, whose solution yields accurate approximations for missing terms involving the boundary and interior temperatures, the heat fluxes and the heat transfer coefficient. Some examples are considered to illustrate the ability of the proposed method.