Physical regularization for inverse problems of stationary heat conduction

In the paper, physical foundation of a functional for solving discontinuous stationary heat conduction problems with a kind of regularisation parameter has been presented. Then, the noncontinuous FEM with Trefftz base functions and a wide range of the regularisation parameter values has been applied to solving direct and inverse problem of linear heat conduction. 2D test problem solution has been discussed. Then a problem of finding heat transfer coefficient and temperature on the inner boundary of a turbine blade has been considered. To solve the problem the numerical entropy production intensity and energy dissipation function have been minimized on the boundary of the blade cross-section. In order to simplify the numerical calculation the Bernstein polynomials have been used to approximate the boundary temperature. Increasing the number of base functions in the finite element substantially decreases the inaccuracies of direct and inverse problem solution. It seems that the only disadvantage of minimising the functionals of entropy production intensity or energy dissipation lead to nonlinear system of algebraic equation. © de Gruyter 2007.