Analytic solution based numerical method for inverse boundary value problems of heat and mass transfer in anisotropic bodies

A new numerical iteration method for inverse boundary value problem of anisotropic heat transfer is constructed using the analytical solution of the second kind boundary value problem of heat conduction in anisotropic half space. Using this method the boundary condition of the second kind and size of the boundary subjected to the heat flow were reconstructed using the temperatures in the domain.

The main specifics of the proposed method is the indirect using of function-s minimum, because the parameters in the gradient method cannot be defined. Initially this function is linearized using Taylor series near the previous iteration with definition of unknown parameters for using in gradient methods.

The based on the proposed method numerical solutions have been shown the good convergence to the parameters, used to define temperatures experimentally, even when initial parameters are 2-3 times different.

The proposed method can be used for the inverse coefficient problems of anisotropic heat conduction problems.