THERMAL QUADRIPOLES METHOD EXTENDED WITH INTEGRAL-TRANSFORMS - CALCULATIONS OF THE HEAT-TRANSFER ACROSS A 2-DIMENSIONAL PLANE CRACK

The quadripole method used in the case of monodirectional diffusion problems, is extended to bi- or tri-directional cases. The main point is to use integral transforms (usually Fourier-transforms) for several space variables and Laplace transform for the time variable. The calculus of the heat transfer across multilayer materials is then presented as a simple matrix product in the transformed space. A second part is devoted to the calculus of the heat transfer across a finite two-dimensional defect. Then we use the quadripole method nor perturbation and matrix inversion method to solve the integral equation, arising in this problem.