Jc. Batsale et al., THERMAL QUADRIPOLES METHOD EXTENDED WITH INTEGRAL-TRANSFORMS - CALCULATIONS OF THE HEAT-TRANSFER ACROSS A 2-DIMENSIONAL PLANE CRACK, International journal of heat and mass transfer, 37(1), 1994, pp. 111-127
The quadripole method used in the case of monodirectional diffusion pr
oblems, is extended to bi- or tri-directional cases. The main point is
to use integral transforms (usually Fourier-transforms) for several s
pace variables and Laplace transform for the time variable. The calcul
us 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-dimen
sional defect. Then we use the quadripole method nor perturbation and
matrix inversion method to solve the integral equation, arising in thi
s problem.