Transverse eigenproblem of steady-state heat conduction for multidimensional two-layered slabs with automatic computation of eigenvalues (Q1434574)

The authors report a method for numerical evaluation of the transverse eigenvalues of a linear steady-state heat conduction problem in a two-layer slab in 3-D geometry. Both layers are assumed to be of finite thickness, isotropic, with temperature independent thermophysical properties and non-zero thermal contact resistance at the contact surface between the layers. The latter assumption results in a continuous heat flux across the contact surface; however the temperature field would have a finite discontinuity there. For the specific assumptions, the transverse eigenvalue problem, in a direction perpendicular to the plane of contact, is decoupled from the problem in any direction parallel to this plane and is reduced to a well known Sturm-Liouville type problem. The author chooses to derive lower and upper bounds for any eigenvalue from the particular physical and geometrical considerations, and converge upon the eigenvalue using a fast and reliable iteration procedure. The approach has been illustrated by numerical examples. Such an approach is efficient when addressing a concrete physical problem, however it impacts on the generality of the procedure.