Volumetric Heating of Oilshales by Electromagnetic Methods. Volume 4. Thermal Properties

摘要

The problem of heat conduction in layered materials is investigated. Equations for heat conduction developed earlier by Murakami et. al have been used to perform numerical studies for oil shale materials. The resulting solutions are compared to the solutions of the heat equation with effective thermal properties. The comparison yields bounds on the validity of using effective medium values for the thermal properties for time dependent problems. The anisotropic nature of heat conduction in layered materials is also studied. A new solution to the heat equation in composite media is derived using a variational principle developed by Ben-Amoz. The model micro-structure is fed into the equations via a term for the polar moment of the inclusions in a representative volume. The general solution is presented as an integral in terms of sources and a Green function. The problem of uniqueness is studied to determine appropriate boundary conditions. The solution reduces to the solution of the normal heat equation in the limit of homogeneous media. A solution to the heat conduction equation for multi-dimensional composite media, with discontinuities of thermal properties, and having contact resistance at inclusion interfaces is presented. This solution utilizes a quasi-orthogonal expansion technique developed by Tittle. The temperature is expressed as an integral over sources and boundary surfaces in terms of a Green function. The solution is thereby reduced to solving the related eigenfunction problem for the Green function. This solution is also expressed in an alternative form utilizing a technique developed by Olcer which promotes faster convergence of the eigenfunction expansion in regions of discontinuities. 42 refs., 19 figs. (ERA citation 10:048177)