A NUMERICAL METHOD FOR CONDUCTION IN COMPOSITE MATERIALS, FLOW IN IRREGULAR GEOMETRIES AND CONJUGATE HEAT TRANSFER
For the finite-difference solution of heat conduction, it is shown that, in the case of non-uniform thermal conductivity, the heat flux across the face between two finite-difference cells can be accurately represented by the harmonic mean of the conductivities of the two cells, rather than by the arithmetic mean. The resulting method can handle large discontinuities in thermal conductivity (and other transport properties). A further advantage of the method is that it can be used for fluid-flow calculation in arbitrary geometries by representing the solid regions outside the fluid domain simply as regions of very high viscosity. The method is particularly attractive when a conjugate heat transfer problem involving conduction in the solid and convection in the fluid is to be solved. As examples of the use of the method, the problems of heat conduction in a composite slab, flow in a duct with an internal fin and the fully developed heat transfer in a square duct with finite wall thickness are solved.