The rate of capillary rise of a liquid into a porous medium made up of consolidated particulates is analyzed. The infiltration distance is parabolic in time and can be modeled using the Washburn analysis. The effective pore radius is measured to be one to two orders of magnitude smaller than the particle size, particle spacing, and the median pore size as measured by mercury porosimetry. This result is interpreted using a modification of the Washburn model which models the porous medium as a single pore with varying diameter. Using a two‐sized single pore model, the predicted infiltration rate is consistent with the measured values. In applying the two‐sized single pore model to the reactive capillary infiltration of silicon into a carbonaceous preform in the Silcomp process, the effect of pore closure by the conversion of carbon to SiC is predicted. Using pore closure dimensions measured in a partial infiltration experiment, a decrease in the infiltration rate constant is predicted and is consistent with the measured infiltration rate.

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SUMMARYAn algorithm is presented for the finite element solution of three-dimensional mixed convection gas flows in channels heated from below. The algorithm uses Newton's method and iterative matrix methods. Two iterative solution algorithms, conjugate gradient squared (CGS) and generalized minimal residual (GMRES), are used in conjunction with a preconditioning technique that is simple to implement. The preconditioner is a subset of the full Jacobian matrix centred around the main diagonal but retaining the most fundamental axial coupling of the residual equations. A domain-renumbering scheme that enhances the overall algorithm performance is proposed on the basis of an analysis of the preconditioner. Comparison with the frontal elimination method demonstrates that the iterative method will be faster when the front width exceeds approximately 500. Techniques for the direct assembly of the problem into a compressed sparse row storage format are demonstrated. Elimination of fixed boundary conditions is shown to decrease the size of the matrix problem by up to 30%. Finally, fluid flow solutions obtained with the numerical technique are presented. These solutions reveal complex three-dimensional mixed convection fluid flow phenomena at low Reynolds numbers, including the reversal of the direction of longitudinal rolls in the presence of a strong recirculation in the entrance region of the channel.