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In the paper, a numerical simulation of the Beavers-Joseph experiment is presented. The simulation is based on a meshless method which is called the Trefftz method with the special purpose Trefftz functions. The porous medium is modeled as a regular array of fibers. Three kinds of arrays are taken under consideration: triangular, square, and hexagonal. Firstly, the permeability of the fibrous porous medium is determined by consideration of flow between an infinite array of fibers. In the next step the considered region is divided into two parts. The first half of the channel is a porous medium modeled by a regular array of fibers and the second part which is a free fluid flow region. In the paper, the slip constant existing in the Beavers-Joseph boundary condition is determined in terms of the volume fraction of fibers.

In this study, fully developed laminar flow and heat transfer in an internally longitudinally finned tube are investigated through application of the meshless method. The flow is assumed to be both hydrodynamically and thermally developed, with a uniform outside-the-wall temperature. The governing equations have been solved numerically by means of the method of fundamental solutions in combination with the method of particular solutions to obtain the velocity and temperature distributions. The advantage of the proposed approach is that it does not require mesh generation on the considered domain or its boundary, but uses only a cloud of arbitrarily located nodes. The results, comprising the friction factor as well as the Nusselt number, are presented for varied length values and fin numbers, as well as the thermal conductivity ratio between the tube and the flowing fluid. The results show that the heat transfer improves significantly if more fins are used.

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