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MODELLING THE FLUID FLOW AND MASS TRANSFER THROUGH POROUS MEDIA WITH EFFECTIVE VISCOSITY ON THE THREE-DIMENSIONAL BOUNDARY LAYER

Volume 21, Edição 11, 2018, pp. 1069-1084
DOI: 10.1615/JPorMedia.2018021347
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RESUMO

The Brinkman model is used to investigate the steady three-dimensional laminar boundary-layer viscous flow over a constant and permeable wedge surface in a porous medium by taking an effective viscosity (which is different from fluid viscosity μ) μeff . The wall surface is assumed to be permeable so that suction/injection is possible. This work is motivated mainly by the lack of consensus in the available literature on the range of effective viscosity, and therefore most of the investigations have considered μeff = μ. Also, the porosity factor of a porous medium has been neglected in several studies. Thus the present work provides a model for quantifying the effective viscosity by incorporating the porosity in the volume averaged Prandtl's boundary layer equations, which are derived from the averaged Navier-Stokes equations for large Reynolds number. Using appropriate similarity transformations to transform the nonlinear boundary-layer equations into two third-order nonlinear coupled ordinary differential equations, a new form of equations is proposed. A well-known numerical Keller-box method is used for the solution of these equations to study fluid flow near the interface between a free fluid and a porous medium. Various results for the velocity profiles and skin frictions are discussed for all physical parameters involved in the study. The results show that the boundary-layer thickness increases for enhanced viscosity ratio and porosity, whereas it is found to decrease for other parameters. For certain parameters, the boundary-layer separation appears near the surface but reattachment takes place away from it. However, due to influences of porous and suction, the separation can effectively be controlled. Further, these results are affirmed by the asymptotic solution of the governing equations for far-field behavior. The physical dynamics of these mechanisms are discussed.

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