The modelling of viscous dissipation in a porous medium saturated by an incompressible fluid is discussed, for the case of Darcy, Forchheimer and Brinkman models. An apparent paradox relating to the effect of inertial effects on viscous dissipation is resolved, and some wider aspects of resistance to flow (concerning quadratic drag and cubic drag) in a porous medium are discussed. Criteria are given for the importance or otherwise of viscous dissipation in various situations.

Resolution of a Paradox Involving Viscous Dissipation and Nonlinear Drag in a Porous Medium

Heat and mass transfer of thermophoretic MHD flow over an inclined radiate isothermal permeable surface in the presence of heat source/sink

Natural convection from an inclined plate embedded in a variable porosity porous medium due to solar radiation

Exact analytical solutions for the magnetohydrodynamic (MHD) flows of an Oldroyd-B fluid through a porous space are developed. The fractional calculus approach is used to describe the constitutive model of a generalized Oldroyd-B fluid. The porous space is taken into account using modified Darcy's law for fractional viscoelastic fluid. The effect of Hall current is taken into account. Some interesting flows induced due to certain special oscillations are given. In each case, the analytical solutions are obtained using Fourier transform for fractional calculus. The present analysis with fractional calculus approach seems a first attempt for the study of MHD viscoelastic flows in a porous medium.

Influence of Hall current on the flows of a generalized Oldroyd-B fluid in a porous space

Nonsimilar, laminar, steady, electrically-conducting forced convection liquid metal boundary layer flow with induced magnetic field effects

The effect of transverse magnetic field parameter (Hartmann number, Ha), Reynolds number (Re) and Prandtl number (Pr) on the mixed convection flow past a semi-infinite vertical porous plate in a non-Darcian porous medium with variable viscosity and porosity, viscous dissipation and fluid–solid thermal conductivity ratio in the presence of plate transpiration (lateral mass flux) is investigated theoretically and numerically using Keller's implicit finite difference scheme. It is shown that the Hartmann number acts as a retarding force and increases the momentum boundary layer thickness, analogous to the flow against a positive pressure gradient, simultaneously decreasing local skin friction (shear stress). The heat transfer rate is however enhanced by the magnetic field (for positive values of the Eckert number) since the fluid is heated and temperature gradients become reduced between the fluid and the plate, with important potential applications in MHD power generators, materials processing and geothermal systems containing electrically-conducting fluids. The effects of high velocity flow (larger Re) and different Prandtl numbers corresponding to different industrial and geophysical fluids on heat transfer are also discussed. © 1997 by John Wiley & Sons, Ltd.

Effects of transverse magnetic field, prandtl number and reynolds number on non‐darcy mixed convective flow of an incompressible viscous fluid past a porous vertical flat plate in a saturated porous medium

Reply to Professor D.A. Nield’s Comments on &E!ects of a transverse magnetic "eld, Prandtl number andReynolds number on non-Darcy mixed convective #ows of an incompressible viscous #uid past a porousvertical #at plate in a saturated porous medium’.The authors would like to greatly thank Professor Nield for his excellent comments. We discuss each ofProfessor Nield’s four comments.1. There is indeed a typographical error in the statement * heat transfer rate is &

http://www.researchgate.net/profile/O_Beg/publication/264637214_Reply_to_comments/links/551c044a0cf20d5fbde2471e.pdf

O. A. Beg

Papers

Effects of transverse magnetic field, prandtl number and reynolds number on non‐darcy mixed convective flow of an incompressible viscous fluid past a porous vertical flat plate in a saturated porous medium

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