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Finite element solutions for two-phase magneto-heat transfer in a particle-suspension through a non-Darcian porous channel with heat source and buoyancy effects

Bhargava R., Rawat S., Takhar H. S., Beg T. A., Anwar Beg o.

International Journal of Applied Mechanics and Engineering

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2008

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Vol. 13, no 2

325-357

EN

We consider the steady, laminar natural convection heat transfer of a particulate suspension in an electrically-conducting fluid through a two-dimensional channel containing a non-Darcian porous material in the presence of a transverse magnetic field. The transport equations for both fluid and particle phases are formulated using a two-phase continuum model and a heat source term is included which simulates either absorption or generation. A set of transformations are implemented to reduce the partial differential equations for momentum and energy conservation (for both phases) from a two-dimensional coordinate system to a one-dimensional system. Finite element solutions are obtained for the transformed model. A comprehensive parametric study of the effects of the heat source parameter (E), Prandtl number (Pr), Grashof number (Gr), momentum inverse Stokes number (Skm), Darcy number (Da), Forchheimer number (Fs), particle loading parameter (PL), buoyancy parameter (B), Hartmann number (Ha), temperature inverse Stokes number (SkT), viscosity ratio [...], specific heat ratio [...], dimensionless particle-phase wall slip parameter [...] on the dimensionless fluid phase velocity (U), dimensionless particle phase velocity ( ), dimensionless fluid phase temperature [...] and the dimensionless temperature of particle phase [...] are presented graphically. In addition, we also describe numerical solutions for several special cases of the model, for example, the inviscid hydromagnetic two phase non-Darcian free convection, heat transfer [...], forced convection case (GrŽ0) etc. Fluid phase velocities are found to be strongly reduced by the magnetic field, Darcian drag and also Forchheimer drag; a lesser reduction is observed for the particle phase velocity field. The Prandtl number is shown to depress both the fluid temperature and particle phase temperature in the left hand side of the channel but to boost both temperatures at the right hand side of the channel [...]. The inverse momentum Stokes number is seen to reduce fluid phase velocities and increase particle phase velocities. The influence of other thermophysical parameters is discussed in detail and computations compared with previous studies. The model finds applications in MHD plasma accelerators, astrophysical flows, geophysics, geothermics and industrial materials processing.

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Non-isothermal hydromagnetic convection in a porous medium with heat sink: hypergeometric function solutions

Beg O. A., Takhar H. S., Beg T. A., Singh A. K.

International Journal of Applied Mechanics and Engineering

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2007

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Vol. 12, no 2

337-351

EN

The present paper deals with the free convection laminar boundary layer flow and heat transfer of an incompressible, electrically conducting, viscous fluid through a porous medium caused by stretching a porous wall in the presence of a heat source and under the influence of uniform magnetic field. Exact solutions of the basic equations of momentu m and energy ar e obtained after reducing them i n to non-linear ordinary differential equations and using confluent hypergeometric functions. The variations in the velocity field and temperature distribution with the Prandtl number (Pr), hydromagnetic parameter (M), permeability param eter (K), suction parameter (N), wall temperature parameler (S), and the heat sink parameter (Q) are obtained and depicted graphically. The skin-friction at the wall is also derived, and the numerical values for various physical parameters are also tabulaled. Magnetic field (M) is seen to reduce both longitudinal and translational velocities and also lower temperalures, aiding in controlling momentum and heat transfer during materiaIs processing. Suction (N) posivitely influences the transverse velocity but depresses the longitudinal velocity magnitudes as we II as decreasing tempcratures. Suction therefore also assists in controlling heat transfer in Ihe boundary layer. Increasing permeability parameter (K) depresses the longitudinal velocity but elevates transverse velocities and increases the skin friction at the wall. Both rising temperature (non-isothermal wall) parameter (S) and heat sink parameter (Q) decrease temperature values. The model finds applications in nucIear engineering control systems and MHD energy systems.

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Finite element modeling of laminar flow of a third grade fluid in a Darcy-Forcheimmer porous medium with suction effects

Takhar H. S., Bhargava R., Rawat S., Beg T. A., Beg O. A.

International Journal of Applied Mechanics and Engineering

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2007

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Vol. 12, no 1

215-233

EN

A mathematical model to simulate the steady laminar flow of an incompressible, third grade, non-Newtonian fluid past an infinite porous plate embedded in a Darcy-Forcheimmer porous medium is presented. A number of special cases are examined for the governing nonlinear differential equation. The model is solved with appropriate boundary conditions using the finite element method. Velocity and velocity gradient are plotted graphically for variation in permeability (k), Forcheimmer parameter (b), third grade materiaI parameter (f3 3 ) , and suction effect (Vo). It is shown that velocities are generally decreased transverse to the plate surface with increasing Forcheimmer parameter; increasing permeability conversely boosts the velocities, as this corresponds to an increasingly fluid (Le., progressively less porous) regime. The third grade material parameter is also seen to substantially increase the velocities in the direction normal to the plate surface. The special case of a second order viscoelastic flow is also studied. The flow scenario finds applications in polymer extrusion processes, and other important industrial rheology systems.