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MHD free convection-radiation interaction in a porous medium - part II: soret/dufour effects

Vasu B., Gorla Rama Subba Reddy, Murthy P. V. S. N., Prasad V. R., Beg O. A., Siddiqa S.

International Journal of Applied Mechanics and Engineering

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2020

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Vol. 25, no. 2

157--175

EN

This paper is focused on the study of two dimensional steady magnetohydrodynamics heat and mass transfer by laminar free convection from a radiative horizontal circular cylinder in a non-Darcy porous medium by taking into account of the Soret/Dufour effects. The boundary layer equations, which are parabolic in nature, are normalized into non-similar form and then solved numerically with the well-tested, efficient, implicit, stable Keller–Box finite-difference scheme. Numerical results are obtained for the velocity, temperature and concentration distributions, as well as the local skin friction, Nusselt number and Sherwood number for several values of the parameters, namely the buoyancy ratio parameter, Prandtl number, Forchheimer number, magnetohydrodynamic body force parameter, Soret and Dufour numbers. The dependency of the thermophysical properties has been discussed on the parameters and shown graphically. Increasing the Forchheimer inertial drag parameter reduces velocity but elevates temperature and concentration. Increasing the Soret number and simultaneously reducing the Dufour number greatly boosts the local heat transfer rate at the cylinder surface. A comparative study of the previously published and present results in a limiting sense is made and an excellent agreement is found between the results.

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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.

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Mixed radiation-convection boundary layer flow of an opically dense fluid along a vertical flat plate in a non-Darcy porous medium

Takhar H. S., Beg O. A., Chamkha A. J., Filip D., Pop I.

International Journal of Applied Mechanics and Engineering

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2003

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Vol. 8, no 3

483-496

EN

The combined effects of thermal radiation flux, thermal conductivity, Reynolds number and non-Darcian (Forcheimmer drag and Brinkman boundary resistance) body forces on steady laminar boundary layer flow along a vertical surface in an idealized geological porous medium are investigated. The classical Rosseland one-dimensional diffusion approximation is implemented in the energy equation to avoid solving the general integro-differential equation for radiative transfer. Pseudo-similarity transformations are invoked and the resulting highly coupled and non-linear set of ordinary differential equations for momentum and energy equations are solved numerically using a well-tested and highly accurate shooting Runge-Kutta quadrature with a Merson-Gill algorithm. It is shown that the dimensionless velocity functions generally increase with rising radiation parameter and the Prandtl number, and the dimensionless temperature functions decrease as the non-Darcian body forces decrease. It is also shown that the dimensionless temperature functions rise in magnitude with rising radiation parameter and the Prandtl number but are depressed by lowered non-Darcian resistance parameter and rising Reynolds number. Generally radiation is seen to substantially boost the overall heat transfer.

5

Computational fluid dynamics modelling of buoyancy induced viscoelastic flow in a porous medium with magnetic field effects

Beg O. A., Takhar H. S., Kumari M., Nath G.

International Journal of Applied Mechanics and Engineering

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2001

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Vol. 6, no 1

187-210

EN

A 2-dimensional computational fluid dynamics analysis of steady state thermal boundary layer flow of a second order non-Newtonian fluid past a horizontal wedge in a Brinkman-Darcy porous medium, in the presence of a transverse magnetic field, is presented. The governing equations are transformed from Cartesian coordinates (x,y) into a sixth order system of partial differential equations in a 'ksi'-n coordinate system. These complex equations are then reduced to a set of six first order equations which are solved using the robust Keller finite difference method, and a block tridiagonal iterative solver, SOLV6. It is shown that heat transfer magnitude is depressed by magnetic field parameter (Hartmann number, Ha) and also considerably reduced with increasing viscoelasticity parameter (K). Surface shear stresses are also reported to fall considerably with increase in viscoelasticity of the fluid. Effects of other hydrodynamic and thermal parameters on the flow are discussed in detail.