Heat and mass transfer in MHD free convection from a moving permeable vertical surface by a perturbation technique

Abdelkhalek, M.M.

doi:10.1016/j.cnsns.2008.06.001

Cited by 21 publications

(8 citation statements)

References 23 publications

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“…It is also assumed that the temperature and the species concentration at the plate are T w (x) and C w (x), while that of the ambient (inviscid) fluid are T ∞ and C ∞ , respectively. Under these assumptions the basic boundary layer equations can be written in Cartesian coordinates x and y as (see Abdelkhalek [33]),…”

Section: Basic Equationsmentioning

confidence: 99%

Lie group symmetry method for MHD double-diffusive convection from a permeable vertical stretching/shrinking sheet

Roşca

Pop

2016

Computers & Mathematics with Applications

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a b s t r a c tIn this paper, the problem of the steady magnetohydrodynamics (MHD) double-diffusive convection of a viscous and electrically conducting fluid from a permeable vertical stretching/shrinking sheet with the presence of buoyancy force is investigated numerically. The effect of the MHD on the flow, heat transfer and species concentration has been also discussed. The partial differential equations are reduced to ordinary (similarity) equations using the method of the Lie group symmetry. Numerical solutions of the resulting nonlinear boundary value problem are carried out using the function bvp4c from Matlab for different values of the governing parameters. It is found that the solutions of the ordinary (similarity) differential equations have two branches, upper and lower branch solutions, in a certain range of the stretching/shrinking, buoyancy, suction and magnetic parameters. It is shown that the reported results are in excellent agreement with those from the open literature for a forced convection flow when the concentration gradient is absent and the stretching sheet is impermeable. In order to establish which of upper and lower solutions are stable and which are not, a stability analysis has been performed. Thus, it is found that the upper branch solution is stable and, therefore, physically realizable in practice, while the lower branch solution is not stable and, thus, physically not realizable. The effects of the governing parameters on the reduced skin friction coefficient, reduced Nusselt number and reduced Sherwood number are shown in tables and figures. It results in that the governing parameters affect considerably the flow, heat transfer and concentration characteristics. In our opinion, the results are new and original.

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Section: Basic Equationsmentioning

confidence: 99%

Lie group symmetry method for MHD double-diffusive convection from a permeable vertical stretching/shrinking sheet

Roşca

Pop

2016

Computers & Mathematics with Applications

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“…1. (7) It is assumed that the induced magnetic field, the imposed magnetic and electrical fields, and the induced electrical field due to polarization (including Hall Effect) are negligible. (8) Based on the studies of Kahveci and Oztuna (2009) and Abdelkhalek (2008), the viscous dissipation and Joule heating effects are neglected. (9) Two kinds of fluids are investigated: one of low electrical conductivity and the other of strong electrical conductivity.…”

Section: Porous Finmentioning

confidence: 99%

The Effect of MHD on a Porous Fin Attached to a Vertical Isothermal Surface

2010

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The effect of MHD on the total heat transfer from a porous fin attached to a vertical isothermal surface has been investigated. The Maxwell equations have been used, and also Rosseland approximation for radiation heat transfer and Darcy model for simulating the flow in porous medium have been adapted. The governing equations are reduced to a nonlinear ODE. The fin is supposed to be an infinite fin, which is exposed to a magnetic field. The dimensionless temperature profile, and the average Nusselt number profiles have been obtained for different Rayleigh numbers and porosities. Validation is carried out by comparing the results obtained in this study with those predicted by Darcy-Brinkman-Forchheimer model. KeywordsHeat transfer · Porous fin · Darcy model · Darcy-Brinkman-Forchheimer · MHD List of Symbols ACross sectional area (m 2 ) B 0 Magnetic field intensity (T)Thermal conductivity (W m −1 K −1 ) k r Thermal conductivity ratio, k eff /k f A. Taklifi (B) 123 216 A. Taklifi et al. KPermeability of the porous fin (m 2 ) mMass flow rate (kg s −1 ) P Fin perimeter (m) RdRadiation-conduction parameter,Temperature at the fin base (K) uAxial velocity (m s −1 ) v Normal velocity (m s −1 ) V Macroscopic velocity of electrons (m s −1 ) ϑ w Average velocity of the fluid passing through the fin at any point (m s −1 ) x Axial coordinate y Transverse coordinateGreek Symbols α Thermal diffusivity (m 2 s −1 )Kinematic viscosity (m 2 s −1 ) σ Electric conductivity ( −1 m −1 ) σ st Stefan-Boltzmann constant (W m 2 K 4 ) ρDensity of the fluid (kg m −3 ) ρ ε Electrical density (A m −3 )

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“…Sahoo et al [15] studied MHD unsteady free convection flow with heat source/sink. Heat and mass transfer in MHD free convection from a moving permeable vertical surface using perturbation technique has been investigated by Abdelkhalek [1]. Attia [2] studied unsteady MHD Couette flow of a viscoelastic fluid with heat transfer.…”

Section: Introductionmentioning

confidence: 99%

Free Convective Unsteady MHD Flow in Slip-Flow Regime Past A Vertical Plate with A Convective Surface Boundary Condition

Garg

Purohit

Chaudhary

2018

Jour. Inform. Math. Sci.

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This paper examines the unsteady free convective viscous incompressible MHD flow past a vertical porous flat plate with convective surface boundary condition in slip flow regime under the influence of uniform magnetic field acting perpendicular to the porous surface. Assuming time dependent variable suction velocity at the porous plate, analytical expressions for the flow characteristics are obtained by using perturbation technique which converts the non-linear partial differential equations into ordinary differential equations. The effect of various parameters such as Prandtl number, Grashoff number, the Magnetic field parameter, Suction parameter and Convective heat change parameter on the transient velocity, transient temperature, skin friction coefficient and the rate of heat transfer are discussed with the help of graphs.

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Heat and mass transfer in MHD free convection from a moving permeable vertical surface by a perturbation technique

Cited by 21 publications

References 23 publications

Lie group symmetry method for MHD double-diffusive convection from a permeable vertical stretching/shrinking sheet

Lie group symmetry method for MHD double-diffusive convection from a permeable vertical stretching/shrinking sheet

The Effect of MHD on a Porous Fin Attached to a Vertical Isothermal Surface

Free Convective Unsteady MHD Flow in Slip-Flow Regime Past A Vertical Plate with A Convective Surface Boundary Condition

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