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

Preeti Garg, G. N. Purohit, R. C. Chaudhary

Abstract


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.

Keywords


Free convection; Magneto-hydrodynamics; Boundary layer; Vertical porous plate; Suction velocity; Convective boundary condition; Slip-flow regime

Full Text:

PDF

References


M.M. Abdelkhalek, Heat and mass transfer in MHD free convection from a moving permeable vertical surface by a perturbation technique, Commun. Nonlinear Sci. Numer. Simulat. 14 (2009), 2091 – 2102.

H.A. Attia, Unsteady MHD couette flow of a viscoelastic fluid with heat transfer, Kragujevac J. Sci. 32 (2010), 5 – 15.

A. Aziz, A similarity solution for laminar thermal boundary layer over a flat plate with a convective surface boundary condition, Communications in Nonlinear Science and Numerical Simulation 14 (2009), 1064 – 1068.

R.C. Chaudhary and A.K. Jha, Effects of chemical reactions on MHD micropolar fluid flow past a vertical plate in slip-flow regime, Appl. Math. Mech. - Engl. Ed. 29 (9) (2008), 1179 – 1194.

U.N. Das, R.K. Deka and V.M. Soundalgekar, Transient free convection flow past an infinite vertical plate with periodic temperature variation, J. Heat Transfer (ASME) 121 (1999), 1091 – 1094.

K. Gangadhar, N.B. Reddy and P.K. Kameshwaran, Similarity solution of hydro magnetic heat and mass transfer over a vertical plate with a convective surface boundary condition and chemical reaction, International Journal of Nonlinear Science 13 (3) (2012), 298 – 307.

P. Garg, G.N. Purohit and R.C. Chaudhary, Similarity solutions for combined free-forced convection past a vertical porous plate in a porous medium with a convective surface boundary condition, Int. J. of Applied Mechanics and Engineering 21 (4) (2016), 827 – 836.

T. Hayat, T. Javed and Z. Abbas, Slip flow and heat transfer of a second grade fluid past a stretching sheet through a porous space, Int. J. of Heat and Mass Transfer. 51 (2008), 4528 – 4534.

M.A. Hossain, S. Hussain and D.A. Rees, Influence of fluctuating surface temperature and concentration on natural convection flow from a vertical flat plate, Z. angew. Math. Mech. (ZAMM) 81 (2001), 699 – 709.

A.R.A. Khaled and K. Vafai, The effect of the slip condition on stokes and couette flows due to an oscillatory wall: exact solution, Int. J. Nonlinear Mech. 39 (2004), 795 – 809.

O.D. Makinde, Effect of variable viscosity on thermal boundary layer over a permeable flat plate with radiation and a convective surface boundary condition, Journal of Mechanical Science and Technology 26 (2012), 1615 – 1622.

O.G. Martynenko, A.A. Berezovsky and Y.A. Sokovishin, Laminar free convection from a vertical plate, Int. J. Heat Mass Transfer. 27 (1984), 869 – 881.

A. Mehmood and A. Ali, The effect of slip condition on unsteady MHD oscillatory flow of a viscous fluid in a planer channel, Rom. Journ. Phys. 52 (2007), 85 – 91.

P. Olanrewaju, T. Anake, O.T. Arulogun and D. Ajadi, Further results on the effects of variable viscosity and magnetic field on flow and heat transfer to a continuous flat plate in the presence of heat generation and radiation with a convective boundary condition, American Journal of Computational and Applied Mathematics 2 (2012), 42 – 48.

P.K. Sahoo, N. Datta and S. Biswal, Magneto hydrodynamic unsteady free convection flow past an infinite vertical plate with constant suction and heat sink, Ind. J. Pure Appl. Math. 34 (2003), 145 – 155.

P.K. Sharma and R.C. Chaudhary, Effect of variable suction on transient free convection viscous incompressible flow past a vertical plate with periodic temperature variations in slip-flow regime, Emirates Journal for Engineering Research 8 (2003), 33 – 38.




DOI: http://dx.doi.org/10.26713%2Fjims.v10i1-2.1050

eISSN 0975-5748; pISSN 0974-875X