Effects of Variable Fluid Properties and Viscous Dissipation on Mixed Convection Fluid Flow past a Vertical Plate in Porous Medium

Full Text(PDF, ) PP.398402


Author(s) 
P.K.Singh 

KEYWORDS 
Porous medium, variable permeability, thermal conductivity, viscosity, viscous dissipation,vertical plate. 

ABSTRACT 
In the present work, free and forced convection boundary layer flow of an incompressible and viscous dissipative fluid with variable thermal conductivity and temperature dependent viscosity past a an isothermal vertical plate is investigated. The convective flow is taking place in such a porous medium whose permeability is assumed to be spatially variable. The convective flow is due to two factors which influence the flow simultaneously (1) free stream along the plate and (2) the buoyancy force caused by the variations in density due to temperature difference. The governing equations for the the boundary layer flow are converted into to a system of coupled ordinary differential equations by using suitable similarity transformations. These equations are solved numerically and effects of Grashof number, Eckert number and permeability parameter on the velocity and temperature are discussed and presented graphically 

References 

[1]. K.Pohlhausen, “Zur naherungsweisen Integration der Differentialgleichung der laminaren Grenzschicht”, ZAMM, 1921,
252268
[2]. J.H. Merkin, “The effect of buoyancy forces on the boundary layer flow over a semi infinite vertical flat plate in a uniform free stream”, J. Fluid Mech., 35, 1969, 439450.
[3]. J.H Merkin, “Free convection with blowing and suction”,
Int. J. Heat Mass Transfer, 15, 1972, 989999.
[4]. P. Cheng and W.J. Minkowycz, “Free convection about a
vertical plate embedded in a porous medium with application
to heat transfer from a dick”, J. Geophys Res, 28, 1977, 2040
2048.
[5]. P. Ranganathann and R. Viskanta, “Mixed convective
boundary layer flow along a vertical surface in a porous medium”, Num Heat Transfer, 7, 1984, 305317.
[6]. C. H. Chen, T. S. Chen and C. K. Chen, “NonDarcy
mixed convection along non isothermal vertical surfaces in
porous medium”, Int. J. Heat Mass Transfer, 39, 1996, 1157
1164.
[7]. H. Schlichting, “Boundary layer Theory”, Mc Graw Hill,
NewYork, 1979
[8]. W.M. Kays and M.E. Crawferd, “Convective Heat and
Mass Transfer”, McGraw Hill, NewYork, 1980.
[9]. I. G. Choi, “The effect of variable properties of air on the boundary layer for a moving continuous cylinder”, Int. J. Heat
Mass Transfer, 25, 1982, 597602.
[10]. F. C. Lai and F. A. Kulacki, “The effect of variable viscosity on convective heat transfer along a vertical surface in a saturated porous medium”, Int.J. Heat Mass Transfer, 33, 1990,
10281031.
[11]. I. Pop, R. S. R. Gorla and M. Rashid, “The effect of variable viscosity on flow and heat transfer to a continuous moving
flat plate”, Int. J. Engg,Sc., 30, 1992, 16.
[12]. A.T. Eswara and G. Nath, “Unsteady non similar two dimensional and axisymmetric water boundary layer with variable viscosity and Prandtl number”, Int. J. Engg,Sc., 32, 1994,
267279.
[13]. E. M. A. Elbashbeshy, “Free convection flow with variable viscosity and thermal diffusivity along a vertical plate in the
presences of the magnetic field”, Int.J.Eng.Sci. 38, 2000, 207
213.
[14]. M. A. Seddeek, “Effects of variable viscosity on hydromagnetic flow and heat transfer past a continuously moving
porous boundary with radiation”, Int. Comm. Heat Mass Transfer, 27, 2000, 10371064
[15]. M. A. Seddeek and A.A. Almushigeh, “Effects of radiation
and variable viscosity on MHD free convective flow and mass
transfer over a stretching sheet with chemical reaction”, Applications and Applied Mathematics, 5, 2010, 181197.
[16]. E. M. A. Elbashbeshy and F.N. Ibrahim, “Steady free convection flow with variable viscosity and thermal diffusivity along
a vertical plate”, J.Phys.26 (12), 1993 237243.
[17]. P. K. Khound and G.C. Hazarika, “The effect of variable
viscosity and thermal conductivity on liquid film on an unsteady stretching surface”, Proc. Of 46th Annual Tech. Session,
Ass. Sc. Soc., 2000, 4756.
[18]. J. W. Tierney, L.H.S. Roblee and R.M. Barid, “Radial
porosity variation in packed beds”, A.I.Ch.E. J., 1958 , 460464
[19].R.F. Benenati and C.B. Brosilow, “Void fraction distribution
in beds of sphere”, A.I.Ch.E. J., 1962, 359361.
[20]. B. C. Chandrasekhar, A. R. Hanumanthappa and S.
Chandranna, “Mixed convection in the presence of horizontal
impermeable surfaces in saturated porous media with variable
to permeability”, Proc. 12th Natl Conf Fluid Dynamics Fluid
Power, IIT, Delhi, 1983, Dec.810.
[21]. B. C. Chandrasekhar and P. M. S. Namboodiri, “Influence
of variable permeability and combined free and forced convection about inclined surfaces in porous media”,Int. J. Heat Mass
Transfer, 28, 1985, 199206.
[22]. M. Mansour and N. ElShaer, “Mixed convection radiation
in power law fluids along a nonisothermal wedge in a porous
medium with variable permeability, Transport in porous Medium” Transport in porous Medium, 57 (3), 2004, 336346.
[23]. M. G. Reddy and N.B. Reddy, “Unsteady MHD convective heat and mass transfer past a ssemiinfinite vertical porous plate with variable viscosity and thermal conductivity”,
Inernational Journal of Applied Mathematics and Computation,
1(2), 2009, 104117.
[24]. I. A. Hassanien, “Variable permeability effects on mixed
convection along a vertical wedge embedded in a porous medium with variable surface heat flux”, Applied Mathematics and
Computation, 138 (1), 4159, 2003.


