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Research Papers: Porous Media

Thermophoretic and Nonlinear Convection in Non-Darcy Porous Medium

[+] Author and Article Information
P. K. Kameswaran

School of Math, Statistics & Computer Science,
University of KwaZulu-Natal,
P/Bag X01, Scottsville,
Pietermaritzburg 3209, South Africa
e-mail: Perik@ukzn.ac.za

P. Sibanda

School of Math, Statistics & Computer Science,
University of KwaZulu-Natal,
P/Bag X01, Scottsville,
Pietermaritzburg 3209, South Africa
e-mail: sibandap@ukzn.ac.za

M. K. Partha

Department of Mathematics,
Malnad College of Engineering,
Salagame Road,
Hassan 573 201, India
e-mail: mkpartha@rediffmail.com

P. V. S. N. Murthy

Department of Mathematics,
Indian Institute of Technology,
Kharagpur 721 302, India
e-mail: pvsnm@maths.iitkgp.ernet.in

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received December 3, 2012; final manuscript received August 20, 2013; published online January 9, 2014. Assoc. Editor: Jose L. Lage.

J. Heat Transfer 136(4), 042601 (Jan 09, 2014) (9 pages) Paper No: HT-12-1644; doi: 10.1115/1.4025902 History: Received December 03, 2012; Revised August 20, 2013

In this paper, we study the effects of nonlinear convection and thermophoresis in steady boundary layer flow over a vertical impermeable wall in a non-Darcy porous medium. Both the fluid temperature and the solute concentration are assumed to be nonlinear while at the wall, both the temperature and concentration are maintained at a constant value. A similarity transformation was used to obtain a system of nonlinear ordinary differential equations, which were then solved numerically using the Matlab bvp4c solver. A comparison of the numerical results with previously published results for special cases shows a good agreement. The effects of the nonlinear temperature and concentration parameters on the velocity and heat and mass transfer are shown graphically. A representative sample of the results is presented showing the effects of thermophoresis on the fluid velocity and heat and mass transfer rates. It is found among other results, that the concentration profiles decreased with increasing values of the thermophoretic parameter.

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References

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Figures

Grahic Jump Location
Fig. 1

Schmidt diagram and coordinate system

Grahic Jump Location
Fig. 2

Nondimensional velocity for F = 2.5,N = 1,Le = 10,Peγ = Peξ = 0,MC = 0.01,MT = 0.5,Pr = 0.72,k = 0.5,Ra/Pe = 1

Grahic Jump Location
Fig. 3

Nondimensional temperature for F = 2.5,N = 10,Le = 1,Peγ = Peξ = 0,MC = 0.01,MT = 0.5,Pr = 0.72,k = 0.5,Ra/Pe = 1

Grahic Jump Location
Fig. 4

concentration profile for F = 2.5,N = 10,Le = 1,Peγ = Peξ = 0,MC = 0.01,MT = 0.5,Pr = 0.72,k = 0.5,Ra/Pe = 1

Grahic Jump Location
Fig. 5

Heat transfer coefficient as a function of thermophoretic constant, when F = 0,N = -0.5,Pr = 0.72,MC = 0.01,MT = 0.5,α1 = α2 = 0.5,Ra/Pe = 2

Grahic Jump Location
Fig. 6

Mass transfer coefficient as a function of thermophoretic constant when F = 0,N = -0.5,Pr = 0.72,MC = 0.01,MT = 0.5,α1 = α2 = 0.5,Ra/Pe = 2

Grahic Jump Location
Fig. 7

Heat transfer coefficient as a function of nonlinear temperature or nonlinear concentration, when F = 0,N = -0.5,Pr= 0.72,MC = 0.01,MT = 0.5,Peγ = Peξ = 5,Ra/Pe = 2

Grahic Jump Location
Fig. 8

Heat transfer coefficient as a function of nonlinear temperature or nonlinear concentration, when N = -0.5,Pr = 0.72,Le = 10,MC = 0.01,MT = 0.5,Peγ = Peξ = 0,k = 0.5

Grahic Jump Location
Fig. 9

Heat transfer coefficient as a function of nonlinear temperature or nonlinear concentration, when N = -0.5,Pr = 0.72,Le = 10,MC = 0.01,MT = 0.5,k = 0.5,Ra/Pe = 1

Grahic Jump Location
Fig. 10

Nondimensional velocity profile as a function of nonlinear temperature, when N = -0.5,Pr = 0.72,Le = 1,MC = 0.01,MT = 0.5,k = 0.5,α2 = 1.5,Peγ = Peξ = 1

Grahic Jump Location
Fig. 11

concentration profile for F = 0,N = -0.5,Pr = 0.72,MC = 0.01,MT = 0.5,α1 = α2 = 0.5,k = 0.5,Ra/Pe = 1

Grahic Jump Location
Fig. 12

concentration profile for N = -0.5,Pr = 0.72,Le = 10,Peγ = Peξ = 0,α1 = α2 = 1,MC = 0.01,MT = 0.5,Ra/Pe = 2

Grahic Jump Location
Fig. 13

Effect of thermophoretic coefficient k on wall thermophoretic deposition velocity for different values of Le,Peγ,Peξ when F = 0,N = -0.5,Pr = 0.72,MC = 0.01,MT = 0.5,α1 = α2 = 0.5,Ra/Pe = 1 are fixed

Grahic Jump Location
Fig. 14

Effect of nonlinear temperature α1 on wall thermophoretic deposition velocity for different values (F = 0,N = -0.5,Pr = 0.72,MC = 0.01,MT = 0.5,α2 = 1,Ra/Pe = 1 are fixed)

Grahic Jump Location
Fig. 15

Effect of nonlinear concentration α2 on wall thermophoretic deposition velocity for different values of (F=0,N=-0.5,Pr=0.72,MC=0.01,MT=0.5,α1=1,Ra/Pe = 1 are fixed)

Grahic Jump Location
Fig. 16

Effect of MT on wall thermophoretic deposition velocity for different values of (F = 0,N = -0.5,Pr = 0.72,MC = 0.01,α1 = α2 = 1,Ra/Pe = 1,k = 0.5 are fixed)

Grahic Jump Location
Fig. 17

Effect of MC on wall thermophoretic deposition velocity for different values of (F = 0,N = 1,Pr = 0.72,MT = 0.5,α1 = α2 = 1,Ra/Pe = 1,k = 0.5 are fixed)

Grahic Jump Location
Fig. 18

Nondimensional concentration for different values of F = 0,N = 10,Pr = 0.72,Peγ = Peξ = 0,α1 = α2 = 0.5,Le = 1.5,Ra/Pe = 1,k = 0.5,MC = 3.5

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