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Research Papers: Natural and Mixed Convection

Soret Effect on the Natural Convection From a Vertical Plate in a Thermally Stratified Porous Medium Saturated With Non-Newtonian Liquid

[+] Author and Article Information
M. Narayana

e-mail: narayana@ukzn.ac.za

A. A. Khidir

e-mail: 209539773@stu.ukzn.ac.za

P. Sibanda

e-mail: sibandap@ukzn.ac.za
School of Mathematical Sciences,
University of KwaZulu-Natal,
Private Bag X01 Scottsville,
Pietermaritzburg 3209, South Africa

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 13, 2011; final manuscript received June 1, 2012; published online February 8, 2013. Assoc. Editor: Andrey Kuznetsov.

J. Heat Transfer 135(3), 032501 (Feb 08, 2013) (10 pages) Paper No: HT-11-1566; doi: 10.1115/1.4007880 History: Received December 13, 2011; Revised June 01, 2012

The paper highlights the application of a recent seminumerical successive linearization method (SLM) in solving highly coupled, nonlinear boundary value problem. The method is presented in detail by solving the problem of free convection flow due to a vertical plate embedded in a non-Darcy thermally stratified porous medium saturated with a non-Newtonian power-law liquid. Thermal-diffusion (Soret) and variable viscosity effects are taken into consideration. The Ostwald–de Waele power-law model is used to characterize the non-Newtonian behavior of the fluid. The governing partial differential equations are transformed into a system of ordinary differential equations and solved by SLM. The accuracy of the SLM has been tested by comparing the results with those obtained using the shooting technique. The effect of various physical parameters such as power-law index, Soret number, variable viscosity parameter, and thermal stratification parameter on the dynamics of the fluid is analyzed through computed results. Heat and mass transfer coefficients are also shown graphically for different values of the parameters.

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Figures

Grahic Jump Location
Fig. 1

Variation of θ(η) and ϕ(η) with η for varying ε and n when γ = 1.2, Gr*= 1, Sr = 0.1, Le = 1, and Λ = −0.1

Grahic Jump Location
Fig. 2

Variation of θ(η) and ϕ(η) with η for varying γ and n when ε = 0.1, Gr*= 1, Sr = 0.1, Le = 1, and Λ = 0.1

Grahic Jump Location
Fig. 3

Variation of θ(η) and ϕ(η) with η for varying γ and n when ε = 0.1, Gr*= 1, Sr = 0.1, Le = 1, and Λ = −0.1

Grahic Jump Location
Fig. 4

Variation of θ(η) and ϕ(η) with η for varying Sr and n when ε = 0.1, γ = 1.5, Gr*= 1, Le = 1, and Λ = −0.1

Grahic Jump Location
Fig. 5

Variation of heat and mass transfer coefficients against ε for varying n and Sr when γ = 1.2, Gr*= 1, Le = 1, and Λ = −0.2

Grahic Jump Location
Fig. 6

Variation of heat and mass transfer coefficients against Sr for varying ε and n when γ = 1, Gr*= 1, Le = 1 and Λ = 0.1

Grahic Jump Location
Fig. 7

Variation of heat and mass transfer coefficients against γ for varying ε and n when Sr = 0.5, Gr*= 1, Le = 1, and Λ = 0.1

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