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Research Papers: Bio-Heat and Mass Transfer

Cross-Diffusion Effects on Unsteady Bioconvective Flow Past a Stretching Sheet

[+] Author and Article Information
Musawenkhosi P. Mkhatshwa

Department of Pure and Applied Mathematics,
University of Johannesburg,
P.O. Box 524,
Auckland Park 2006, Republic of South Africa
e-mail: patsonmkhatshwa@gmail.com

Faiz G. Awad

Department of Pure and Applied Mathematics,
University of Johannesburg,
P.O. Box 524,
Auckland Park 2006, Republic of South Africa
e-mail: awad.fga@gmail.com

Melusi Khumalo

Department of Pure and Applied Mathematics,
University of Johannesburg,
P.O. Box 524,
Auckland Park 2006, Republic of South Africa
e-mail: mkhumalo@uj.ac.za

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received December 14, 2015; final manuscript received October 5, 2016; published online November 16, 2016. Assoc. Editor: Andrey Kuznetsov.

J. Heat Transfer 139(3), 031101 (Nov 16, 2016) (11 pages) Paper No: HT-15-1789; doi: 10.1115/1.4034937 History: Received December 14, 2015; Revised October 05, 2016

This paper presents a mathematical analysis of bioconvection heat, mass, and motile microorganisms transfer over a stretching sheet in a medium filled with a fluid containing gyrotactic microorganisms. Cross-diffusion is taken into account in the medium. Using the boundary layer approximations, the set of unsteady partial differential equations governing the fluid flow is transformed into nonlinear PDEs form and then solved numerically using bivariate spectral relaxation method (BSRM) and bivariate spectral quasi-linearization method (BSQLM). A comparison between BSRM and BSQLM is made for the first time in this work. The accuracy and convergence analysis of the methods are also discussed. The methods are found to be convergent and give very accurate results with very few grid points in the numerical discretization procedure. A parametric study of the entire flow regime is carried out to illustrate the effects of various governing parameters on the fluid properties and flow characteristics. The results obtained show a significant effect of cross-diffusion on the fluid properties and flow characteristics. The Dufour number was found to increase the local Sherwood number and density number of motile microorganisms while decreasing the Nusselt number, and the reverse effect is true for the Soret number. Furthermore, the Nusselt number, Sherwood number, and density number of motile microorganisms are highly influenced by buoyancy and bioconvection parameters.

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References

Figures

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Fig. 1

Physical model and coordinate system

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Fig. 2

BSRM and BSQLM variation of solution errors against iterations when ξ=0.5,Gr=0.5, Rab=1 Pr=1, Df=0.5,Sr=0.2, Le=1, Lb=2, Pe = 1, and δ = 0.5

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Fig. 3

Effects of Gr and Rab on the velocity profiles for ξ=0.5, Pr=1, Df=0.5, Sr=0.2, Le=1, Lb=2, Pe = 1, and δ = 0.5

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Fig. 4

Effects of Gr and Rab on the temperature profiles for ξ=0.5, Pr=1, Df=0.5, Sr=0.2, Le=1, Lb=2, Pe = 1, and δ = 0.5

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Fig. 5

Effects of Gr and Rab on the concentration profiles for ξ = 0.5, Pr = 1, Df = 0.5, Sr = 0.2, Le = 1, Lb = 2, Pe = 1, and δ = 0.2

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Fig. 6

Effects of Gr and Rab on the microorganism density profiles for ξ=0.5, Pr=1, Df=0.5, Sr=0.2, Le=1, Lb=2, Pe = 1, and δ = 0.5

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Fig. 7

Effect of Sr on the temperature and concentration profiles for ξ=0.5, Gr=0.5, Rab=1, Pr=1, Df=0.5, Le=1,Lb=2, Pe = 1, and δ = 0.5

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Fig. 8

Effect of Df on temperature and concentration profiles for ξ=0.5, Gr=0.5, Rab=1, Pr=1, Sr=0.2, Le=1, Lb=2, Pe = 1, and δ = 0.5

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Fig. 9

Effects of Sr and δ on the microorganism density profiles for ξ=0.5, Gr=0.5, Rab=1, Pr=1, Df=0.5, Le=1, Lb=2, and Pe = 1

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Fig. 10

Effect of δ on temperature and concentration profiles for ξ=0.5, Gr=0.5, Rab=1, Pr=1, Df=0.5, Sr=0.2, Le=1, Lb=2, and Pe = 1

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Fig. 11

Effects of Lb and Pe on microorganism density profiles for ξ=0.5, Gr=0.5, Rab=1, Pr=1, Df=0.5, Le=1, Sr=0.2, and δ = 0.5

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Fig. 12

Effect of Gr and Rab on the skin friction coefficient for Pr=1, Le=1, Df=0.5, Sr=0.2, Pe=1, δ=0.5, and Lb = 2

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Fig. 13

Effect of Sr on the heat and mass transfer coefficients, respectively, for ξ=0.5, Pr=1, Le=1, Gr=0.5, Rab=1,Df=0.5, Pe=1, δ=0.5, and Lb = 2

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Fig. 14

Effect of Df on the heat and mass transfer coefficients, respectively, for ξ=0.5, Pr=1, Le=1, Gr=0.5, Rab=1,Sr=0.2, Pe=1, δ=0.5, and Lb = 2

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Fig. 15

Effects of Sr and Df on the density number of motilemicroorganisms for ξ=0.5, Pr=1, Le=1, Gr=0.5,Rab=1, Df=0.5, Sr=0.2, Pe=1, δ=0.5, and Lb = 2

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