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Research Papers: Porous Media

Magnetohydrodynamics and Soret Effects on Bioconvection in a Porous Medium Saturated With a Nanofluid Containing Gyrotactic Microorganisms

[+] Author and Article Information
S. Shaw, P. Sibanda

School of Mathematics,
Statistics & Computer Science,
University of KwaZulu-Natal, P/Bag X01,
Scottsville, Pietermaritzburg 3209,
South Africa

A. Sutradhar

Department of Mathematics,
Indian Institute of Technology,
Kharagpur 721 302, India

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 4, 2012; final manuscript received October 23, 2013; published online February 26, 2014. Assoc. Editor: Andrey Kuznetsov.

J. Heat Transfer 136(5), 052601 (Feb 26, 2014) (10 pages) Paper No: HT-12-1647; doi: 10.1115/1.4026039 History: Received December 04, 2012; Revised October 23, 2013

We investigate the bioconvection of gyrotactic microorganism near the boundary layer region of an inclined semi infinite permeable plate embedded in a porous medium filled with a water-based nanofluid containing motile microorganisms. The model for the nanofluid incorporates Brownian motion, thermophoresis, also Soret effect and magnetic field effect are considered in the study. The governing partial differential equations for momentum, heat, solute concentration, nanoparticle volume fraction, and microorganism conservation are reduced to a set of nonlinear ordinary differential equations using similarity transformations and solved numerically. The effects of the bioconvection parameters on the thermal, solutal, nanoparticle concentration, and the density of the micro-organisms are analyzed. A comparative analysis of our results with previously reported results in the literature is given. Some interesting phenomena are observed for the local Nusselt and Sherwood number. It is shown that the Péclet number and the bioconvection Rayleigh number highly influence the local Nusselt and Sherwood numbers. For Péclet numbers less than 1, the local Nusselt and Sherwood number increase with the bioconvection Lewis number. However, both the heat and mass transfer rates decrease with bioconvection Lewis number for higher values of the Péclet number.

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Figures

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Fig. 1

Schematic diagram of the present problem

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Fig. 4

The effect of the parameters Nt and Le on (a) temperature profiles (b) nanoparticle concentration profiles with Nc = 0.1,Nr = 0.1,Rb = 0.1,Nb = 0.1,Nt = 0.1,Ln = 1,Sr = 0.8,Lb = 1,Pe = 1,τ0 = 1

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Fig. 3

The temperature profiles for different (a) Ha,fw (Nr = 1,Rb = 1) (b) Nr,Rb (Ha = 0.5,fw = 0.5) with Nc = 0.1,Nb = 0.1,Nt = 0.1,Ln = 1,Sr = 0.8,Le = 1,Lb = 5,Pe = 3,τ0 = 1

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Fig. 2

The velocity profiles for different (a) Ha,fw (Nr = 1,Nc = 0.1,Rb = 1,Nb = 0.1,Nt = 0.1,Ln = 1,Sr = 0.8,Le = 1,Lb = 5,Pe = 3,τ0 = 1) (b) Nr,Rb (Ha = 0.5,Nc = 0.1,Nb = 0.1,Nt = 0.1,Ln = 1,Sr = 0.8,Le = 1,Lb = 5,Pe = 3,τ0 = 1,fw = 0.5) (c) Sr,Ln (Ha = 0.5,Nr = 1,Nc = 0.1,Nb = 0.1,Nt = 0.1,Le = 1,Lb = 5,Pe = 3,τ0 = 1,fw = 0.5) (d) Pe,Lb (Ha = 0.5,Nc = 0.1,Nr = 1,Rb = 1,Nb = 0.1,Nt = 0.1,Ln = 1,Sr = 0.8,Le = 1,τ0 = 1,fw = 0.5)

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Fig. 5

The solute concentration profiles for different (a) Ha,fw (Sr = 0.8,Ln = 1) (b) Sr,Ln (Ha = 0.5,fw = 0.5) with Nc = 0.1,Nr = 1,Rb = 1,Nb = 0.1,Nt = 0.1,Le = 1,Lb = 5,Pe = 3,τ0 = 1

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Fig. 6

The microorganism concentration profiles for different (a) Nt,Le (Pe = 1,Lb = 1,Rb = 0.1,Nr = 0.1) (b) Pe,Lb (Nt = 0.1,Le = 1,Nr = 1,Sr = 0.8,Ln = 1) with Ha = 0.5,Nc = 0.1,Nb = 0.1,Sr = 0.8

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Fig. 7

Local Nusselt number for different (a) Nr,Sr (Pe = 3,Rb = 1) (b) Pe,Rb (Nr = 1,Sr = 0.8) with Ha = 0.5,Nc = 0.1,Nb = 0.1,Nt = 0.1,Le = 1,Ln = 1,Lb = 1,τ0 = 1

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Fig. 8

Local Sherwood number for different (a) Nr,Sr (Pe = 3,Rb = 1) (b) Pe,Rb (Nr = 1,Sr = 0.8) with Ha = 0.5,Nc = 0.1,Nb = 0.1,Nt = 0.1,Le = 1,Ln = 1,Lb = 1,τ0 = 1

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Fig. 9

The local nanoparticle volume fraction for different (a) Nr,Sr (Pe = 3,Rb = 1) (b) Pe,Rb (Nr = 1,Sr = 0.8) with Ha = 0.5,Nc = 0.1,Nb = 0.1,Nt = 0.1,Le = 1,Ln = 1,Lb = 1,τ0 = 1

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Fig. 10

Local density of motile microorganisms for different (a) Pe,Rb with Ha = 0.5,Nc = 0.1,Nb = 0.1,Nt = 0.1,Le = 1,Ln = 1,Lb = 1,τ0 = 1

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