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Research Papers: Forced Convection

Stagnation-Point Flow Toward a Stretching/Shrinking Sheet in a Nanofluid Containing Both Nanoparticles and Gyrotactic Microorganisms

[+] Author and Article Information
Khairy Zaimi

Institute of Engineering Mathematics,
Pauh Putra Campus,
Universiti Malaysia Perlis,
02600 Arau, Perlis, Malaysia

Anuar Ishak

School of Mathematical Sciences,
Faculty of Science and Technology,
Universiti Kebangsaan Malaysia,
43600 UKM Bangi, Selangor, Malaysia

Ioan Pop

Department of Mathematics,
Babeş-Bolyai University,
Cluj-Napoca 400084, Romania e–mail: popm.ioan@yahoo.co.uk

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received June 18, 2013; final manuscript received October 24, 2013; published online January 31, 2014. Assoc. Editor: Andrey Kuznetsov.

J. Heat Transfer 136(4), 041705 (Jan 31, 2014) (9 pages) Paper No: HT-13-1308; doi: 10.1115/1.4026011 History: Received June 18, 2013; Revised October 24, 2013

The stagnation-point flow and heat transfer toward a stretching/shrinking sheet in a nanofluid containing gyrotactic microorganisms with suction are investigated. Using a similarity transformation, the nonlinear system of partial differential equations is converted into nonlinear ordinary differential equations. These resulting equations are solved numerically using a shooting method. The skin friction coefficient, local Nusselt number, local Sherwood number, and the local density of the motile microorganisms as well as the velocity, temperature, nanoparticle volume fraction and the density of motile microorganisms profiles are analyzed subject to several parameters of interest, namely suction parameter, thermophoresis parameter, Brownian motion parameter, Lewis number, Schmidt number, bioconvection Péclet number, and the stretching/shrinking parameter. It is found that dual solutions exist for a certain range of the stretching/shrinking parameter for both shrinking and stretching cases. The results indicate that the skin friction coefficient, local Nusselt number, local Sherwood number, and the local density of the motile microorganisms increase with suction effect. It is also observed that suction widens the range of the stretching/shrinking parameter for which the solution exists.

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Figures

Grahic Jump Location
Fig. 1

Physical model and the coordinate system

Grahic Jump Location
Fig. 7

Effect of the suction parameter S on the temperature profiles θ(η) when Le = 2, Nt = 0.5, Nb = 0.5, Pr = 6.2, Pe = 1, Sc = 1, σ = 1, λ = -3 (shrinking surface), and m = 1

Grahic Jump Location
Fig. 10

Effect of the suction parameter S on the velocity profiles f'(η), λ = 2 (stretching surface), and m = 1

Grahic Jump Location
Fig. 6

Effect of the suction parameter S on the velocity profiles f'(η) for λ = -3 (shrinking surface) when m = 1

Grahic Jump Location
Fig. 5

Variation of Rex-1/2Nnx with λ for various values of S when Pe = 1, Sc = 1, σ = 1, Le = 2, Nt = 0.5, Nb = 0.5, Pr = 6.2, and m = 1

Grahic Jump Location
Fig. 4

Variation of Rex-1/2Shx with λ for various values of S when Pe = 1, Sc = 1, σ = 1, Le = 2, Nt = 0.5, Nb = 0.5, Pr = 6.2, and m = 1

Grahic Jump Location
Fig. 8

Effect of the suction parameter S on the nanoparticle volume fraction profiles ϕ(η) when Le = 2, Nt = 0.5, Nb = 0.5, Pr = 6.2, Pe = 1, Sc = 1, σ = 1, λ = -3 (shrinking surface), and m = 1

Grahic Jump Location
Fig. 9

Effect of the suction parameter S on the density of motile microorganisms profiles χ(η) when Le = 2, Nt = 0.5, Nb = 0.5, Pr = 6.2, Pe = 1, Sc = 1, σ = 1, λ = -3 (shrinking surface), and m = 1

Grahic Jump Location
Fig. 11

Effect of the suction parameter S on the temperature profiles θ(η) when Le = 2, Nt = 0.5, Nb = 0.5, Pr = 6.2, Pe = 1, Sc = 1, σ = 1, λ = 2 (stretching surface), and m = 1

Grahic Jump Location
Fig. 12

Effect of the suction parameter S on the nanoparticle volume fraction profiles φ(η) when Le = 2, Nt = 0.5, Nb = 0.5, Pr = 6.2, Pe = 1, Sc = 1, σ = 1, λ = 2 (stretching surface), and m = 1

Grahic Jump Location
Fig. 13

Effect of the suction parameter S on the density of motile microorganisms profiles χ(η) when Le = 2, Nt = 0.5, Nb = 0.5, Pr = 6.2, Pe = 1, Sc = 1, σ = 1, λ = 2 (stretching surface) and m = 1.

Grahic Jump Location
Fig. 3

Variation of Rex-1/2Nux with λ for various values of S when Pe = 1, Sc = 1, σ = 1, Le = 2, Nt = 0.5, Nb = 0.5, Pr = 6.2, and m = 1

Grahic Jump Location
Fig. 2

Variation of Rex1/2Cf with λ for various values of S and m = 1

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