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Research Papers: Bio-Heat and Mass Transfer

Lie Group Analysis of a Nanofluid Bioconvection Flow Past a Vertical Flat Surface With an Outer Power-Law Stream

[+] Author and Article Information
Hang Xu

State Key Laboratory of Ocean Engineering,
School of Naval Architecture,
Ocean and Civil Engineering,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: hangxu@sjtu.edu.cn

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received July 14, 2014; final manuscript received November 19, 2014; published online January 21, 2015. Assoc. Editor: Andrey Kuznetsov.

J. Heat Transfer 137(4), 041101 (Apr 01, 2015) (9 pages) Paper No: HT-14-1465; doi: 10.1115/1.4029362 History: Received July 14, 2014; Revised November 19, 2014; Online January 21, 2015

In this paper, an analysis on a bioconvection flow of a nanofluid past a vertical flat plate in the presence of an out power-law stream is made. The passively controlled nanofluid model is used to approximate this flow problem, which is believed to be physically more realistic than previously commonly used actively controlled nanofluid models. The Lie group transformation method is introduced to seek similarity solutions of such nanobioconvection flows for the first time. The reduced governing equations are then solved numerically with a finite difference technique. Besides, the influences of various parameters such as the Grashof number, the Prandtl number, the bioconvection Rayleigh number, the Lewis number, the bioconvection Péclet number, and the Schimdt number on the distributions of the density of motile micro-organisms profiles, as well as the local skin friction coefficient, the local Nusselt number, the local wall mass flux, and the local density of the motile micro-organisms are analyzed and discussed.

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Figures

Grahic Jump Location
Fig. 1

The physical sketch and coordinate system

Grahic Jump Location
Fig. 2

The density of motile micro-organisms profiles w(η) for various values of the Grashof number Gr in the case of Nr = Rb = 1,Nt = Nb = 0.1, Le = 10, Pr = 6.8, and Pe = Sc = 1

Grahic Jump Location
Fig. 3

The density of motile micro-organisms profiles w(η) for various values of the bioconvection Rayleigh number Rb in the case of Nr = Gr = 1,Nt = Nb = 0.1, Le = 10, Pr = 6.8, and Pe = Sc = 1

Grahic Jump Location
Fig. 4

The density of motile micro-organisms profiles w(η) for various values of the Brownian motion parameter Nb in the case of Gr = Nr = Rb = 1,Nt = 0.1, Le = 10, Pr = 6.8, and Pe = Sc = 1

Grahic Jump Location
Fig. 5

The density of motile micro-organisms profiles w(η) for various values of the thermophoresis Nt in the case of Gr = Nr = Rb = 1,Nb = 0.1, Le = 10, Pr = 6.8, and Pe = Sc = 1

Grahic Jump Location
Fig. 6

The density of motile micro-organisms profiles w(η) for various values of the Prandtl number Pr in the case of Gr = Nr = Rb = 1,Nt = Nb = 0.1, Le = 10, and Pe = Sc = 1

Grahic Jump Location
Fig. 7

The density of motile micro-organisms profiles w(η) for various values of the Lewis number Le in the case of Gr = Nr = Rb = 1,Nt = Nb = 0.1, Pr = 6.8, and Pe = Sc = 1

Grahic Jump Location
Fig. 8

The density of motile micro-organisms profiles w(η) for various values of the Péclet number Pe in the case of Gr = Nr = Rb = 1,Nt = Nb = 0.1, Pr = 6.8, Le = 10, and Sc = 1

Grahic Jump Location
Fig. 9

The density of motile micro-organisms profiles w(η) for various values of the Schmidt number Sc in the case of Gr = Nr = Rb = 1,Nt = Nb = 0.1, Pr = 6.8, Le = 10, and Pe = 1

Grahic Jump Location
Fig. 10

Variation of various physical quantities with the bioconvection Rayleigh number Rb

Grahic Jump Location
Fig. 11

Variation of various physical quantities with the Brownian motion parameter Nb

Grahic Jump Location
Fig. 12

Variation of various physical quantities with the thermophoresis parameter Nt

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