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Impact of Chemical Reaction on MHD 3D Flow of a Nanofluid Containing Gyrotactic Microorganism in the Presence of Uniform Heat Source/Sink

  • B.J. Gireesha , K. Ganesh Kumar and S Manjunatha EMAIL logo
Published/Copyright: October 19, 2018

Abstract

The purpose of current study is to deliberate the effect of chemical reaction on 3D flow and heat transfer of an MHD nanofluid in the vicinity of plate containing gyrotactic microorganism over a elastic surface. Influence of uniform heat source/sink on temparature transfer has been considerd. The governing standard nonlinear system of equalities is resolved numerically via Runge-Kutta  method of  45th order based shooting scheme. Role of substantial parameters on flow fields as well as on the, heat, mass and microorganism transportation rates are determined and discussed through ploted graphs.

Nomenclature

B

magnetic field

Sc

Schmidt number

C

nanoparticles volume fraction

Sb

bioconvection Schmidt number

c

ratio of stretching rates

T

fluid temperature

Cw

wall nanoparticles volume fraction

Tw

temperature at the surface and

C

ambient nanoparticle volume fraction

T

Temperature far away from the surface.

cp

specific heat at constant pressure

u,v,w

velocity components along the x,y,z direction

d

chemotaxis constant

w

denotes the wall condition

Dm

constant microorganism diffusivity

Wc

maximum cell swimming speed

DB

Brownian diffusion coefficient

S and h

dimensionless stream function

DT

thermophoretic diffusion coefficient

Greek symbols

k

thermal conductivity

ν

kinematic viscosity of the fluid

K1

Reaction rate

μ

coefficient of fluid viscosity

K

Chemical reaction parameter

ρ

fluid density,

Le

Lewis number

σ

electrical conductivity of the fluid

M

magnetic parameter

α

thermal diffusivity of the fluid

n

number of motile microorganism

τ

ratio of heat capacity of the fluid,

Nb

Brownian motion parameter

ξ

order of derivatives

Nt

thermophoresis parameter

γ

dimensionless temperature

Pr

Prandtl number

δ

dimensionless nanoparticles volume fraction

Pe

bioconvection Peclet number

χ

dimensionless number of motile microorganism

Q0

Volumetric rate of heat generation and absorption

S

heat source parameter

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Received: 2018-01-19
Revised: 2018-05-18
Accepted: 2018-09-16
Published Online: 2018-10-19

© 2018 Walter de Gruyter GmbH, Berlin/Boston

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