MHD flow of Powell-Eyring nanofluid containing nanoparticles and gyrotactic microorganisms over a stretched surface

MHD flow of Powell-Eyring nanofluid containing nanoparticles and gyrotactic microorganisms over a stretched surface

Govind R. RajputVishwambhar S. Patil J.S.V.R. Krishna Prasad 

Department of Applied Mathematics, SVKMs, NMIMS, Mukesh Patel School of Technology Management & Engineering, Shirpur Campus, Shirpur-425505, India

Department of Mathematics, Govt. College of Engineering, Karad 415124, India

Department of Mathematics, M. J. College, Jalgaon 425001, India

Corresponding Author Email: 
g.rajput7@gmail.com
Page: 
405-420
|
DOI: 
https://doi.org/10.3166/RCMA.28.405-420
| |
Published: 
30 September 2018
| Citation

ACCESS

Abstract: 

The purpose of this study is to investigate behavioural features of nanoparticles and microorganisms of Powell-Eyring nanofluid flow past a stretching surface with a magnetic influence. Consequences regarding stretching sheet with respect to velocity, temperature, nanoparticle concentration and motile microorganism density were analysed to focus associated parameters. Intention of introducing gyrotactic microorganisms was initially to keep nanoparticle suspension in steady state. The governing flow equations are remodel invariantly to the system of nonlinear ordinary differential equations using appropriate similarity variables. To described nanofluid flow characteristics, associated parameters were computed and analysed using numerical shooting technique. Pertinent results were revealed through graphs. Our investigation shows significant effect of Newtonian heating over a stretching sheet for associated physical parameters. Comparison was carried out between Newtonian and Powell-Eyring nanofluid on velocity and temperature field.

Keywords: 

micro-organismes gyrotactiques, nanofluide de Powell-Eyring

1. Introduction
2. Problem formulation
3. Numerical treatment
4. Results and discussions
5. Conclusion
Nomenclature

B0

b

M

T

u

v

$T_∞$

$T_w$

magnetic field strength

chemotaxis constant

dimensionless magnetic number

temperature of the fluid

velocity component along x-axis

velocity component along y-axis

temperature of the fluid in the free stream

temperature of the fluid at surface

C

$C_w$

$C_∞$

Pr

DT

DB

Dn

N

j

nanoparticle volume fraction

nanoparticle volume fraction at the surface

nanoparticle volume fraction in the free stream

Prandtl number

Thermophoresis diffusion coefficient

Brownian diffusion coefficient

diffusivity of microorganisms

motile microorganism concentration

flux of microorganism

Nb

Nt

Nw

Pe

Sc

uw(x)

Wc

Brownian motion parameter

Thermophoresis parameter

wall concentration of microorganism

bioconvection Peclet number

Schmidt number

stretching velocity

maximum cell swimming speed

Greek symbols

 

η

dimensionless similarity variable

σ

Dimensionless number

θ

dimensionless temperature

ϕ

dimensionless nanoparticle volume fraction

μ

γ

v

ψ

α

ΔC

ΔN

τ

Viscosity

Mixed convection parameter

kinematic viscosity

stream function

thermal diffusivity of the nanofluid

characteristic nanoparticle volume fraction

characteristic motile microorganisms density difference

ratio of the effective heat capacity of the nanoparticle to that of the fluid

 

Subscripts

 

 

condition at free steam

w

 

Superscripts

 

'

condition at the surface

 

 

 

differentiation with respect to η

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