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Microgravity Science and Technology

, Volume 30, Issue 4, pp 445–455 | Cite as

Magnetohydrodynamics Nanofluid Flow Containing Gyrotactic Microorganisms Propagating Over a Stretching Surface by Successive Taylor Series Linearization Method

  • A. Shahid
  • Z. Zhou
  • M. M. Bhatti
  • D. Tripathi
Original Article
  • 60 Downloads

Abstract

Nanofluid dynamics with magnetohydrodynamics has tremendously contributed in industrial applications recently since presence of nanoparticle in base fluids enhances the specific chemical and physical properties. Owing to the relevance of nanofluid dynamics, we analyze the nanofluid flow in the presence of gyrotactic microorganism and magnetohydrodynamics through a stretching/shrinking plate. The impacts of chemical reaction and thermal radiation on flow characteristics are also studied. To simplify the governing equations of microorganisms, velocity, concentration and temperature, the similarity transformations are employed. The couple governing equations are numerically solved using Successive Taylor Series Linearization Method (STSLM). The velocity profile, motile microorganism density profile, concentration profile, temperature profile as well as Nusselt number, skin friction coefficient, Sherwood number and density number of motile microorganisms are discussed using tables and graphs against all the sundry parameters. A numerical comparison is also given for Nusselt number, Sherwood number, skin friction, and density number of motile microorganisms with previously published results to validate the present model. The results show that Nusselt number, Sherwood number and density number diminish with increasing the magnetic field effects.

Keywords

Nanofluiddynamics Magnetohydrodynamics STSLM Gyrotactic microorganism Thermophoresis 

Nomenclature

\(\bar {B}_{0}\)

Magnetic field (T)

x\(\bar {u}\bar {v}\)

Components of velocity (m/s)

\(\tilde {\alpha } \)

Thermal conductivity (W/mK)

\(D_{\bar {T}}\)

Thermophoretic coefficient

Kc

Chemical reaction parameter

Sc

Schmidt number

Sb

Bioconvection Schmidt number

M

Magnetic field parameter (T)

S

Suction/injection parameter

\(\bar {T}_{w}\)

Temperature of the wall (K)

\(\bar {T}_{\infty } \)

Ambient temperature (K)

𝜃

Temperature profile (K)

ϕ

Concentration profile (mol/m3)

\(\bar {C}_{w}\)

Concentration at the wall (mol/m3)

\(\bar {C}_{\infty } \)

Ambient concentration (mol/m3)

σ

Electrical conductivity (S/m)

\(\bar {\sigma } \)

Stefan-Boltzmann constant (J/K)

Φ

Motile microorganism density profile (kg/m3)

μm

Magnetic permeability,

Characteristic length

\(\bar {W}_{c}\)

maximum cell swimming speed (m/s)

\(\bar {b}\)

chemotaxis constant

Pr

Prandtl number (m2/s)

\(D_{\bar {n}}\)

diffusivity of microorganisms (m2/s)

\(\bar {k} \)

mean absorption coefficient

Nt

thermophoresis parameter

α

stretching/shrinking parameter (m)

Pe

Peclet number

Nr

Radiation parameter

\(\tilde {\sigma } \)

dimensionless constant

\(m\bar {c}\bar {a}\)

Constants

υ

kinematic viscosity (m2/s)

ρ

density (kg/m3)

[ρcpf]

heat capacity of fluid (J/kg)

[ρcpp]

nanoparticles heat capacity (J/kg)

Rex

local Reynolds number

\(D_{\bar {B}}\)

Brownian diffusion coefficient (m2/s)

\(\bar {N}\)

concentration of microorganism (mol/m3)

\(\widetilde {V}\)

is characteristic velocity,

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Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mathematics and Information SciencesGuangzhou UniversityGuangzhouChina
  2. 2.Shanghai Institute of Applied Mathematics and MechanicsShanghai UniversityShanghaiChina
  3. 3.Department of Mechanical EngineeringManipal University JaipurRajasthanIndia

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