Neural Computing and Applications

, Volume 30, Issue 4, pp 1237–1249 | Cite as

A mathematical model of MHD nanofluid flow having gyrotactic microorganisms with thermal radiation and chemical reaction effects

  • M. M. BhattiEmail author
  • S. R. Mishra
  • T. Abbas
  • M. M. Rashidi
Original Article


In this article, we have examined three-dimensional unsteady MHD boundary layer flow of viscous nanofluid having gyrotactic microorganisms through a stretching porous cylinder. Simultaneous effects of nonlinear thermal radiation and chemical reaction are taken into account. Moreover, the effects of velocity slip and thermal slip are also considered. The governing flow problem is modelled by means of similarity transformation variables with their relevant boundary conditions. The obtained reduced highly nonlinear coupled ordinary differential equations are solved numerically by means of nonlinear shooting technique. The effects of all the governing parameters are discussed for velocity profile, temperature profile, nanoparticle concentration profile and motile microorganisms’ density function presented with the help of tables and graphs. The numerical comparison is also presented with the existing published results as a special case of our study. It is found that velocity of the fluid diminishes for large values of magnetic parameter and porosity parameter. Radiation effects show an increment in the temperature profile, whereas thermal slip parameter shows converse effect. Furthermore, it is also observed that chemical reaction parameter significantly enhances the nanoparticle concentration profile. The present study is also applicable in bio-nano-polymer process and in different industrial process.


Magnetic field Chemical reaction Nanofluid Numerical solution Gyrotactic microorganisms 

List of symbols


Velocity components


Cylindrical coordinate


Reynolds number




Nanoparticle volume fraction




Suction/injection parameter

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

Atmosphere temperature

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

Atmosphere concentration


Surface temperature


Thermophoresis parameter


Brownian motion parameter


Velocity slip parameter


Surface density of motile-organism


Permeability of porous medium




Heat flux of microorganisms

a0 (>0)



Forchheimer coefficient


Heat source/sink


Thermal slip factor


Thermophoretic diffusion coefficient


Density of motile microorganisms


Chemotaxis constant


Maximum cell swimming speed


Unsteady parameter


Brownian diffusion coefficient


A micro-organism diffusivity


Prandtl number


Schmidt number


Bio-convection Schmidt number


Peclet number


Forchheimer number


Magnetic parameter


Thermal radiation parameter


Heat source/sink parameter


Surface heat flux


Surface mass flux


Motile surface microorganism flux


Mean absorption coefficient


Skin friction coefficient


Nusselt number


Sherwood number


Density number of motile microorganisms

Greek symbols

\(\bar{\beta }\)

Contraction expansion strength

\(\bar{\alpha }_{m}\)

Thermal conductivity


Heat capacity of the fluid


Heat capacity of nanoparticle


Electrical conductivity


Viscosity of nanofluid


Temperature profile


Nanoparticle concentration profile


Motile microorganism density profile

\(\bar{\sigma }\)

Stefan–Boltzmann constant


Velocity slip


Shear stress


Density of nanoparticles


Electrical conductivity


Thermal slip




Kinematic viscosity


Chemical reaction parameter


Compliance with ethical standards

Conflict of interest

The authors declare no conflict of interest.


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Copyright information

© The Natural Computing Applications Forum 2016

Authors and Affiliations

  • M. M. Bhatti
    • 1
    Email author
  • S. R. Mishra
    • 2
  • T. Abbas
    • 3
  • M. M. Rashidi
    • 4
  1. 1.Shanghai Institute of Applied Mathematics and MechanicsShanghai UniversityShanghaiChina
  2. 2.Department of MathematicsSiksha ‘O’ Anusandhan UniversityKhandagiri, BhubaneswarIndia
  3. 3.Department of MathematicsQuaid-I-Azam UniversityIslamabadPakistan
  4. 4.Shanghai Key Lab of Vehicle Aerodynamics and Vehicle Thermal Management SystemsTongji UniversityShanghaiChina

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