Flow of nanofluid with Cattaneo–Christov heat flux model

  • Jawdat AlebraheemEmail author
  • M. Ramzan
Original Article


This study explores the heat and mass transfer of Casson nanofluid flow containing gyrotactic microorganisms past a swirling cylinder. Fluid flow is generated owing to the torsional movement of the cylinder. An analysis is performed in the presence of gyrotactic microorganisms. The effects of chemical reaction, magnetohydrodynamics, heat generation/absorption, and zero mass flux condition are also considered. The Cattaneo–Christov heat flux model is initiated instead of conventional Fourier heat flux. Apposite transformations are betrothed to attain the coupled system of equations. The numerical solution is developed from the novel mathematical model via bvp4c function utilizing MATLAB software. Numerous graphs and tables are established to portray the inspiration of embroiled parameters on the flow distributions. To corroborate the presented results; a comparison to an already done published paper is also made. An excellent synchronization between the two results is obtained thus endorsing the presented model. Also, form the graphical structures and numerically erected tables, it is professed that concentration of the fluid is lessened owing to an upsurge in values of Reynolds number and Brownian motion parameter. Furthermore, diminishing density of microorganism is perceived for mounting estimates of bioconvection Péclet number.


Gyrotactic microorganisms Swirling cylinder Cattaneo–Christov heat flux Casson nanofluid Zero mass flux condition Chemical reaction 

Lis of symbols

u, v, w

Velocity component


Radius of cylinder


Casson parameter


Constant rotating speed of cylinder


Thermal relaxation time


Local density number of the motile microorganisms


Dimensionless fluid temperature

\(f(\eta )\)

Dimensionless stream function


Strain rate at the surface of cylinder


Magnetic parameter

\(\Delta T\)

Characteristic temperature


Nanoparticle volume friction


Bioconvection Péclet number


A scaled boundary-layer coordinate


Rate of chemical reaction


Brownian motion parameter


Brownian diffusion coefficient


Maximum cell swimming speed


Diffusivity of microorganisms


Thermal relaxation parameter


Electric conductivity of fluid


Skin friction coefficient


Nusselt number




Lewis number


Ambient temperature


Prandtl number




Characteristic length


Coefficient of heat generation/absorption


Density of nanofluid


Local Reynolds number


Constant magnetic flux density


Magnetic field strength


Volumetric rate of heat source


Thermal diffusivity


Fluid dynamic viscosity


Thermophoresis parameter


Bioconvection Lewis number


Chemical reaction parameter



This work is funded by the Basic Science Research Unit, Scientific Research Deanship at Majmaah University under the research project no. 76/38. The author is extremely grateful to Majmaah University, Deanship of Scientific Research and Basic Science Research Unit, Majmaah University.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© King Abdulaziz City for Science and Technology 2019

Authors and Affiliations

  1. 1.Department of Mathematics, College of ScienceMajmaah UniversityAl-ZulfiSaudi Arabia
  2. 2.Department of Computer ScienceBahria University, Islamabad CampusIslamabadPakistan
  3. 3.Department of Mechanical EngineeringSejong UniversitySeoulKorea

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