# Flow of nanofluid with Cattaneo–Christov heat flux model

## Abstract

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.

## Keywords

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

*u*,*v*,*w*Velocity component

*R*Radius of cylinder

- \(\beta\)
Casson parameter

*G*Constant rotating speed of cylinder

- \(\lambda_{2}\)
Thermal relaxation time

- \({\text{Nn}}_{x}\)
Local density number of the motile microorganisms

- \(\theta\)
Dimensionless fluid temperature

- \(f(\eta )\)
Dimensionless stream function

*H*Strain rate at the surface of cylinder

- \(M\)
Magnetic parameter

- \(\Delta T\)
Characteristic temperature

- \(\phi\)
Nanoparticle volume friction

- \(P_{\text{e}}\)
Bioconvection Péclet number

- \(\eta\)
A scaled boundary-layer coordinate

- \(k_{\text{r}}\)
Rate of chemical reaction

- \(N_{\text{b}}\)
Brownian motion parameter

- \(D_{\text{B}}\)
Brownian diffusion coefficient

- \({\text{Wc}}\)
Maximum cell swimming speed

- \(D_{\text{m}}\)
Diffusivity of microorganisms

- \(\gamma\)
Thermal relaxation parameter

- \(\sigma\)
Electric conductivity of fluid

*C*_{f}Skin friction coefficient

- \(Nu_{x}\)
Nusselt number

*T*Temperature

- \(L_{\text{e}}\)
Lewis number

*T*_{∞}Ambient temperature

*Pr*Prandtl number

*p*Pressure

- \(l\)
Characteristic length

*D*_{c}Coefficient of heat generation/absorption

- \(\rho\)
Density of nanofluid

*Re*Local Reynolds number

- \(B_{0}\)
Constant magnetic flux density

*B*Magnetic field strength

- \(Q_{0}\)
Volumetric rate of heat source

- \(\alpha\)
Thermal diffusivity

- \(\mu_{\text{f}}\)
Fluid dynamic viscosity

- \(N_{\text{t}}\)
Thermophoresis parameter

- \(S_{\text{b}}\)
Bioconvection Lewis number

- \(\delta\)
Chemical reaction parameter

## Notes

### Acknowledgements

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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