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A mathematical model for bioconvection flow of Williamson nanofluid over a stretching cylinder featuring variable thermal conductivity, activation energy and second-order slip

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The significant bioconvection phenomenon with the utilization of nanoparticles encountered fundamental industrial and technological applications in recent years. This communication addressed the bioconvection phenomenon in the flow of magnetized Williamson nanoparticles with additional features of activation energy and heat absorption/generation. The analysis has been suggested by imposing the interesting features of the second-order slip effects and convective Nield boundary constraints. The flow problem based on the relevant laws results in a set of partial differential equations which are further retarded into ordinary differential forms. The numerical approach based on shooting algorithm is introduced to impose the numerical solution by using MATLAB software. The flow parameters governed with the flow equations are graphically explored with associated physical consequences. The numerical division for local Nusselt number, local Sherwood number and motile number is presented while assigning diverse values to the involved parameters. The reported theoretical simulations can be more effective to enhance the thermal extrusion processes and solar energy systems. It is observed that the presence of first- and second-order slip parameters significantly controls the associated boundary layers of velocity, temperature, concentration and gyrotactic microorganism profiles.

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\( v \) :

Kinematic viscosity

\( \sigma \) :

Electrical conductivity

\( \rho_{{\rm p}} \) :

Liquid density

\( \alpha_{1} \) :

Thermal diffusivity

\( Q_{0} \) :

Heat source coefficient

\( \rho_{{\rm f}} \) :

Nanoparticles density

\( D_{{\rm T}} \) :

Thermophoretic constant

\( W_{{\rm c}} \) :

Speed of gyrotactic cell

\( {{\rm Kr}} \) :

Chemical reaction

\( \beta_{1} \) :

Molecular mean path

\( \varGamma \) :

Curvature parameter

\( M \) :

Hartmann number

\( {{\rm Nc}} \) :

Bioconvection Rayleigh number

\( {{\rm Nt}} \) :

Thermophoresis parameter

\( \Pr \) :

Prandtl number

\( \lambda \) :

Heat source/sink parameter

\( {{\rm Pe}} \) :

Peclet number

\( \varOmega_{1} \) :

Concentration difference parameter

\( B \) :

Second-order slip

\( {{\rm Nu}}_{{\rm x}} \) :

Local Nusselt number

\( {{\rm Nn}}_{{\rm x}} \) :

Motile density number

\( \varGamma_{1} \) :

Williamson fluid parameter

\( g \) :


\( B_{0} \) :

Magnetic field strength

\( \rho_{{\rm m}} \) :

Motile microorganism particles density

\( C \) :

Volume fraction constant

\( T \) :

Nanoparticles temperature

\( D_{{\rm B}} \) :

Brownian motion constant

\( b^{ * } \) :

Chemotaxis constant

\( \tilde{\alpha } \) :

Momentum coefficient

\( K_{{\rm n}} \) :

Knudsen number

\( \varOmega \) :

Weissenberg number

\( \varLambda \) :

Mixed convection parameter

\( {{\rm Nr}} \) :

Buoyancy ratio parameter

\( {{\rm Nb}} \) :

Brownian motion

\( {{\rm Le}} \) :

Lewis number

\( \gamma \) :

Biot number

\( {{\rm Lb}} \) :

Bioconvection Lewis number

\( A \) :

First-order slip

\( {\rm Re}_{{\rm x}}^{{ - \frac{1}{2}}} \) :

Local Reynolds number

\( {{\rm Sh}}_{{\rm x}} \) :

Local Sherwood number


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Abdelmalek, Z., Khan, S.U., Waqas, H. et al. A mathematical model for bioconvection flow of Williamson nanofluid over a stretching cylinder featuring variable thermal conductivity, activation energy and second-order slip. J Therm Anal Calorim 144, 205–217 (2021).

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