Exploring the magnetohydrodynamic stretched flow of Williamson Maxwell nanofluid through porous matrix over a permeated sheet with bioconvection and activation energy

Sohaib Abdal,Qasem Al-Mdallal,Dalal Alrowaili,Sajjad Hussain,Imran Siddique

doi:10.1038/s41598-021-04581-1

Abstract

The evolution of compact density heat gadgets demands effective thermal transportation. The notion of nanofluid plays active role for this requirements. A comparative account for Maxwell nanofluids and Williamson nanofluid is analyzed. The bioconvection of self motive microorganisms, non Fourier heat flux and activation energy are new aspects of this study. This article elaborates the effects of viscous dissipation, Cattaneo–Christov diffusion for Maxwell and Williamson nanofluid transportation that occurs due to porous stretching sheet. The higher order non-linear partial differential equations are solved by using similarity transformations and a new set of ordinary differential equations is formed. For numerical purpose, Runge–Kutta method with shooting technique is applied. Matlab plateform is used for computational procedure. The graphs for various profiles .i.e. velocity, temperature, concentration and concentration of motile micro-organisms are revealed for specific non-dimensional parameters. It is observed that enhancing the magnetic parameter M, the velocity of fluid decreases but opposite behavior happens for temperature, concentration and motile density profile. Also the motile density profile decrease down for Pe and Lb. The skin friction coefficient is enhanced for both the Williamson and Maxwell fluid.

Highlights

Nomenclature Latin symbols u, v Velocity components (x,y) Cartesian coordinates uw Velocity of the fluid at wall n Power law index Bo Magnetic field strength C Concentration of nanoparticles T Temperature of nanoparticles N Micro-rotation vector k∗ Mean absorption co-efficient k1 Permeability of porous medium k Fluid parameter
Rb in case of Maxwell fluid (β = 0.5) as well as Williamson fluid ( = 0.1) and the magnitude of −f ′′(0) is enhanced because of the additional resistance to the flow that comes into play with enhancement of magnetic parameters
It is observed that Maxwell nanofluid takes larger values than that of Williamson nanofluid for Nusselt number −θ ′(0), −φ′(0) and for motile density −χ ′(0)

Summary

Introduction

Nomenclature Latin symbols u, v Velocity components (x,y) Cartesian coordinates uw Velocity of the fluid at wall n Power law index Bo Magnetic field strength C Concentration of nanoparticles T Temperature of nanoparticles N Micro-rotation vector k∗ Mean absorption co-efficient k1 Permeability of porous medium k Fluid parameter. In modelling of fluids flows with shear-dependent viscosity, the power-law model is commonly used. The viscosity is not shear-dependent in these models. They are unable to determine the impacts of calming stress. Ahmed et al.[4] reviewed the impact of radiative heat flux in Maxwell nanofluid flow over a chemically reacted spiralling disc. Jawad et al.[6] calculated the entropy generation for magnetohydrodynamic (MHD) mixed convection and Maxwell nano-fluid flow over an elongating and penetrable surface in the presence of heat conductivity, velocity slip boundary condition and thermal radiation. Perturbation solution of incompressible flows in a rock fracturing with a non-Newtonian Williamson fluid was studied by Scientific Reports | (2022) 12:278 |

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Conclusion