Bio-convective and chemically reactive hybrid nanofluid flow upon a thin stirring needle with viscous dissipation

Arshad Khan,Asifa Tassaddiq,Taza Gul,Poom Kumam,Anwar Saeed,Ishtiaq Ali,Wiyada Kumam

doi:10.1038/s41598-021-86968-8

Abstract

In this work, the thermal analysis for bio-convective hybrid nanofluid flowing upon a thin horizontally moving needle is carried out. The chemical reaction and viscous dissipation has also considered for flow system in the presence of microorganism. The hybrid nanoparticles comprising of Copper left( {Cu} right) and Alumina left( {Al_{2} O_{3} } right) are considered for current flow problem. Mathematically the flow problem is formulated by employing the famous Buongiorno’s model that will also investigate the consequences of thermophoretic forces and Brownian motion upon flow system. Group of similar variables is used to transform the model equations into dimensionless form and have then solved analytically by homotopy analysis method (HAM). It has established in this work that, flow of fluid declines due to increase in bioconvection Rayleigh number, buoyancy ratio and volume fractions of nanoparticles. Thermal flow grows due to rise in Eckert number, Brownian, thermophoresis parameters and volume fraction of nanoparticles. Concentration profiles increase due to growth in Brownian motion parameter and reduces due to increase in thermophoresis parameter and Lewis number. Motile microorganism profile declines due to augmentation in Peclet and bioconvection Lewis numbers. Moreover, the percentage enhancement in the drag force and rate of heat transfer using conventional nanofluid and hybrid nanofluid are observed and discussed. The hybrid nanofluid increases the skin friction and heat transfer rate more rapidly and efficiently as compared to other traditional fluids. A comparison of the present study with the existing literature is also conducted with a closed agreement between both results for variations in thickness of the needle.

Highlights

In this work, the thermal analysis for bio-convective hybrid nanofluid flowing upon a thin horizontally moving needle is carried out
In this work the modeled equations have been transformed to dimensionless form by using set of transformable variables and have solved the resultant equations numerically by employing MATLAB software
In our work we have considered the thermal analysis for bioconvection of hybrid nanofluid flowing upon a thin horizontally moving needle

Summary

Method of solution

For determination the semi-analytical solution of Eqns. (9–12) using the boundary conditions stated in Eq (14) we shall employ the semi analytical technique HAM38,39. For determination the semi-analytical solution of Eqns. (9–12) using the boundary conditions stated in Eq (14) we shall employ the semi analytical technique HAM38,39. The HAM method is implemented through BVP 2.0 package. For application of this semi-analytical technique some initial guesses are required which are stated as follows: f0(η) = 1 − eη, 0(η) γ1 e−η, 1 + γ1. The above linear operators in their expanded form are given as Lf e1 + e2eη + e3e−η = 0, L e4eη + e5e−η =, L e6eη + e7e−η = 0, Lξ e8eη + e9e−η = 0 (26). In Eq (26) the expressions ei for i = 1, 2, 3, .

Results and discussion

Conclusion

Methods