Lie Group Analysis of a Nanofluid Bioconvection Flow Past a Vertical Flat Surface With an Outer Power Law Stream

Abstract

In this paper, an analysis on a bioconvection flow of a nanofluid past a vertical flat plate in the presence of an out powerlaw stream is made. The passively controlled nanofluid model is used to approximate this flow problem, which is believed to be physically more realistic than previously commonly used actively controlled nanofluid models. The Lie group transformation method is introduced to seek similarity solutions of such nanobioconvection flows for the first time. The reduced governing equations are then solved numerically with a finite difference technique. Besides, the influences of various parameters such as the Grashof number, the Prandtl number, the bioconvection Rayleigh number, the Lewis number, the bioconvection Pأ©clet number, and the Schimdt number on the distributions of the density of motile microorganisms profiles, as well as the local skin friction coefficient, the local Nusselt number, the local wall mass flux, and the local density of the motile microorganisms are analyzed and discussed.