Two-dimensional gyrotactic microorganisms flow of hydromagnetic power law nanofluid past an elongated sheet

Abstract

This article, describes two-dimensional magnetohydrodynamic steady incompressible viscous power law nanofluid comprising gyrotactic microorganisms adjacent to a vertical stretching sheet. The governing non-linear partial differential equations are lessened to a set of non-linear ordinary differential equation using similitude transformation. The non-dimensional boundary value problem is then solved under spectral relaxation method. The influences of different parameters such as buoyancy convection parameters (Formula presented.), magnetic field parameter M, power law parameter (Formula presented.), Prandtl number (Formula presented.), modified Prandtl number (Formula presented.), thermophoresis parameter (Formula presented.), Peclet number (Formula presented.), Lewis number (Formula presented.), Brownian motion parameter (Formula presented.), bioconvection Lewis number (Formula presented.), and bioconvection constant (Formula presented.) on flow convective characteristics phenomena are explored via plots and tables. The skin friction factor, rate of heat transfer, rate of mass transfer, and the density number of the motile microorganisms near the surface are also computed. Our results are compared with the existing results to support our model. Residual error analysis is determined for showing the convergence rate against iteration. Our result showed that the momentum thickness reduces as the value of (Formula presented.) induces and thermal boundary thickness increases as the value of (Formula presented.) induces. We also revealed that the density of the motile microorganisms (Formula presented.) is a reducing function of (Formula presented.) and concentration boundary layer induces with the increase of (Formula presented.), whereas its thickness close to the surface decreases with increasing of (Formula presented.). Also, the stream line patterns are exhibited to the impact of physical sundry variables.