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

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 (lambda 1,lambda 2,lambda 3), magnetic field parameter M, power law parameter n, Prandtl number Pr, modified Prandtl number Prm, thermophoresis parameter Nt, Peclet number Pe, Lewis number Le, Brownian motion parameter Nb, bioconvection Lewis number Lb, and bioconvection constant sigma 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 M induces and thermal boundary thickness increases as the value of M induces. We also revealed that the density of the motile microorganisms chi is a reducing function of Pe,Lb,sigma and concentration boundary layer induces with the increase of Nt,M,n, whereas its thickness close to the surface decreases with increasing of Nb,Le,n,Prm,lambda 1,lambda 3. Also, the stream line patterns are exhibited to the impact of physical sundry variables.