A mathematical model of magneto hydrodynamics unsteady nanofluid flow containing gyrotactic micro-organism through a bidirectional stretching sheet

The phenomenon of motile microorganisms enhances the stability of nanoparticles as well as improves heat transfer. The microorganism concept is accepted only for the stabilization of suspended nanomaterials due to bioconvection, which is facilitated by combined impacts of a magnetic field and buoyancy forces. The activity of gyrotactic microorganisms contained in time-dependent MHD nanofluid through a bidirectional extending surface with thermal radiation is viewed as in this ongoing article. Thermophoresis with diffusive Brownian movement is additionally noticed. The governing equations have been converted into a system of nonlinear ordinary differential equations (ODEs) by applying suitable similarity transformation. This framework then has been tackled mathematically by utilizing the spectral quasilinearization method (SQLM). The efficiency of this method has been presented and compared with previous data by showing in a table. The graphical portrayal of significant fluid parameters is evaluated by MATLAB programming. For physical interest skin friction, the Nusselt number, Sherwood number and microorganisms’ density number are determined numerically. We found that the unsteady parameter decreases the velocity and concentration boundary layer of microbes. Bioconvection Peclet numbers also decline the microorganisms’ concentration.