Abstract
The present article addressed the hydromagnetic flow of a specific type of water-based nanofluid (NF) including motile microbes and nanomaterials across a permeable upright moving surface. Nanofluid bioconvection is induced by the combined interaction of buoyancy forces and magnetic fields on motile microorganisms and nanomaterials. The consequences of thermal slip condition, thermophoresis effect, Brownian motion, heat generation and absorption, Darcy Forchhemier impact, second-order chemical reaction and activation energy are all incorporated into the nonlinear system of model equations. The numerical solution of the modeled boundary value problem is achieved through the use of appropriate similarity substitution and the parametric continuation methodology (PCM). The energy, velocity, motile microbes' density, skin friction, Nusselt number and Sherwood number are all used in the parametric assessment of flow physical characteristics. It has been perceived that the rising values of heat absorption and generation, Hartmann number and Eckert number dramatically improves the energy transfer rate. While the energy contour is lowered by increasing the values of Brownian motion parameter, Prandtl number and suction/injection.