Abstract
In this article magnetohydrodynamic third-grade fluid flow with gyrotactic microorganisms over a horizontal porous extending sheet is presented. The influences of viscous dissipation, magnetic field, thermophoresis, Brownian motion, and thermal radiation are mainly focused in this research work. The modeled problem is solved analytically. The impressions of embedded factors on the fluid flow are displayed through graphs. Variation in Skin friction, local Nusselt, Sherwood and density number of motile microorganisms are calculated numerically and investigated. The second-grade parameters augmented the fluid flow velocity while the Hartmann number, third-grade parameter, and porosity parameter have a reverse influence on the fluid flow. The thermal stratification parameter and Prandtl number diminish the temperature of the fluid while other parameters increase the fluid flow temperature. The Peclet number increases the motile density function while other parameters have the opposite impact on the motile density of the fluid. (C) 2019 The Authors. Published by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University.