Gyrotactic micro-organism dusty fluid flow over an extended surface

The conventional magnetohydrodynamics (MHD) equations are modeled for the dusty fluid flow past a stretching sheet embedded in a porous medium. These equations are coupled with motile microorganisms, temperature and concentration equations for both fluid and dust particles dynamical equations. The two-phase dusty fluid flow is subjected to magnetic effect, porosity factor, 2nd order chemical reaction, Brownian diffusion, thermophoretic effect and Arrhenius activation energy. An appropriate transformation is used to reset the system of partial differential equations (PDEs) into non-linear system of ODEs (ordinary differential equations). The flow equations are numerically solved by using the parametric continuation method (PCM). For validity of the applied methodology, the results are compared using numerical and graphical results of Matlab built-in package “BVP4c”. Both results show accuracy up to four decimal places. Furthermore, from graphical results, it can be noticed that the fluid particles interaction parameter causes an attractive force among fluid particles which prevents the dust particles phase flow. This technique can be used for biological separations, filters, fluid dust separators and crude oil purification.