Stagnation-Point Flow of the Williamson Nanofluid Containing Gyrotactic Micro-organisms

The present work deals with the unsteady stagnation-point flow of a Williamson nanofluid containing motile gyrotactic micro-organisms passing a horizontal linearly stretching/shrinking sheet with active and passive controls on the wall mass flux numerically. In the present study we consider the case when the nanofluid particle fraction on the boundary is passively rather than actively controlled, which make the model more physically realistic. The governing partial differential equations including continuity, momentums, energy, concentration of the nanoparticles and density of motile micro-organisms are converted into a system of the ordinary differential equations via a set of similarity transformations and are solved using the bvp4c package in MATLAB. The term bioconvection refers to macroscopic convection induced in water by the collective motion of a large number of self-propelled motile micro-organisms that lead to an unstable density stratification. The numerical results for profiles of velocity, temperature, nanoparticles concentration and density of motile micro-organisms as well as the local skin friction coefficient, the local Nusselt number, the local Sherwood number and the local density number of the motile micro-organism are expressed graphically and described in detail. To show the validity of the current results, a comparison between the present results and the existing literature has been made. Results show that the velocity increases, but density of micro-organisms decreases with stretching/shrinking parameter in the vicinity of surface. The identical behavior of temperature and nanoparticle volume fraction is analyzed.