Bidirectional non-linear stretched flow of Williamson nanofluid with swimming of motile gyrotactic microorganisms

The fields of material manufacture, graphic designing, information science, aerodynamics, plastic industry and biotechnology have been found to have a greater reliance on the phenomenon of fluid flow over three-dimensional realms. Consequently, this article has been focused to the study of Williamson nanofluid containing microorganisms over three-dimensional surface under the influence of magnetic field through bidirectional non-linearly stretched surface. To transform the set of nonlinear partial differential equations into ordinary differentials equations by using appropriate similarity transformation. These obtained fundamental ordinary differential equations are solved numerically by exploiting bvp4c process built-in MATLAB mathematical software. The presentation of the results has been made in form of graphs and tables to warrant the comparison between different scenarios. More specifically the parameters like temperature profile, velocity profile, motility of organisms, concentration profiles, Peclet numbers, Lewis number, Williamson parameters, material parameter, Brownian motion parameters, Rayleigh numbers and Prandtl number were presented as the graphical outcomes. The numerical data suggested that greater values of Schmidt number, thermophoresis parameters and Brownian motion reduce the coefficient of wall heat transfer. The study has its applications in transportation hypothesis that is utilized in many automotive and industrial processes. The field of industrial manufacturing has also many applications that consider flow over a bidirectional stretched surface. The current approach explores the cumulative effect of different physical features on the flow of Williamson fluid, and there is no such effort in the reviewed studies.