Significance of gyrotactic microorganism and bioconvection analysis for radiative Williamson fluid flow with ferromagnetic nanoparticles

•This paper covers the following key points.•Gyrotactic microorganism’s phenomenon for Williamson is considered here.•Characteristics of ferromagnetic nanomaterials with bioconvection analysis is deliberated.•Numerical analysis is employed here.•Radiation characteristics are accounted for modeling ferromagnetic nanofluid. Research on nanotechnology took interest of scientists as well as researchers because of its vast range of applications like curing cancer, medicines, aircraft manufacturing industry, use of nano-robot technology, bio-nano, heat exchanger instruments, used as coolants in engines of vehicles, microelectronics, water distillation, pharmaceutical procedures and rubber materials. Major purpose of this inspection is to examine the usefulness of radiation phenomena with magnetic effects micro-polar nanofluid by use of impermeable surface. The concept of microorganism’s notion is used to make suspended nano-particles stable by using effect of bioconvection influenced by synchronizing deliberation of suitable magnetic field. Since bioconvection is also an appealing research field for bioengineering and biotechnology, in recent year’s variety of bio-convection models are studied for production of microorganisms. The determination of current exploration is to compute the 2-dimensional flow of Williamson ferrofluid under the influence of magnetic dipole. Characteristics of Brownian motion parameter and thermophoresis diffusion for Williamson ferrofluid model apprehending the properties of convective boundary conditions, thermal motile as well as thermal gradients are considered. The system of nonlinear PDEs is transformed in form of ODEs with the help of apt transformations; additionally obtained ODEs are then solved with the help of bvp4c numerical scheme. Impacts of some important physical parameters are expressed pictorially. Results perceived that fluids temperature increases by increasing thermal radiation as well as thermophoresis parameter moreover shows declining behavior in case of Prandtl number. Moment of motile microorganism rises for larger δ1 and Pe whereas microorganism have opposite trend againstLb.