A novel model of non-linear radiative Williamson nanofluid flow along a vertical wavy cone in the presence of gyrotactic microorganisms.

A novel mathematical technique for an unsteady bioconvective flow of Williamson nanofluids over a vertical wavy cone in the presence of non-linear radiation and viscous dissipation impacts is investigated. The cone surface is described by a sinusoidal function while the components of the extra stress tensor are presented in terms of the dynamic viscosity. The irregular wavy surface is referred to the convective boundary conditions and nanoparticle passively controls conditions. The governing equations are presented in general forms then the condition $$G{r_L} \to \infty $$ G r L → ∞ and suitable transformations are used to map the wavy cone to regular domain. A fully implicit finite differences method (FDM) is applied to solve the converted system and wide ranges of independent variables are assumed. $$0 \le X\le 7, 0 \le Y\le 25$$ 0 ≤ X ≤ 7 , 0 ≤ Y ≤ 25. The major outcomes disclosed that the increase in the Williamson number $$We$$ We causes a reduction the nanofluid flow while the skin friction coefficient is rising. Further, there is an enhancement in the values of the Nusselt number up to 75% is obtained as Biot number $$Bi$$ Bi is altered from 0.1 to 0.4. Also, the convective boundary conditions in presence of the non-linear radiations are recommended to enhance the velocity, temperature and rate of the heat transfer. [ABSTRACT FROM AUTHOR]