Impulsive mixed convection of Williamson ternary nanofluid over a spinning rough sphere: influence of periodic magnetic field

There are numerous real-world applications of phenomena caused by abruptly started or stopped object motion. One such illustration is an application of airbags in motor vehicles. The primary purpose of this research is to investigate impulsive mixed convective Williamson ternary nanofluid flow over a rotating rough sphere in the presence of periodic magnetic effects. The external stream is primarily responsible for the time-dependent flow. A sinusoidal waveform mathematically models the rough surface of the sphere with small amplitude and high frequency. Thus, surface gradient and skin-friction exhibit wavy effects in the boundary layer regime. Under suitable initial and boundary conditions, the governing equations of the Williamson fluid flow, which in the current flow problem include the effects of heat diffusion and rotation, are highly coupled nonlinear PDEs. These are converted to non-dimensional forms by applying the semi-similar transformations, for which numerical semi-similar solutions are produced using the quasi-linearization technique followed by implicit finite difference approximation. The ranges of some important parameters considered are 2 ≤ Ri ≤ 10 (Richardson number), 0 ≤ M ≤ 4 (magnetic), 0 ≤ ϕ_i ≤ 0.04, i = 1, 2, 3 (nanoparticles volume fraction), 0 ≤ Wp ≤ 1 (Williamson parameter), 0 ≤ λ ≤ 5 (rotation parameter). The streamwise velocity Fξ,η, skin-friction Re1122Cfx and rotational skin-friction Re1122Cfy are all enhanced by increasing Ri and λ values. The upsurging λ values from 0 to 4 amend the Re1122Cfx approximately by 17% at ξ = 1 and Ri = 10. The amplitude of Re1122Cfx for n = 50 is enhanced by about 98% at ξ = 0.5 when the roughness ε upsurge from 0.001 to 0.005. Changing the shape of the nanoparticles from spherical to laminar results in an increase in approximately 46% at ξ = 0.5. Furthermore, the current results strongly correlate with similar outcomes reported in the literature.