Thermal Convection of a Casson Nanofluid With Helical Force

Initiation of convection in the horizontal layer is studied in the Casson nanofluids. The current investigation examines the onset of convective instability in a Casson nanofluid subjected to a helical force, employing both linear and weakly nonlinear analyses. Two distinct methodologies are employed to investigate the linear and weakly nonlinear behaviors. The linear theory is investigated using the Galerkin approach, while the weakly nonlinear theory is explored through multiple scale analysis. In this, the Prandtl and Lewis numbers exhibit no discernible impact on stationary convection. But in the Casson parameter, the nanoparticle Rayleigh number, adjusted diffusivity proportion (modified diffusivity ratio), and helical force parameter destabilize the flow. While in oscillatory convection, it is found that the nanoparticle Rayleigh number, the Lewis number, and helical force parameter stabilize the flow, but the Prandtl number, adjusted diffusivity proportion (modified diffusivity ratio), and the Casson parameter are the destabilizing effects on the flow. Amplitude equation is derived in weakly nonlinear analysis.