Onset of Magneto - Convective Instability of a Casson Nanofluid with Helical Force: Linear and Weakly Non-Linear Analyses

Abstract

The study investigates the thermal convection of a Casson nanofluid in a horizontal layer influenced by magnetic and helical force parameters. Both linear and weakly non-linear analyses are performed to assess the fluid's stability. The critical Rayleigh number is calculated in the linear analysis, while the Nusselt number is determined in the weakly non-linear analysis which is used to study heat transfer. A one-term Galerkin approach is employed to study the linear theory, while multiple scale analysis is used to investigate the weakly non-linear theory. The Hartman number ( ) exerts a stabilizing effect on the system in both stationary and oscillatory convection. Meanwhile, the helical force parameter ( ), the adjusted diffusivity ratio ( ) and the nanoparticle Rayleigh number ( ) have a destabilizing effect on the system in both stationary and oscillatory convection. The Lewis number ( ) and Prandtl number ( ) exhibit a stabilizing effect on oscillatory convection, but in the case of stationary convection, they do not have any impact on the system. The Casson parameter (β) has a destabilizing effect in the case of stationary convection, whereas it shows a stabilizing effect on the system in oscillatory convection.