Onset of rotating convection of a nanofluid with helical force: Stability analysis

Abstract

Employing linear stability analysis of nanofluids holds promising advantages across diverse domains. The impact of rotation and helical force on the onset of convection in the nanofluid is investigated using the linear stability analysis. The method of normal modes is used to solve the governing nondimensional equations, which results in an eigenvalue problem for the linear stability analysis. The bvp4c in MATLAB R2021a is employed to solve the eigenvalue problem. Three different lower-upper boundary conditions are considered: free-free, rigid-free, and rigid-rigid. The Rayleigh and wave number are determined for various required values of the other physical parameters and graphically displayed. Specifically, as the Taylor number rises, there is a corresponding grow in the critical Rayleigh number. This indicates that higher values of the Taylor number stabilize the system, making it less prone to convective instabilities. Conversely, the Lewis number and Helical force parameter destabilize the critical Rayleigh number, making the system more prone to convective instabilities across all boundaries. This information provides valuable insights into the system’s dynamics under study and can be crucial for predicting and understanding its behavior under different conditions.