Effects of control on the onset of Bénard–Marangoni convection in a micropolar fluid

A linear stability analysis was conducted to assess the feasibility of using a feedback control strategy on the onset of Bénard–Marangoni convection in a micropolar fluid. The single-term Galerkin technique was used to obtain the closed-form solution for the Marangoni number M for the onset of convection, satisfying three different non-uniform basic state temperature profiles. It is demonstrated that the controller gain parameter can successfully increase the critical Marangoni number.