Behaviour of the Onset of Rayleigh-Bénard Convection in Double-Diffusive Micropolar Fluids Under the Influence of Cubic Temperature and Concentration Gradient

Abstract

Convection heat transfer especially Rayleigh-Bénard convection plays a significant role either in nature or industry applications. Particularly, in industry, the instability of the Rayleigh-Bénard convection process is important to see whether the quality of final goods is excellent or not. Therefore, in this study linear stability theory has been performed to investigate the influence of cubic temperature gradient and cubic concentration gradient on the onset of convection in a double-diffusive micropolar fluid. By adopting the single-term Galerkin procedure, parameters N1,N3,N5 , and Rs have been analyzed to investigate their influence on the onset of convection. The results found that the coupling parameter N1 and micropolar heat conduction parameter N5 will put the system in stable conditions. Meanwhile, the couple stress parameter N3 and solutal Rayleigh number Rs will destabilize the system. The results also show that by increasing the value of the solutal Rayleigh number Rs , the value of the critical Rayleigh number Rac will decrease. By enclosing the micron-sized suspended particles, we can slow down the process of Rayleigh-Bénard convection in double-diffusive micropolar fluids. It is possible to control the process of the onset of Rayleigh-Bénard convection by selecting suitable non-uniform temperature and concentration gradient profiles.