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

Convection heat transfer especially Rayleigh-Benard convection plays a significant role either in nature or industry applications. Particularly, in industry, the instability of the Rayleigh-Benard 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 N-1, N-3, N-5, and R-s 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 N-5 will put the system in stable conditions. Meanwhile, the couple stress parameter N-3 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 Ra-c will decrease. By enclosing the micron-sized suspended particles, we can slow down the process of Rayleigh-Benard convection in double-diffusive micropolar fluids. It is possible to control the process of the onset of Rayleigh-Benard convection by selecting suitable non-uniform temperature and concentration gradient profiles.