Malaysian Journal of Mathematical Sciences, September 2023, Vol. 17, No. 3
Behaviour of the Onset of Rayleigh-Bénard Convection in Double-Diffusive Micropolar Fluids Under the Influence of Cubic Temperature and Concentration Gradient
Idris, R., Alias, A., and Miqdady, A.
Corresponding Email: ruwaidiah@umt.edu.my
Received date: 22 June 2023
Accepted date: 8 August 2023
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 $N_1, N_3, N_5$, and $Rs$ have been analyzed to investigate their influence on the onset of convection. The results found that the coupling parameter $N_1$ 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-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.
Keywords: Rayleigh-Bénard convection; temperature gradient; concentration gradient; micropolar fluids; double-diffusive; single-term Galerkin technique
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