Abstract
Abstract Natural convection in superimposed layers of fluids heated from below is commonly observed in many industrial and natural situations, such as crystal growth, co-extrusion processes and atmospheric flow. The stability analysis of this system reveals a complex dynamic behavior, including the potential multiplicity of stationary states and occurrence of periodic regimes. In this study, a linear stability analysis (LSA) was performed to determine the onset of natural convection as a function of imposed boundary conditions, geometrical configuration and specific perturbations. To investigate the effects of the non-linear terms neglected in LSA, a direct simulation of the full nonlinear problem was performed using computational fluid dynamics (CFD) techniques. The numerical simulation results show an excellent agreement with the LSA results near the onset of convection and an increase in the deviation as the Rayleigh number increases above the critical value.
Highlights
Single layer Rayleigh-Bénard (RB) convection is one of the most widely studied systems in the field of transport phenomena, mainly due to the large number of applications and the relative simplicity of the governing equations. This system represents a natural convection condition occurring in a horizontal layer of fluid where energy is added from below and removed from above, giving rise to cellular structures called Bénard cells when the buoyancy forces are sufficiently stronger than the viscous forces
Whenever the Rayleigh number is below a certain critical value, the heat transfer will occur
For Ra 103 the critical Rayleigh number is approximately 1163 and the results shown in Figure 6(a) are very close to the critical value
Summary
Single layer Rayleigh-Bénard (RB) convection is one of the most widely studied systems in the field of transport phenomena, mainly due to the large number of applications and the relative simplicity of the governing equations This system represents a natural convection condition occurring in a horizontal layer of fluid where energy is added from below and removed from above, giving rise to cellular structures called Bénard cells (or convective cells) when the buoyancy forces are sufficiently stronger than the viscous forces. Even though it has been investigated for more than a century, the RB problem has been the subject of a large number of studies in recent years, involving, in particular, modifications of the classical RB system. Whenever the Rayleigh number is below a certain critical value, the heat transfer will occur
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
