Abstract
A linear stability analysis is used to investigate the influence of mechanical vibration on the onset of thermosolutal convection in a horizontal porous layer heated and salted from above. Vibrations are considered with arbitrary amplitude and frequency. The Brinkman extended Darcy model is used to describe the flow and the Oberbeck-Boussinesq approximation is employed. Continued fraction method and Floquet theory are used to determine the convective instability threshold. It is found that the solutal Rayleigh number has the stabilizing effect. The existence of a closed disconnected loop of synchronous mode is predicted in the marginal curve for moderate values of solutal Rayleigh number and vibration amplitude.
Highlights
The study of thermal convection in a fluid layer with modulated gravitational field is an important class of problem in heat transfer
The existence of a closed disconnected loop of synchronous mode is predicted in the marginal curve for moderate values of solutal Rayleigh number and vibration amplitude
Attention is paid to the situation in which the vibrating porous layer is both heated and soluted from above
Summary
The study of thermal convection in a fluid layer with modulated gravitational field is an important class of problem in heat transfer. Gresho and Sani [1] and Gershuni et al [2] have first investigated the e ffect of sinusoidal gravity modulation in a differentially heated fluid layer through linear stability analysis They found that the system is stabilized for small amplitude vertical oscillations. Aniss et al [4] studied the influence of time dependent gravity on the instability threshold for a fluid layer confined in a Hele-Shaw geometry They found that the parametric oscillations can affect the convective instability threshold when the Prandtl number is small compared to unity. The first experimental study on Rayleigh-Benard convection in the presence of vertical vibration was conducted by Rogers et al [5] Their interest was in the study of the complex ordered patterns of convection generated under such conditions. These and all other related studies found in the literature involving thermal convection with time dependent gravity were all motivated by the difficulties faced during crystal growth, solidification of molten alloys and other related industrial processes
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