Primary bifurcation mechanism, heat transfer and bicriticality in time temperature-modulated Rayleigh–Bénard convection in a Hele–Shaw cell

• Published in: International journal of heat and mass transfer 2024-05, Vol.223, p.125264, Article 125264
• Main Authors: Riahi, Mehdi, Hayani Choujaa, Mohamed, Er Rajy, Salma, Aniss, Saïd
• Format: Article
• Language: English
• ISSN: 0017-9310
• DOI: 10.1016/j.ijheatmasstransfer.2024.125264

In this paper, we perform a detailed numerical study of the linear dynamics of Rayleigh–Bénard convection in a fluid layer confined in a Hele–Shaw cell and subjected to a temperature gradient with a stationary and a periodic time-dependent component. Using Floquet theory for time and the spectral method for space, we show that the system exhibits three classes of time-dependent solutions, namely harmonic, sub-harmonic and quasi-periodic instabilities. These compete into the primary bifurcation driven by two different mechanisms depending on the modulation amplitude. Indeed, harmonic convective rolls, driven by the stationary thermal gradient, arise below critical modulation amplitudes beyond which the well-known parametric resonance mechanism is responsible for the development of convective rolls. In addition, it is revealed that the convective flow reversal could identify this exchange of instability mechanisms occurring via either bicritical states with codimension-two bifurcation points between harmonic and subharmonic modes or via displacement of Floquet multipliers in the Floquet-complex plane. This latter scenario sets in between subharmonic and quasiperiodic instability modes in the high frequency limit by varying the phase-lag between the temperatures of the lower and upper boundaries. Moreover, it is shown that the nature of the instability mechanism alters considerably the heat transfer dynamics of the system. •A Floquet-based analysis on time-modulated Rayleigh-Bénard convection in a Hele-Shaw cell is presented.•Three classes of time-dependent instability modes are found namely harmonic, subharmonic and quasiperiodic instabilities.•Flow reversal is used to identify the primary bifurcation mechanism.•The effect of the instability mechanism on the heat transfer of the system is also presented.