In‐phase, out‐of‐phase, bottom‐wall two‐frequency boundary temperature modulations on the onset of Rayleigh‐Bénard convection

Abstract

AbstractThe onset of convection in a Newtonian liquid‐containing system is investigated using a two‐frequency boundary temperature. The consequences of three types of two‐frequency boundary temperature modulations have been thoroughly investigated: (i) in‐phase, (ii) out‐of‐phase, and (iii) bottom‐wall. The combined effect of two frequencies with sinusoidal and nonsinusoidal wave types is also documented under these various types of boundary temperature modulations. To facilitate the study, the Venezian method is approved and the critical Rayleigh number and its correction are calculated. The parameters resulting from the study's two frequencies of modulation are the mixing angle, , the amplitudes, , and the set of coprime integers, . The system's thermodynamics determines the range of these parameters. The research discovered that out‐of‐phase two‐frequency boundary temperature modulation is the most stable, while in‐phase is the least stable. Besides that, any combination of wave type with square wave type yields the most excellent stability. Furthermore, the two‐frequency boundary temperature modulation is more stable than the single‐frequency and no‐modulation cases.