The onset of Rayleigh–Bénard convection and heat transfer under two‐frequency rotation modulation

Abstract

The impact of 16 combinations of sinusoidal (sine) and nonsinusoidal (square, triangular, and sawtooth) timeperiodic Coriolis force (rotation modulation) on Rayleigh-Bénard convection in a Newtonian liquid is studied in this paper. This consideration is made to capture the possible effects of two-frequency rotation modulation on stability, that is, the onset of convection and the simultaneous amount of heat transfer in the system. The Venezian approach has been asserted on the linearized Lorenz model to derive the correction Rayleigh number as a function of the two frequencies. The Lorenz model with nonlinearities is evaluated numerically to assess the quantity of heat transfer in the system. The present study states that in comparison with existing studies of no-modulation and singlefrequency rotation modulation, two-frequency rotation modulation yields higher stability bounds and thus diminishes the heat transfer. Heat transfer is found to be enhanced by a pair of coprime integers associated with the harmonics in the system.