Influence of Sinusoidal and Non‐Sinusoidal Two‐Frequency Gravity Modulation in Viscoelastic Fluids Driven by Triple Diffusivity

ABSTRACT This study focuses on understanding the system's response to gravity modulation with two frequency components, characterized by both sinusoidal (sine wave) and non‐sinusoidal (square, triangular, and sawtooth) waveforms, on three‐component convection, considering a viscoelastic fluid modelled using an Oldroyd‐B fluid. We apply the Venezian approach to evaluate the Rayleigh number, its corrected form, and the wave number by deriving a five‐mode Lorenz model to investigate the onset of convection. A nonlinear analysis is conducted to investigate the dynamics of heat and mass transfer by solving an extended eight‐mode Lorenz model, capturing higher order interactions. The onset of convection and the transport properties were observed to be influenced by combinations of sinusoidal and non‐sinusoidal waveforms. This study optimizes convection‐driven systems subjected to external periodic forcing by offering a more comprehensive understanding of convective instabilities in viscoelastic fluids.