Numerical investigation of vibration-induced heat transfer and entropy production in Rayleigh–Benard nanofluid flow: resonance effects under variable-frequency sinusoidal forcing

Purpose This study aims to examine how vertical sinusoidal vibration influences heat transfer and entropy generation in Rayleigh–Bénard (RB) nanofluid convection. Design/methodology/approach This study analyzes the coupling between RB instability and externally applied time-varying vertical forcing with adjustable frequencies and amplitudes. The governing equations for the nanofluid RB system are solved numerically using the finite element method to capture the transient and steady convective regimes. Findings The results show that increasing the vibration parameter φ elevates both the intrinsic and extrinsic thermal irreversibilities during the transient and stationary regimes, respectively. The onset of instability in the nanofluid lags behind that of a base fluid, with increasing delay as φ grows. Within the studied frequency range, the system’s thermal and entropic responses to sinusoidal excitation are nearly sinusoidal, and the flow can exhibit heat-transfer and entropy-production resonances at specific critical frequencies corresponding to natural modes of the system. Practical implications Understanding how vertical vibrations affect heat transfer and entropy generation in convective flows has broad relevance for thermal management in microgravity environments, advanced electronics cooling, heat exchanger design and process engineering where vibrational effects are significant. Originality/value The literature shows limited exploration of the interplay between vibration and RB flow instability in nanofluids and numerically investigates entropy production and heat-transfer resonances under variable-frequency and variable-amplitude forcing, contributing new insights into vibrational modulation of RB convection in nanofluids.