Impacts of nano-fluid on the dynamical and transitional behaviors of Rayleigh Bénard convection
Purbasha Deb, G. C. Layek
Abstract
This study investigates the non-linear dynamical aspects of nano-fluid convection heated from below, with a focus on the influence of nano-particle volume fraction (ϕ) on stability, bifurcations, and heat transfer efficiency. Understanding these effects is crucial for optimizing thermal transport in engineering and industrial applications. The novelty of this work lies in demonstrating how increasing ϕ delays convective instability, suppresses chaos, and alters heat transfer mode from convection to conduction—an aspect not extensively explored in previous studies. Single-phase water-Cu nano-fluid model is considered under specific assumptions. A low-dimensional system of coupled non-linear ordinary differential equations is derived using truncated Fourier expansions. Stationary convection emerges through a pitchfork bifurcation at a critical Rayleigh number rPF=M2M3M4, followed by oscillatory convection via Hopf bifurcation, where M2, M3 and M4 are thermo-physical parameters of the base fluid and nano-particles. Homoclinic explosions and preturbulent states are identified as global dynamical transitions. Results indicate that at the fixed pitchfork bifurcation point, the Nusselt number (Nu) decreases by 33.6% over 100 time units as ϕ increases to 0.1. Additionally, increasing ϕ suppresses intermittent frequency variations and induces several periodic solutions. Notably, beyond ϕ≥0.187, the system undergoes a transition to a conduction-dominated steady state. This work establishes the role of ϕ in modulating convective flow dynamics, providing critical insights into controlling nano-fluid instabilities. The findings contribute to advancing non-linear thermal transport models and enhancing heat management strategies in nano-fluid-based systems.