Optimizing heat transfer and convective cell dynamics in 2D Rayleigh–Bénard convection: The effect of variable boundary temperature distribution

Abstract

The influence of temperature distributions on heat transfer dynamics is studied in two-dimensional Rayleigh–Bénard convection cells. Employing a Direct Numerical Simulation technique with an Euler scheme for time integration, the study analyzes three distinct cases: Homogeneous plate temperature distribution, centrally elevated plate temperature configuration, and peripherally dominant plate temperature configuration Rayleigh–Bénard convection cases. With variations in Rayleigh number ($Ra$) ranging between $10^7$ and $10^{10}$, key metrics such as the Nusselt number ($Nu$), Reynolds number ($Re$), as well as thermal and kinetic energy dissipation rates, are examined to gauge efficient heat transfer and fluid flow characteristics. At $Ra=10^7$, the peripherally dominant plate temperature configuration exhibited a higher $Nu$ value of 15.9, indicating a 10.4 percent improvement over the homogeneous or normal temperature distribution. As $Ra$ increased to $10^{10}$, the nonhomogeneous temperature distribution demonstrated a substantial 14.9 percent increase in $Nu$ compared to the homogeneous distribution. Similar trends were observed in $Re$, indicating the impact of nonhomogeneous temperature conditions on fluid flow characteristics. This highlights the significant role of localized temperature gradients in enhancing both heat transfer efficiency and fluid motion. Addressing potential constraints, this study acknowledges uncertainties associated with the scalability of the findings. Despite this challenge, the insights gained offer a deeper understanding of temperature-flow dynamics, with applications in electronics cooling where precise control of heat transfer is crucial, as well as in thermal engineering and climate modeling.