INFLUENCE OF HEAT-SOURCE SIZE ON FLOW-REGIME TRANSITION AND HEAT TRANSFER IN RAYLEIGH-BÉNARD CONVECTION WITH LOCALIZED HEATING

Direct numerical simulations are performed to investigate Rayleigh-Bénard convection in a two-dimensional square cavity with localized heating at the center of the bottom wall and isothermal cooling at the top wall. The Prandtl number is fixed at Pr = 4.3 , while the Rayleigh number Ra and the dimensionless heat-source size \Lambda are systematically varied over a prescribed parameter range. The evolution of flow structures, the deflection-establishment time, the mean flow strength, and the heat-source-averaged heat-transfer characteristics under localized heating are analyzed. Based on the temporal evolution of the mean angular momentum L\left(t\right) , the flow is quantitatively classified into three typical regimes: near-symmetric weak circulation, stable deflected circulation, and nonstationary reversal circulation. A complete regime map in the \left(\Lambda ,Ra\right) parameter space is then constructed. The results show that, as Ra or \Lambda increases, the driving effect of the bottom thermal plume is enhanced, and the system gradually transitions from near-symmetric weak circulation to stable deflected circulation and nonstationary reversal circulation. Increasing the heat-source size shifts the regime-transition region toward lower Ra . The characteristic time for flow deflection, \tau _rev , decreases overall with increasing Ra and \Lambda , and the time scale in the reversal regime is more sensitive to the control parameters. In the statistically steady stage, both the mean Reynolds number Re and the heat-source-averaged Nusselt number Nu_h increase with Ra and \Lambda . The empirical exponents of Re or Nu_h with respect to Ra or \Lambda are close among different flow regimes. Compared with classical Rayleigh-Bénard convection with full-bottom heating, the locally heated system exhibits a slightly larger empirical exponent of Re with respect to Ra than the 1/2 reference value, whereas the empirical exponent of Nu_h with respect to Ra is relatively lower. As the heat-source size \Lambda increases, this localized-heating effect is gradually weakened, and the heat-transfer behavior progressively approaches that of the full-bottom-heating case. These results provide a reference for understanding the coupling between localized thermal forcing, flow-regime transition, and heat transport in confined convection systems.