Buoyancy-driven flows on a horizontal plate subject to a ramp heating of finite time are studied in this paper. The dynamics of the thermal boundary layer and the subsequent starting plume on the heated horizontal plate are revealed and the scaling laws for different scenarios and regimes are obtained using a scaling analysis, which are further verified against results of direct numerical simulations (DNS) at the Rayleigh number of 5 × 10² ~ 5 × 10⁴, the Prandtl number of 7 and the non-dimensional time of ramp heating from 0.072 to 0.143. A distinct sequential development of the thermal boundary layer, thermal bulges and starting plume is observed in the DNS and characterised by the scaling laws. The thicknesses of the thermal boundary layer and plume are found to decrease as the Rayleigh number increases because the convection intensifies. In addition, the scaling analysis suggests that the development of the starting plume may undergo five scenarios, each of which has a series of different regimes, depending on the Rayleigh number, the Prandtl number and the time of ramp heating. In a typical scenario, the starting plume may ascend under an unsteady viscosity conduction regime, a quasi-steady viscosity conduction regime or a steady viscosity conduction regime.

本文研究了有限时间的斜坡加热作用下水平板上浮力驱动的流动。揭示了热边界层和随后加热的水平板上的初始羽流的动力学特性，并使用比例分析获得了不同情况和方案的比例定律，并针对直接数值模拟（DNS）的结果进一步验证了这一点。的5×10瑞利数²〜5×10 ⁴，Prandtl数为7，斜坡加热的无量纲时间从0.072到0.143。在DNS中观察到了热边界层，热凸起和起始羽状流的明显顺序发展，并以缩放定律为特征。由于对流加剧，热边界层和羽流的厚度随着瑞利数的增加而减小。另外，定标分析表明，起始羽状流的发展可能会经历五个场景，每个场景都有一系列不同的模式，具体取决于瑞利数，普朗特数和斜坡加热的时间。在典型情况下，起始羽状流可以在非稳态粘度传导方案，准稳态粘度传导方案或稳态粘度传导方案下上升。