Heat transfer enhancement and thermal boundary-layer modification in turbulent Rayleigh–Bénard convection over Cantor fractal roughness

We present a systematic experimental investigation of turbulent Rayleigh–Bénard convection (RBC) in a thin rectangular cell with a Cantor fractal rough bottom plate. Experiments were conducted using water (Pr≃4.3) over a Rayleigh number range 8.7×10⁸≤Ra≤9.6×10¹⁰. The fractal roughness produces approximately 150% enhancement of Nusselt number, while the scaling exponent remains unchanged at Nu∼Ra^0.28. Measurements of vertical temperature profiles reveal complex, multiscale modifications of the thermal boundary layer (BL) across lateral locations, including the emergence of a quasi-plateau region in the central valley and a secondary peak in temperature variance near the sidewall. Shadowgraph visualizations indicate a self-organized plume emission process, in which numerous small plumes emitted from roughness tips interact and merge into larger coherent structures. Furthermore, both the modified mean and variance temperature profiles, as well as the strongly non-Gaussian temperature probability density functions (PDFs) observed near the rough surface, are well described by recently developed theoretical models originally formulated for smooth-wall RBC. These results demonstrate that Cantor fractal roughness substantially enhances convective heat transfer and flow fluctuations while the scaling exponent β remains unchanged at 0.28 between the smooth and rough cells within the classical turbulent convection regime (8.7×10⁸≤Ra≤9.6×10¹⁰, Pr≈4.3). These findings highlight the potential of Cantor fractal roughness for optimizing industrial thermal management and establish it as a valuable multiscale model for studying heat transfer processes and temperature distributions in urban environments and the low-altitude atmospheric BL.