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Thermal convection in porous media is a ubiquitous process governing heat and mass transport in natural and engineering systems, such as geothermal energy extraction, geological CO2 sequestration, and permafrost thawing. While the classical Grossmann-Lohse (GL) theory and extensive numerical studies have characterized Rayleigh-Darcy convection over flat, smooth boundaries, realistic geological interfaces, such as stratigraphic layers and fracture surfaces, inevitably exhibit non-straight, undulating geometries. This study bridges the gap between idealized models and realistic conditions by investigating the impact of non-straight bottom boundaries (see Fig. 1a) on convection dynamics and heat transfer efficiency.
Using high-resolution numerical simulations based on the Brinkman-extended Darcy model, we explored a broad parameter space with Rayleigh-Darcy numbers (Ra) ranging from 1 to 3×10^5. As shown in Fig. 1b, our results identify a critical "crossover" phenomenon in the Nusselt number (Nu) scaling, revealing that non-straight boundary does not monotonically enhance heat transfer. Instead, we observe two distinct regimes separated by a transition point at Ra ≈ 1300.
In the diffusion-dominated and transitional regimes (Ra < 1300), the non-straight boundary acts as a localized trigger for instability. The geometric troughs induce localized convection even at low Ra, effectively integrating the fluid within the troughs into the global circulation (see Fig. 1c&d). This mechanism increases the effective heat-transfer height to approximately the domain height plus the wavy boundary amplitude (h + e), resulting in a significant enhancement of heat transfer efficiency (Nu/Ra)—up to 2.43 times that of a flat boundary at Ra=1.
Conversely, in the vigorous convection regime (Ra > 1300), a counter-intuitive suppression effect emerges. As the flow intensifies, the fluid trapped deep within the boundary troughs becomes hydrodynamically isolated, forming stagnant "dead zones" with homogenized density (see Fig. 1e). These stagnant pockets prevent the penetration of the large-scale circulation, creating a "thermal short-circuit" where the main convective flow bypasses the non-straight elements. Consequently, the effective convective height is reduced to h－e. At Ra = 3×10^5, this flow stratification leads to a ~32% reduction in heat transfer efficiency compared to the flat-boundary case.
Furthermore, we analyze the competition between convective finger generation and flow stratification. Interestingly, while the non-straight boundary begins to suppress the number of convective fingers at Ra > 1000, the efficiency enhancement persists until Ra ≈ 1300 due to the compensating effect of geometric area extension. These findings challenge the conventional view that non-straight boundary always enhances transport and provide a unified physical framework, validated against GL theory scaling, for predicting heat transport in complex geological media.
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