Thermal Symmetry Breakdown in Finned Natural Convection Cavities: Band-Resolved Nusselt Statistics and Multivariate Analysis Across Conductivity Ratios

This study investigates the breakdown of thermal symmetry in finned square cavities under natural convection, focusing on how the fin-to-fluid conductivity ratio governs heat-transfer redistribution and localization. A band-resolved statistical framework is employed to analyze hot- and cold-wall Nusselt number responses across conductivity ratios (kr) ranging from symmetric to highly contrasting conditions. At kr=1, the cavity exhibits a fully symmetric conduction–convection regime with complete wall-to-wall coupling and a unified thermal response. Increasing the conductivity ratio to kr=10 introduces a transitional regime marked by mild but systematic asymmetry, with convective activity beginning to favor the cold wall. At kr=100, the system undergoes a structural transition to a strongly asymmetric state, characterized by attenuation of hot-wall convection and sustained cold-wall dominance. Under extreme ratio (kr=1000), convective heat transfer becomes highly localized at the cold wall, forming a directional thermal pathway. Joint Gaussian envelopes, regression scaling, principal component analysis, and Hotelling separation collectively demonstrate that symmetry breakdown proceeds through distinct, statistically separable stages, rather than emerging as a gradual shift in mean heat-transfer intensity. The results establish cold-wall localization as the governing physical mechanism and provide a unified framework for controlling convective heat transfer in fin-assisted natural-convection systems.