We present a three-dimensional (3D) numerical study of Rayleigh–Bénard convection (RBC) under a horizontal magnetic field in a small-aspect-ratio rectangular cell (2/3:8/3:1, $Pr=0.025$). The Rayleigh number ($Ra$) is fixed at $5\times {10}^5$ and ${10}^6$, while the Hartmann number ($Ha$) spans 3 orders of magnitude to provide a comprehensive view ($0\sim {10}^3$). With increasing magnetic field strength, the flow evolves from a 3D cellular structure to a quasi-two-dimensional (Q2D) rolls state. This transition reorients the main circulation plane and alters the dominant heat transport mechanism, leading to nonmonotonic variations in both Nusselt ($Nu$) and Reynolds ($Re$) numbers. The initial anomalous drop in $Nu$ under weak fields arises from disrupted vertical plume coherence. In contrast to large-aspect-ratio systems, where more rolls enhance heat transport, the small-aspect-ratio cell favors a single domain-spanning large-scale circulation (LSC) as the most efficient heat carrier. Flow reversals are observed at intermediate $Ha$, with both regular and irregular types. These reversals result from the growth of one vortex in a vertically stacked roll pair, differing from the classical reversal mechanism based on roll breakup and reconnection. Proper orthogonal decomposition (POD) analysis further confirms that mode interaction and competition play a crucial role in triggering the reversals. Based on the dissipation-dominance framework, we derive a transport scaling for the strong-field regime, $Nu\sim R{a}^{1/3}H{a}^{-1/6}, Re\sim R{a}^{2/3}H{a}^{-1/3}P{r}^{-1}$, and validate it against available RBC datasets, revealing a unified decay law of transport efficiency across different geometries. Furthermore, we extend elliptical instability theory to Q2D magnetoconvection, showing that stronger magnetic fields increase the stability threshold, allowing for more deformed elliptical rolls—findings consistent with observed flow topologies and dimensionality transitions.

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• High Hartmann number flows
• Magnetohydrodynamic turbulence
• Rayleigh-Bénard convection
• Thermal convection