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Medium-frequency (MF) transformer has gained much popularity in power conversion systems. Temperature control is a paramount concern, as the unexpected high temperature declines the safety and life expectancy of transformer. The scrutiny of losses and thermal-fluid behavior are thereby critical for the design of MF transformers. This paper proposes a coupled, semi-numerical model for electromagnetic and thermal-fluid analysis of MF oil natural air natural (ONAN) transformer. An analytical model that is based on spatial distribution of flux density and AC factor is exploited to calculate the system losses, while the thermal-hydraulic behavior is modelled numerically leveraging the computational fluid dynamics (CFD) method. A close-loop iterative framework is formulated by coupling the analytical model-based electromagnetic analysis and CFD-based thermal-fluid analysis to address the temperature dependence. Experiments are performed on two transformer prototypes with different conductor types and physical geometries for validation purpose. Results suggest that the proposed model can accurately model the AC effects, losses, and the temperature rises at different system components. The proposed model is computationally more efficient than the full numerical method but it reserves accurate thermal-hydraulic characterization, thus it is promising for engineering utilization. [ABSTRACT FROM AUTHOR]