Coherent Structure Dynamics of Heat Transfer in Wakes of an Inclined Elliptical Cylinder: A Novel Lagrangian Framework

This work introduces a novel Lagrangian-based framework to analyze forced convective heat transfer in the unsteady wake of a heated elliptical cylinder inclined at angles ranging from $θ= 0^\circ$ to $90^\circ$, in $15^\circ$ increments with $Pr = 0.71$ at a fixed Reynolds number of $Re = 100$. The framework correlates the temporal evolution of the surface-averaged Nusselt number with the dynamic behavior of Lagrangian saddle points, formed at the intersection of repelling and attracting Lagrangian Coherent Structures (LCSs) extracted via Finite-Time Lyapunov Exponent (FTLE) fields.The study is carried out within a precisely constructed observational domain, a previously unreported influential region in the near-wake, where the trajectory analysis of the newly defined key saddle points (active saddle points) consistently aligns with the trends in surface heat transfer. This domain enables predictive identification of key transitional events in the Nusselt number profile, including local extrema and slope inflections, across all inclination angles. The analysis reveals that oblique displacement of active saddle points enhances heat transfer by promoting the shedding of repelling LCSs, while parallel displacement leads to weakened heat transfer due to the delayed detachment of repelling coherent structures. The proposed framework enables the construction of a temporal function that closely replicates the monotonicity and transitional features of the Nusselt number evolution. Furthermore, threshold displacement metrics are defined for dominant repelling LCSs to correspond with peak heat transfer efficiency. The proposed methodology not only generalizes across a wide range of inclination angles but also provides a physically interpretable framework for predicting heat transfer enhancement based on coherent structure evolution in unsteady flows.