The existing standard current-temperature calculations for overhead line (OHL) conductors have been adequate for conventional conductors and their operating temperatures. However, these calculations make assumptions and include simplifications about conductor geometry and aero-thermal-dynamics, introducing an error in the High-Temperature Low-Sag conductors operating temperatures. To quantify the error introduced by the shape of strands, the paper employs a Multi-Physics Finite Element Modeling approach that calculates the conjugate heat transfer for trapezoidal stranded OHL conductors. Furthermore, it proposes corrective equations to improve the accuracy of existing methods. The equations incorporate a new Nusselt number correlation for mixed convection and capture the surface area ignored by current calculations. The outer conductor geometry assumptions and the combined natural and forced convective cooling omission in the IEEE and CIGRE methods introduce an error at low (below 0.12 m/s) cross-flow wind speeds suggesting an underestimation of conductor temperature by up to 4%. In medium wind speeds, typically at 0.5 m/s–0.61 m/s, the standard methods overestimate the conductor temperature limiting its current-carrying capability. A 5% uprating for existing OHLs is potentially feasible, particularly for the trapezoidal stranded conductors, when removing the assumptions made in existing methods.

This work presents results of flow around a heated circular cylinder in mixed convection regime and demonstrates that Prandtl number and angle of attack of the incoming flow have a large influence on the characterisation of the flow transition from 2-D to 3-D. Previous studies show that heat transfer can enhance the formation of large 3-D structures in the wake of the cylinder for Reynolds numbers between 75 and 127 and a Richardson number larger than 0.35. This transitional mode is generally identified as �mode E�. In this work, we compare the results for water-based flow (large Prandtl number) with the ones for air-based flows (low Prandtl number). The comparison is carried out at two Reynolds numbers (100 and 150) and at a fixed Richardson number of 1. It shows that at the low Reynolds number of 100 the low Prandtl number flow does not enter into transition. This is caused by the impairment of the baroclinic vorticity production provoked by the spanwise temperature gradient. At low Prandtl number temperature gradients are less steep. For an air-based flow at Reynolds number 150, several Richardson numbers have been simulated. In this situation, the flow enters into transition and exhibits the characteristics of �mode E�, with the development of ?-shaped structures in the near wake and mushroom-like structures in the far wake. It is also observed that the transition is delayed at Richardson number of 0.5. Simulations are also carried to investigate the effect of the angle of attack on the incoming flow on the development of large coherent structures. When the angle of attack is positive, the development of the wake tends to return to a more bi-dimensional configuration, where large scale coherent structures are impaired. In contrast, when the angle of attack is negative, large scale tri-dimensional structures dominate the flow in the wake, but with a very chaotic behaviour and the regular pattern of zero angle of attack is destroyed. The different behaviour of the flow with the variation of the angle of attack is also related to the baroclinic vorticity production, where new terms appear in the equations, leading to a positive effect of the vorticity production in case of a negative angle of attack and the opposite for a positive angle of attack.