Heat transfer affects a motor's sizing, its performance, and, ultimately, the overall vehicle's range and endurance. However, the thermal literature does not have early-stage models for outrunner brushless DC (BLDC) motors found in small unmanned aerial systems (UASs). To address this gap, we have developed a non-dimensional heat transfer model (Nusselt correlation). Parametric experiments of four different-sized BLDC motors under load in Reynolds-matched wind tunnel tests generated data for model correlation. The motors' aspect ratios (diameter/length) ranged from 0.9 to 1.5. The freestream Reynolds number of the axial flow over the motors ranged from 20,000 to 40,000. The rotational Reynolds number ranged from 10,000 to 20,000. The results showed that aspect ratio had the largest influence on heat transfer, followed by rotational and freestream Reynolds numbers. A steady-state model used the correlation to predict the motor's ambient temperature differential within 10 K of experimental data. A case study applied the correlation to predict a hypothetical motor's continuous torque in different environments. The correlation enables conceptual designers to capture thermally-driven trade-offs in early design stages and reduce costly revisions in later stages.
