Heat transfer via Föppl vortices in the wake of a circular cylinder

For steady flow past a circular cylinder, analytical solutions can be obtained describing uniform flow and a stable pair of symmetric vortices. The latter approximates the viscous vortex flow at low Reynolds number, prior to the onset of vortex shedding. Herein, we employ the analytical Föppl vortex solution to model idealised steady and unsteady heat transfer from a cylinder, and explore connections with viscous theory for this problem. We use numerical methods based on the combination of a streamline-tracing technique with operator splitting to obtain fast, accurate solutions of the convection–diffusion equation. Comparison between results from our model with those for viscous flows, based on geometric similarity criteria, show significant similarity at low Reynolds numbers, but exhibit systematic discrepancies at higher Reynolds numbers. This paper showcases important differences between viscous and inviscid heat transfer, and suggests the use of the simple Föppl vortex case as a benchmark for numerical studies.