Hot shapes: Nusselt numbers for superellipsoidal particles suspended in Stokes flow

Convective heat transfer between micron-sized particles and a surrounding viscous fluid plays a crucial role in a wide range of applications, including aerosol transport, particulate flows, and particle inhalation modeling. Although spherical and ellipsoidal particles have been studied extensively regarding their convective heat transfer characteristics, accurate convective heat transfer models for irregularly shaped particles remain scarce. In this work, we consider convective heat transfer from non-spherical particles of superellipsoidal shape in the (local) Stokes-flow regime characterized by a small particle Reynolds number to learn surrogate models for the corresponding Nusselt number, characterizing the convective heat transfer between a particle and a fluid. We provide a unified framework that captures the influence of particle shape and flow conditions at small Péclet numbers. Direct numerical simulations are performed for superellipsoidal particles in creeping flow, consistent with the assumptions underlying Lagrangian point-particle approaches for particles suspended in typical fluids such as air and water. Like this, we evaluate the Nusselt number from surface-resolved and surface-integrated heat fluxes and analyze it as a function of the particle shape, its orientation, and flow conditions. We demonstrate that at small Péclet numbers ( Pe ≤ 1 ) the particle orientation has a negligible influence on convective heat transfer. Focusing on small Péclet numbers we learn a Nusselt number correlation model and a physics-constrained neural-network model that predict the Nusselt number at small Péclet numbers as a function of particle shape and flow conditions. The resulting surrogate models achieve excellent predictive accuracy and enable efficient evaluation of particle–fluid convective heat transfer in the Lagrangian point-particle setting for a broad class of non-spherical particles.