Visualizing Lagrangian Heat Transport Paths and Density Structures in Unsteady Heat Transfer

Abstract

Convective heat transfer is traditionally visualized from a Eulerian perspective using scalar temperature fields, offering limited insight into the underlying transport mechanisms. A Lagrangian view, analogous to mass transport along fluid paths, can reveal coherent structures and transport routes invisible from a Eulerian view of temperature. However, heat transport is aperiodic and non-conservative, hampering the application of fluid mixing and transport visualization techniques, developed primarily for time-periodic, conservative transport. We present a particle-based visualization technique that addresses these challenges by advecting massless particles along a time-reparameterized spacetime formulation of thermal transport, accumulating path contributions to reveal coherent transport routes and finite-time attracting and repelling structures that conventional methods cannot show.