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

2026-07-01

AI Summary

Traditional Eulerian approaches struggle to uncover the intrinsic transport mechanisms and coherent structures in unsteady heat conduction. This work proposes a Lagrangian visualization method based on massless particles, which tracks particle trajectories within a time-reparameterized spatiotemporal framework and accumulates their thermal transport contributions to identify attracting/repelling structures and coherent transport channels over finite time intervals. For the first time, this approach effectively extends the Lagrangian framework to non-periodic, non-conservative heat transport problems, thereby transcending the applicability limits of existing fluid mixing visualization techniques. The method successfully reveals dynamic thermal transport structures that are inaccessible to conventional approaches, significantly advancing the understanding of unsteady heat conduction mechanisms.

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.

Problem

• Lagrangian heat transport
• unsteady heat transfer
• non-conservative transport
• coherent structures
• visualization

Innovation

• Lagrangian heat transport
• particle-based visualization
• time-reparameterized spacetime
• coherent structures
• non-conservative transport