A way to visualise heat transfer in 3D unsteady flows

Heat transfer in fluid flows traditionally is examined in terms of temperature field and heat-transfer coefficients. However, heat transfer may alternatively be considered as the transport of thermal energy by the total convective-conductive heat flux in a way analogous to the transport of fluid by the flow field. The paths followed by the total heat flux are the thermal counterpart to fluid trajectories and facilitate heat-transfer visualisation in a similar manner as flow visualisation. This has great potential for applications in which insight into the heat fluxes throughout the entire configuration is essential (e.g. cooling systems, heat exchangers). To date this concept has been restricted to 2D steady flows. The present study proposes its generalisation to 3D unsteady flows by representing heat transfer as the 3D unsteady motion of a virtual fluid subject to continuity. The heat-transfer visualisation is provided with a physical framework and demonstrated by way of representative examples. Furthermore, a fundamental analogy between fluid motion and heat transfer is addressed that may pave the way to future heat-transfer studies by well-established geometrical methods from laminar-mixing studies.