Visualisation of heat transfer in 3D unsteady flows

Heat transfer in fluid flows traditionally is examined in terms of temperature field and heat-transfer coefficients at non-adiabatic walls. 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. This unified ansatz enables heat-transfer visualisation with well-known geometrical methods from laminar-mixing studies. These methods lean on the property that continuity “organises” fluid trajectories into sets of coherent structures (“flow topology”) that geometrically determine the fluid transport. Decomposition of the flow topology into its constituent coherent structures visualises the transport routes and affords insight into the transport properties. Thermal trajectories form a thermal topology of essentially equivalent composition that can be visualised by the same methodology. This thermal topology is defined in both flow and solid regions and thus describes the heat transfer throughout the entire domain of interest. The heat-transfer visualisation is provided with a physical framework and demonstrated by way of representative examples.