The geometry of laminar heat transfer

Heat transfer fundamentally is the transport of ``parcels'' of thermal energy by the total advective-diffusiveheat flux in an analogous manner as fluid motion is the transport of fluid parcels by the flow. This puts forwardthermal trajectories along which thermal energy is transferred as thermal counterpart to fluid trajectories. Thisfundamental analogy between heat transfer and fluid motion admits application of methods well-known fromlaminar mixing studies to laminar heat-transfer problems. Key to these methods is description of fluid advection in terms of coherent structures in the web of fluidtrajectories (``flow topology'') that geometrically determine the fluid motion and thus the transport properties. Thesemethods facilitate investigation of the geometry of the thermal trajectories (``thermal topology'') -- and thusthe heat transfer -- in an entirely analogous manner. The concept of thermal topologies and its potential forlaminar heat-transfer studies is demonstrated by way of example.