Chaotic fluid mixing is generally considered to enhance fluid-wall heat transfer and thermal homogenisation in laminar flows. However, this essentially concerns the transient stage towards a fully-developed (thermally-homogeneous) asymptotic state and then specifically for high Pe´clet numbers Pe (convective heat transfer dominates). The role of chaos in the asymptotic state at lower Pe, relevant to continuously-operating compact devices as, for instance, micro-electronics cooling systems, remains largely unexplored to date. The present study seeks to gain first insight into this matter by the analysis of a representative model problem: heat transfer in the 2D time-periodic lid-driven cavity flow induced via non-adiabatic walls. The asymptotic time-periodic thermal state is investigated in terms of both the temperature field and the thermal transport routes. This combined Eulerian-Lagrangian approach enables fundamental investigation of the connection between heat transfer and chaotic mixing and its ramifications for temperature distributions and heat-transfer rates. The analysis exposes a very different role of chaos in that its effectiveness for thermal homogenisation and heat-transfer enhancement is in low-Pe asymptotic states marginal at best. Here chaos may in fact locally amplify temperature fluctuations and thus hamper instead of promote thermal homogeneity. These findings reveal that optimal thermal conditions are not always automatic with chaotic mixing and may depend on a more delicate interplay between flow and heat-transfer mechanisms.

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