Fluid and heat transfer in laminar flows: a unified topological approach

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Abstract

Laminar flows typically result in deterministic and regular flow patterns. However, fluid-parcel trajectories may nonetheless be extremely complicated and even fully chaotic. The phenomenological disconnection between flow pattern and fluid-parcel dynamics is characteristicof laminar flows and consequently advances the parcel-based (or Lagrangian) representation -- instead of the flow-based (or Eulerian) representation -- as most natural description of fluid transport in this flow regime. The lagrangian representation admits description of fluid advection in terms of the topology of the fluid-parcel trajectories.This topological approach has become an integral part in the analysis of laminar transport problems.Scalar transport generically takes place via both fluid advection and molecular diffusion. The Lagrangianrepresentation of the governing mathematical models for fluid advection and advective-diffusivescalar transport nonetheless have an essentially similar structure. This mathematical analogy admitsgeneralisation of the topological description of fluid advection to advective-diffusivescalar transport and thus paves the way to a unified topological description for fluid and scalar transport.The topological approach for investigation of advective-diffusive transport in laminar flows is demonstrated by way of example. Considered is the heat transfer in the point-vortex flow within a square domain with hot isothermal bottom and cold isothermal top wall and adiabatic sidewalls.
Original languageEnglish
Title of host publicationDynamics Days Europe
Place of PublicationUnited Kingdom, Loughborough
Publication statusPublished - 2007

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