2023/09/27 by Silas Alben, Alben, Silas · 1 citation
Engineering · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Turbulent Flows #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.2309.15953
openalex publication_date 2023/09/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We compute steady planar incompressible flows and wall shapes that maximize the rate of heat transfer (Nu) between and hot and cold walls, for a given rate of viscous dissipation by the flow (Pe2). In the case of no flow, we show theoretically that the optimal walls are flat and horizontal, at the minimum separation distance. We use a decoupled approximation to show that flat walls remain optimal up to a critical nonzero flow magnitude. Beyond this value, our computed optimal flows and wall shapes converge to a set of forms that are invariant except for a Pe-1/3 scaling of horizontal lengths. The corresponding rate of heat transfer Nu ∼ Pe2/3. We show that these scalings result from flows at the interface between the diffusion-dominated and convection-dominated regimes. We also show that the separation distance of the walls remains at its minimum value at large Pe.