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Wavy optimal flows for heat transfer in straight channels
Which flow patterns are most effective at cooling hot boundaries? We address this question by optimizing incompressible two-dimensional fluid flows in a straight channel to maximize heat transfer under a fixed input power budget. Using an adjoint-based gradient framework combined with the Broyden–Fletcher–Goldfarb–Shanno (BFGS) optimization algorithm, we find that optimal flows remain predominantly unidirectional up to a critical Péclet number Pe ~ 2^12. Beyond this threshold, our improved numerical scheme uncovers a new class of wavy optimal flows. These flows are characterized by finger-like structures extending from the channel walls, which reorganize transport pathways and enhance thermal exchange. Link to paper
Modeling EPS Transport and Fluid Flow in Sea Ice Brine Inclusions
Extracellular polymeric substances (EPS) produced by algal cells play an important role in sea ice ecosystems. In this project, we investigate how EPS-mediated reductions in permeability affect nutrient availability for algae. Previous studies show that pennate diatoms and other microorganisms adjust EPS production and composition in response to environmental stressors such as nutrient limitation, salinity, and low temperatures. EPS production may create competing effects on nutrient uptake: low EPS levels can lead to nutrient washout, while high EPS may form a dense matrix that restricts nutrient transport. This suggests a possible non-monotonic relationship between EPS concentration and nutrient uptake. Using a computational optimization framework, we explore whether an intermediate EPS secretion level maximizes nutrient availability for algal cells.
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