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Updated: Sep 25, 2025
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Uncoupling Coriolis Force and Rotating Buoyancy Effects on Full-Field Heat Transfer Properties of a Rotating Channel
Published on: October 5, 2018
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Optimal cooling of an internally heated disc
1Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, Chicago, IL 60607, USA.
Summary
Researchers optimized heat transfer in fluid dynamics by developing efficient
Area of Science:
- Fluid dynamics
- Heat transfer
- Mathematical physics
Background:
- Turbulent heat transfer and heat exchanger design require optimal fluid flow solutions.
- Previous studies conjectured convection rolls for energy-constrained cooling.
- Understanding advection-diffusion dynamics is crucial for efficient heat management.
Purpose of the Study:
- To find optimal incompressible flows for cooling an internally heated disc.
- To establish sharp bounds on turbulent heat transfer.
- To design more efficient heat exchangers.
Main Methods:
- Proving one-sided bounds for energy-constrained cooling.
- Constructing self-similar, tree-like 'branching flows' for enstrophy-constrained cooling.
- Utilizing a non-local Dirichlet-like variational principle for advection-diffusion equations.
Main Results:
- Established one-sided bounds for energy-constrained cooling, partially supporting prior conjectures.
- Demonstrated that 'branching flows' achieve cooling within a logarithm of the global optimum under enstrophy constraints.
- Results apply to general, time- and space-dependent source-sink distributions.
Conclusions:
- Developed novel 'branching flows' that significantly improve cooling efficiency.
- Provided theoretical bounds advancing the understanding of optimal heat transfer in fluid systems.
- The findings have implications for designing advanced heat exchangers and managing thermal processes.
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