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Reaction-diffusion Equations Describe Heat Transfer and Flow Structure in Annular Convection by Zhang, Yuejia; Moore, Nicholas J.; Mac Huang, Jinzi is a scholarly article available to read on EtoBox.

What is Reaction-diffusion Equations Describe Heat Transfer and Flow Structure in Annular Convection about?

Heat transfer in a fluid can be be greatly enhanced by natural convection, giving rise to the nuanced relationship between the Nusselt number and Rayleigh number that has been a focus of modern fluid dynamics. Our work explores convection in an annular domain, where the geometry reinforces the large-scale circulatory flow pattern that is characteristic of natural convection. The flow must match the no-slip condition at the boundary, leading to a thin boundary layer where both the flow velocity and the temperature vary rapidly. Within such a geometry, a novel Nusselt-Rayleigh scaling emerges, suggesting subtle differences in the heat transfer mechanisms as compared to the well-known case of Rayleigh-B\'enard convection. To understand the heat transfer characteristics of this system, we derive a reduced model from the Navier-Stokes-Boussinesq equations where the equations of flow and heat are transformed to a system of low-order partial differential equations (PDEs). This system of PDEs takes the form of a reaction-diffusion system, and its solution preserves the same boundary layer structures seen in the direct numerical simulation (DNS). By matching the solutions inside and outside

Author

Zhang, Yuejia; Moore, Nicholas J.; Mac Huang, Jinzi

Published

2024

Language

EN