Hydrodynamic Stability of Free Convection from an Inclined Elliptic Cylinder

Mathematics;free convection;hydrodynamic stability;elliptic cylinder;steady-state

Finlay, Leslie

University of Waterloo

关键词: Mathematics;    free convection;    hydrodynamic stability;    elliptic cylinder;    steady-state;   

Others  :  https://uwspace.uwaterloo.ca/bitstream/10012/2929/1/lafinlay2006.pdf

瑞士|英语

来源: UWSPACE Waterloo Institutional Repository

【 摘 要 】

The steady problem of free convective heat transfer from an isothermal inclined elliptic cylinder and its stability is investigated. The cylinder is inclined at an arbitrary angle with the horizontal and immersed in an unbounded, viscous, incompressible fluid. It is assumed that the flow is laminar and two-dimensional and that the Boussinesq approximation is valid. The full steady Navier-Stokes and thermal energy equations are transformed to elliptical co-ordinates and an asymptotic analysis is used to find appropriate far-field conditions. A numerical scheme based on finite differences is then used to obtain numerical solutions. Results are found for small to moderate Grashof and Prandtl numbers, and varying ellipse inclinations and aspect ratios.

A linear stability analysis is performed to determine the critical Grashof number at which the flow loses stability. Comparisons are made with long-time unsteady solutions.