Abstract/Details

Numerical methods for Rayleigh -Benard convection inside a Hele -Shaw cell


2001 2001

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Abstract (summary)

Fluid dynamics inside a Hele-Shaw cell are investigated computationally. A Hele-Shaw cell is a rectangular chamber, filled with fluid, that consists of two closely placed parallel plates, i.e., it is very thin in one direction as compared with the other two. It effectively turns a three-dimensional situation into a “quasi” two-dimensional situation. Whenever a denser fluid is above a less dense fluid, a potentially unstable situation is created. For large enough density differences, convective motion occurs in the chamber. The fluid dynamics that result due to such an odd density arrangement is a specific example of the better known Rayleigh-Benard convection. Whereas, classic Rayleigh-Benard convection is temperature driven, the fluid dynamics in our chamber will be driven by a solute concentration gradient (an isometric problem). The incompressible Navier-Stoke's equations in the Boussinesq approximation are used to model and simulate the fluid motion. An additional energy equation is coupled to describe the solute concentration evolution. These equations are addressed numerically using a pseudo-spectral technique that utilizes a Fast Fourier Transform, and a projection method that allows for inflow/outflow boundary conditions. A stability analysis is performed to evaluate the strength of the simulation process.

Indexing (details)


Subject
Mathematics
Classification
0405: Mathematics
Identifier / keyword
Pure sciences; Computational fluid dynamics; Hele-Shaw cell; Rayleigh-Benard convection
Title
Numerical methods for Rayleigh -Benard convection inside a Hele -Shaw cell
Author
Stovall, Idris Sadulla
Number of pages
66
Publication year
2001
Degree date
2001
School code
0118
Source
DAI-B 62/10, Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
ISBN
9780493393698, 0493393692
Advisor
Whitaker, Nathaniel
University/institution
University of Massachusetts Amherst
University location
United States -- Massachusetts
Degree
Ph.D.
Source type
Dissertations & Theses
Language
English
Document type
Dissertation/Thesis
Dissertation/thesis number
3027263
ProQuest document ID
304699610
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
Document URL
http://search.proquest.com/docview/304699610
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