University of Illinois Urbana-Champaign

Finite amplitude thermal convection with variable gravity

Riahi, Daniel N.; Hsui, Albert T.

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https://hdl.handle.net/2142/112634

Description

Title
Finite amplitude thermal convection with variable gravity
Author(s)
  • Riahi, Daniel N.
  • Hsui, Albert T.
Issue Date
1999-12
Keyword(s)
  • Variable Gravity
  • Finite Amplitude Thermal Convection
Abstract
Finite amplitude thermal convection is studied in a horizontal layer of infinite Prandtl number fluid with a variable gravity. For the present study, gravity is restricted to vary quadratically with respect to the vertical variable. A perturbation technique based on a small parameter, which is a measure of the ratio of the vertical to horizontal dimensions of the convective cells, is employed to determine the finite amplitude steady solutions. These solutions are represented in terms of convective modes whose amplitudes can be either small or of order unity. Stability of these solutions is investigated with respect to three dimensional disturbances. A variable gravity function introduces two non-dimensional parameters. For certain range of values of these two parameters, double or triple cellular structure in the vertical direction can be realized. Hexagonal patterns are preferred for sufficiently small amplitude of convection, while square patterns can become dominant for larger values of the convective amplitude. Variable gravity can also affect significantly the wavelength of the cellular pattern and the onset condition of the convective motion .
Publisher
Department of Theoretical and Applied Mechanics. College of Engineering. University of Illinois at Urbana-Champaign
Series/Report Name or Number
  • TAM R 925
  • 1999-6027
ISSN
0073-5264
Type of Resource
text
Language
eng
Permalink
http://hdl.handle.net/2142/112634
Copyright and License Information
Copyright 1999 Board of Trustees of the University of Illinois

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Technical Reports - Theoretical and Applied Mechanics (TAM) PRIMARY
TAM technical reports include manuscripts intended for publication, theses judged to have general interest, notes prepared for short courses, symposia compiled from outstanding undergraduate projects, and reports prepared for research-sponsoring agencies.