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Title:Effect of surface corrugation on convection in three-dimensional fluid-saturated porous material
Author(s):Riahi, Daniel N.
Subject(s):Surface Corrugation
Abstract:The problem of finite amplitude thermal convection in a three-dimensional finite box of fluid saturated porous material is investigated, when the lower boundary of the fluid is corrugated. The nonlinear problem of three-dimensional convection in the box for the values of the Rayleigh number close to the classical critical value and for small values of the amplitude of the corrugations is solved by a perturbation technique. The preferred mode of convection is determined by a stability analysis. In the absence of the corrugations three-dimensional modes of convection can be either stable or unstable depending on the values of the aspect ratios of the box, while two-dimensional rolls are always stable, provided that the box aspect ratios allow existence of such modes of convection. In the presence of the boundary corrugation with appropriate form different three-dimensional or two-dimensional modes of corrugation can be stable or unstable. For roughened lower boundary with local roughness sites, the location, size and number of the roughness elements plus the wave numbers of the convection modes and the box aspect ratios all can play a role leading to either stable or unstable particular three or two-dimensional flow patterns. For the wavy lower boundary resonant wave vector excitation can lead to the preference of stable two or three-dimensional flow patterns whose wave vectors are in a subset of those due to the wavy boundary, while non-resonant wave vector excitation can lead to the preference of stable flow patterns whose wave vectors are not generally in a subset of those due to the wavy boundary. Heat transported by convection can either be enhanced or be reduced by certain proper forms of the corrugations and by appropriate values of the box aspect ratios. Due to the surface corrugation highly subcritical modes of convection are stable, while highly supercritical modes of convection are unstable.
Issue Date:1997-10
Publisher:Department of Theoretical and Applied Mechanics. College of Engineering. University of Illinois at Urbana-Champaign
Series/Report:TAM R 865
Genre:Technical Report
Rights Information:Copyright 1997 Board of Trustees of the University of Illinois
Date Available in IDEALS:2021-11-04

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  • Technical Reports - Theoretical and Applied Mechanics (TAM)
    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.

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