Effect of Surface Corrugation on Convection in a Three-Dimensional Finite Box of Fluid Saturated Porous Material |
| |
Authors: | DN Riahi |
| |
Institution: | (1) Department of Theoretical and Applied Mechanics, 216 Talbot Laboratory, University of Illinois, 104 S. Wright Street, Urbana, IL 61801, U.S.A., US |
| |
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 stability analysis.
In the absence of corrugation 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
the existence of such modes of convection. In the presence of boundary corrugation with the appropriate form, different three-dimensional
or two-dimensional modes of corrugation can be stable or unstable. For a rough 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 can all
play a role leading to either stable or unstable particular three- or two-dimensional flow patterns. For a wavy 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 nonresonant 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.
Received 24 July 1998 and accepted 11 April 1999 |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|