The Helmholtz equation for convection in two-dimensional porous cavities with conducting boundaries
Rees, D. A. and Tyvand, P. A., 2004. The Helmholtz equation for convection in two-dimensional porous cavities with conducting boundaries. Journal of Engineering Mathematics, 49 (2), pp. 181-193.
Related documents:This repository does not currently have the full-text of this item.
You may be able to access a copy if URLs are provided below.
It is well-known that every two-dimensional porous cavity with a conducting and impermeable boundary is degenerate, as it has two different eigensolutions at the onset of convection. In this paper it is demonstrated that the eigenvalue problem obtained from a linear stability analysis may be reduced to a second-order problem governed by the Helmholtz equation, after separating out a Fourier component. This separated Fourier component implies a constant wavelength of disturbance at the onset of convection, although the phase remains arbitrary. The Helmholtz equation governs the critical Rayleigh number, and makes it independent of the orientation of the porous cavity. Finite-difference solutions of the eigenvalue problem for the onset of convection are presented for various geometries. Comparisons are made with the known solutions for a rectangle and a circle, and analytical solutions of the Helmholtz equation are given for many different domains. © 2004 Kluwer Academic Publishers.
|Creators||Rees, D. A.and Tyvand, P. A.|
|Uncontrolled Keywords||heat conduction, heat convection, cavitation, porosity, problem solving, boundary conditions, mechanical permeability|
|Departments||Faculty of Engineering & Design > Mechanical Engineering|
Actions (login required)