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Journal of Applied Mathematics
Volume 2014, Article ID 853231, 9 pages
http://dx.doi.org/10.1155/2014/853231
Research Article

Numerical Study of Natural Convection in a Heated Enclosure with Two Wavy Vertical Walls Using Finite Element Method

1Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand
2Centre of Excellence in Mathematics, Commission on Higher Education (CHE), Si Ayutthaya Road, Bangkok 10400, Thailand

Received 22 February 2014; Accepted 13 April 2014; Published 4 May 2014

Academic Editor: Bo Yu

Copyright © 2014 Pensiri Sompong and Supot Witayangkurn. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The effects of wavy geometry on natural convection in an enclosure with two wavy vertical walls and filled with fluid saturated porous media are investigated numerically by using finite element method. The wavy enclosure is transformed to a unit square in the computational domain and the finite element formulations are solved in terms of -coordinate based on iterative method. In order to investigate the effects of interested parameters, the values of wave amplitude ( = 0.05 and 0.1) and number of undulations (n = 1 and 2) are chosen with constants Ra = 105, Da = 10−3, and Pr = 0.71. It is found that the increase in number of undulations has small effect on natural convection inside the enclosure whereas the increase in wave amplitude reduces the strength of convection because higher wave volume plays a barricade role.