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Journal of Applied Mathematics
Volume 2013 (2013), Article ID 840632, 7 pages
Research Article

Natural Convection in a Trapezoidal Enclosure with Wavy Top Surface

1Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand
2Centre of Excellence in Mathematics, CHE, Si Ayutthaya Road, Bangkok 10400, Thailand

Received 15 May 2013; Accepted 8 October 2013

Academic Editor: Subhas Abel

Copyright © 2013 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.


The effects of various parameters, Rayleigh number (Ra), Darcy number (Da), and wave amplitude (), on natural convection inside a trapezoidal enclosure with wavy top surface are studied. The enclosure is filled with seawater having Prandtl number (Pr) of 7.2 and uniformly heated on bottom and partially heated on inclined boundaries. The flow field and temperature distribution are observed when interested parameters are chosen for Ra = 104, 105, and 106, Da = 10−5, 10−4, and 10−3, and , 1, and 1.1. FlexPDE, a finite element model builder, is used to solve the governing equations to obtain the numerical results displayed by streamlines and isotherms. From the study results, convection motion is affected by different parameters in which the increase in flow intensity and temperature distribution can be seen at higher Rayleigh and Darcy numbers. The wavy top surface has small influence on the flow field and temperature distribution compared to the influence of Rayleigh and Darcy numbers.