## Journal of Applied Mathematics

### Natural Convection in a Trapezoidal Enclosure with Wavy Top Surface

#### Abstract

The effects of various parameters, Rayleigh number (Ra), Darcy number (Da), and wave amplitude ($a$), 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 $a=\mathrm{0.9}$, 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.

#### Article information

Source
J. Appl. Math., Volume 2013 (2013), Article ID 840632, 7 pages.

Dates
First available in Project Euclid: 14 March 2014

https://projecteuclid.org/euclid.jam/1394808196

Digital Object Identifier
doi:10.1155/2013/840632

#### Citation

Sompong, Pensiri; Witayangkurn, Supot. Natural Convection in a Trapezoidal Enclosure with Wavy Top Surface. J. Appl. Math. 2013 (2013), Article ID 840632, 7 pages. doi:10.1155/2013/840632. https://projecteuclid.org/euclid.jam/1394808196

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