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Modeling of Laminar Buoyancy Convection in a Square Cavity Containing an Obstacle

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Abstract

The problem of free convection flow and heat transfer of a fluid inside a square cavity having adiabatic obstacle positioned in the center of the cavity has been investigated numerically using a penalty finite element method. Calculations have been made for Rayleigh numbers ranging from \(10^2\) to \(10^7\) for an obstacle of aspect ratios \(\hbox {AR}=0,0.4,0.5,0.6\). Nusselt number results are presented for Prandtl number of 0.71 (assuming the cavity is filled with air). Streamline and isotherm contours are also presented. The obtained results demonstrate the effects of pertinent parameters on the fluid flow, thermal fields and heat transfer inside the cavity. The results show that the heat transfer rates generally increase with the shrink of the obstacle size and with the increase of Rayleigh number. Excellent agreement is obtained with previous results in the literature.

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Acknowledgments

The work is supported by PSRC (A Project Funded by the Basic Science Research Center) of Majmaah University, Saudi Arabia.

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Authors and Affiliations

  1. Department of Mathematics, College of Sciences and Human Studies at Hotat Sudair, Majmaah University, Hotat Sudair, 11982, Saudi Arabia

    M. M. Mousa

  2. Department of Basic Science, Faculty of Engineering at Benha, Benha University, Benha, 13512, Egypt

    M. M. Mousa

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  1. M. M. Mousa
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Correspondence to M. M. Mousa.

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Communicated by Syakila Ahmad.

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Mousa, M.M. Modeling of Laminar Buoyancy Convection in a Square Cavity Containing an Obstacle. Bull. Malays. Math. Sci. Soc. 39, 483–498 (2016). https://doi.org/10.1007/s40840-015-0188-z

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  • DOI: https://doi.org/10.1007/s40840-015-0188-z

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