# hpfem/esco2012-boa

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 \title{Dual Reciprocity Boundary Element Solution of Mixed Convective Heat and Solutal Transport} \tocauthor{N. Alsoy-Akgun} \author{} \institute{} \maketitle \begin{center} {\large Nagehan Alsoy-Akg{\"u}n}\\ Middle East Technical University\\ {\tt nalsoy@metu.edu.tr} \\ \vspace{4mm}{\large M{\"u}nevver Tezer-Sezgin}\\ Middle East Technical University\\ {\tt munt@metu.edu.tr} \end{center} \section*{Abstract} Mixed convective heat and solutal transport is important in engineering applications such as nuclear waste disposal, crystal growth and oceanography. Mixed convective in a lid driven cavity is studied by solving the equations of conservation of mass, momentum, energy and solutal concentration. The governing equations are solved by using dual reciprocity boundary element method (DRBEM) in terms of stream function, vorticity, temperature and concentration for the case of heated bottom wall and cold top wall. Vorticity, energy and concentration equations are transformed to the form of modified Helmholtz equations by utilizing forward difference with relaxation parameters for the time derivatives, and approximating also Laplacian terms at two consecutive time levels. Inhomogeneities in modified Helmholtz equations are approximated with the thin plates radial basis functions. Computations are carried for several values of Richardson number ($Ri$), buoyancy ratio ($N$), Reynolds number ($Re$), for Prandtl number $Pr=1$ and Schmidt number $Sc=1$. As $Ri$ or $N$ increases formation of secondary fluid core starts for streamlines, isotherms and concentration. The increase in terms of buoyancy force influences the growth of the secondary fluid which allows the transport of heat from the bottom hot wall to other parts of the cavity. \bibliographystyle{plain} \begin{thebibliography}{10} \bibitem{kumar} {\sc D. S. Kumar and K. Murugesan and A.Gupta}. {Numerical analysis of the interaction between inertial and thermosolutal buoyancy forces on convective heat transfer in a lid-driven cavity}. Jour. of Heat Transfer, 132, (2010), doi:10.1115/1.4002029 . \bibitem{munevver} {\sc S. G{\"u}mg{\"u}m and M. Tezer-Sezgin}. {DRBEM solution of natural convection flow of nanofluids with a heat source}. Engrg. Analy. with Bound. Elem., 34, (2010), 727-737. \end{thebibliography}
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