AIMS Mathematics, 2016, 1(3): 195-207. doi: 10.3934/Math.2016.3.195

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RBF simulation of natural convection in a nanofluid-filled cavity

Basic Sciences Unit, TED University, Ankara, Turkey

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In this study, natural convection in a cavity filled with a nanofluid is solved numerically utilizing a radial basis function pseudo spectral (RBF-PS) approach in the space domain and a differential quadrature method (DQM) in the time domain. The governing dimensionless equations are solved in terms of stream function, temperature and vorticity. In the cavity, thermally insulated top and bottom walls are maintained while the left and right walls are at constant temperatures.Numerical solutions present the average Nusselt number variation as well as streamlines, isotherms and vorticity contours. The non-dimensional problem parameters, Rayleigh number $Ra$, solid volume fraction $\chi$ and aspect ratio $AR$ are varied as $10^3\leq Ra \leq 10^6,\, 0 \leq \chi \leq 0.2$ and $AR=0.25,\, 0.5,\,1,\, 2,\, 4$, respectively.It is found that the fluid velocity and the heat transfer are enhanced in presence of nanoparticles, and the convective heat transfer is reduced in a rectangular cavity.
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