Natural convection in a square cavity filled with water-Al2 O3 nanofluid is studied numerically. Upper, lower, and left surfaces are insulated. Right wall is at low temperature, while two heat sources are kept at high temperature. The sources are vertically attached to the horizontal walls of a cavity . A uniform magnetic field is applied in a horizontal direction. Effective thermal conductivity and viscosity of nanofluids are obtained using Koo-Kleinstreuer model which implements the Brownian motion of nanoparticles effect. Steady state laminar regime is assumed. The conservation of mass, momentum, and energy equations are solved using finite volume method. The numerical results are reported for the effect of Rayleigh number, solid volume fraction, and Hartmann number on the streamlines as well as the isotherms. In addition, the results for average Nusselt number are presented for various parametric conditions. This study is presented in the following ranges, Rayleigh number from 103 to 105, Hartmann number from 0 to 60, and solid volume fraction from 0 to 0.06, while the Prandtl number which represents water is kept constant at 6.2. The results showed that heat transfer rate decreases with the rise of Hartmann number and increases with the rise of Rayleigh number, and volume fraction. Moreover, results showed that heat sources positions, lengths and intensities have crucial effect on heat transfer rate. Additionally, the effect of nanofluids type was studied, it was found that water-Cu nanofluid enhances the heat transfer better than water-Al2O3, water-CuO and water-TiO2 nanofluids.

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