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Numerical investigation of the laminar mixed convection in two-dimensional   lid driven cavity filled with water-Al2O3, water-Cu or water-TiO2 nanofluids   is done in this work. In the present study, the top and bottom horizontal   walls are thermally insulated while the vertical walls are kept at constant   but different temperatures. The governing equations are given in term of the   stream function-vorticity formulation in the non-dimensionalized form and   then solved numerically by second-order central difference scheme. The   thermal conductivity and effective viscosity of nanofluid have been   calculated by Maxwell-Garnett and Brinkman models, respectively. An excellent   agreement between the current work and previously published data on the basis   of special cases are found. The governing parameters are Rayleigh number 103   ≤ Ra ≤ 106 and solid concentration 0 ≤ φ ≤0.2 at constant Reynolds and Prandtl   numbers. An increase in mean Nusselt number is found as the volume fraction   of nanoparticles increases for the whole range of Rayleigh numbers. In   addition, it is found that significant heat transfer enhancement can be   obtained by increasing thermal conductivity coefficient of additive   particles. At Ra=1.75×105, the Nusselt number increases by about 21% for   TiO2-Water, and almost 25% for Al2O3-Water, and finally around 40% for   Cu-Water nanofluid. Therefore, the highest values are obtained when using Cu   nanoparticles. The result obtained using variable thermal conductivity and   variable viscosity models are also compared to the results acquired by the   Maxwell-Garnett and the Brinkman model

Numerical study of mixed convection heat transfer in lid-driven cavity utilizing nanofluid: Effect of type and model of nanofluid