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The effect of presence of nanoparticles on natural convection and entropy generation in a semi-circular enclosure with present heat flux is investigated numerically in the present work. The enclosure is filled with nanofluids (Cu-water). The heat flux is supplied partly in the center of the base wall, and the other parts of base wall of the enclosure are assumed adiabatic. The center of the circular arc (-45°≤γ≤+45°) is assumed at constant cold temperature and the other parts of the circular arc are adiabatic. Finite element method based on the variational formulation is employed to solve momentum and energy as well as post-processing streamfunctions. The results are based on visualization of isotherms, streamfunction and entropy generation. Comparison with previously published work is performed and the results are found to be in a good agreement. The influence of pertinent parameters such as Rayleigh number (10 4 ≤Ra≤10 7 ) and solid volume fraction of nanoparticles (0≤Φ≤0.15 step 0.05) on the flow, temperature, and entropy generation are examined in the present paper. The results show that the heat transfer rate increases with an increase of the Rayleigh number and the nanoparticles volume fraction. The system irreversibility increases as nanoparticles fraction increase.

A numerical analysis is performed to study the fluid flow, heat transfer and entropy generation inside a square cavity embedded with heat flux and subject to the horizontal magnetic field. The cavity is consist of two same width layers: first layer filled with nanofluid (Al2O3+water) and second one is saturated porous media filled with a same nanofluid. The uniform constant heat flux is applied partly at the base wall, and the other parts of the base wall are assumed adiabatic. The upper horizontal wall kept adiabatic, while the vertical walls are maintained at constant cold temperature. Finite element method based on the variational formulation is employed to solve the main equations. The results of the present study are based on visualization of heat flow via isotherms and heatfunctions (heatlines), fluid flow via streamfunctions, and irreversibility via Bejan number. Comparisons with previously numerical and experimental published works are performed and the results are found to be in a good agreement. In this study, the effect of the main pertinent parameters, such as: nanoparticles volume fraction (0≤Φ≤0.15), Rayleigh number (104≤Ra≤107), Darcy number (10−1≤Da≤10−5), Hartmann number (0≤Ha≤60) on the fluid flow, heat transfer and entropy generation are investigated. The results show that the effect of the Hartmann on Nusselt number increases as Darcy number increases especially at high Rayleigh number. Also, at Ra=107 and Φ=0.15, the percentage decreasing in Nusselt number due to present magnetic field (Ha=40) are 85.89% at Da=10−1, 87.12% at Da=10−3 and 98.69% at Da=10−5.

Natural convection in a parallelogrammic enclosure filled with different types of nanofluids (Al 2 O 3 , Ag and TiO 2 ) subjected to three discrete heated isoflux is examined numerically by using a heatlines visualization method. The position of three discrete isoflux are at left and right sidewalls remark by (λ = 0.25), while the third isoflux at a bottom wall remark by (ζ = 0.5). The top wall with the remaining regions in the bottom wall is insulated, while the remaining regions in the side walls are maintained at low temperatures. Finite element method based on a Chorin's algorithm used to solve the governing equation continuity, momentum and energy. Numerical calculations were achieved for a wide range of Rayleigh numbers (10 4 ≤Ra≤10 7 ), skew angle (−30 o ≤γ≤+30 o ), and volume fraction of nanoparticles (0≤ Φ≤0.2). The result is explained in term of stream functions, isotherms, heatfunctions, local and average Nusselt numbers. It is found that the heat transfer performance considerably improve with the supplement water of various species of nanofluid and changing skew angle. Furthermore, nine correlations are established to approximate the average Nusselt number.