Effectiveness and Economic for Using Ag-Nanoparticles in Porous Media inside Enclosure with Present Heat Generation and Magnetic Field under Natural Convection Conditions

In the present study the effect of the magnetic field and the heat generation on the effectiveness and the economics of using Ag-nanoparticles in porous media under a natural convection with heat flux is studied numerically using finite element method. Four different enclosure shapes are studied. The uniform heat flux is applied partly at the base wall. The vertical or sloped walls are maintained at a constant cold temperature. New criteria are used to evaluate the effectiveness of using nanoparticles depending on the nanoparticles cost and the heat transfer. The results are based on visualization of heat flow via isotherms heatfunctions and Nusselt number fluid flow via streamfunctions and irreversibility via Bejan number. Comparisons with previous published works are performed and the results are found in a good agreement. The influence of main pertinent parameters is investigated such as: Rayleigh number Ra = (10(4) . . . 10(7)) Hartmann number Ha = (0 . . . 60) heat generation constant (lambda = 1 and 10) and nanoparticles volume fraction Phi = (0 . . . 0.15) on the flow heat transfer and entropy generation for constant Darcy number Da = 10(-4). The results show that the benefit of using nanoparticles on the system stability (effectiveness-Be) decreases as the n increases. Also for most cases the maximum cost-heat appears at lambda = 0 : 0 5 and it reduces as nanoparticles volume fraction increases except for high Ra = 10(7). The results show at n = 0 (square cavity) and Ra = 10(4) the streamfunction of pure fluid increases 45.2 times between lambda = 1 and 10, while at Ra = 10(7) the streamfunction of pure fluid increases 1.1 times.