a b s t r a c tAn enhanced cell-centered finite-volume procedure was presented for solving the natural convection of the laminar air flow in a Γ -shaped enclosure with circular corners. An explicit fourth-order Runge-Kutta integration algorithm was applied to find the steady state condition. Also an artificial compressibility technique was applied to couple the continuity to the momentum equations. The discretization of the viscous and thermal conduction terms are very simplified using the enhanced scheme similar to the flux averaging in the convective term. The Rayleigh numbers from 10 2 to 10 6 were considered. In the case of corner radius as r = 0, then the data available in open literature were used to validate the numerical model. The effect of the artificial compressibility parameter in convergence of solution was investigated. Additionally an analysis of the entropy generation in Γ -shaped enclosure with circular corners was performed. It was seen that in the cases of the large radius corners, with a decrease of the irreversibility ratio, then the Bejan number increases.
An enhanced cell-centered finite-volume procedure has been presented for solving the natural convection of the laminar Al O /Water nanofluid flow in a Γ shaped micro-channel in the slip flow region, including the effects of velocity slip and temperature jump at the wall, which are the main characteristics of flow in the slip flow region. In provided FORTRAN code, an explicit fourth-order Runge-Kutta integration algorithm has been applied to find the steady state solutions. Also an artificial compressibility technique has been to couple the continuity to the momentum equations. The Grashof numbers from 10 to 10 have been considered. Results show that decreasing the mean diameters of nanoparticles, increases the Nusselt number.Increasing the mean nanoparticle volume fraction increases the Nusselt number. Also by increasing the Knudsen number, the Nusselt number decreases.
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