In this work, we interested to the numerical simulation of natural convection in a closed model greenhouse heated by tubes. A greenhouse box subjected to different boundary conditions on the roof like the imposed temperature, convective flux and mixed flux was studied. The considered mathematical model is a system of partial differential equations formed by the continuity, the momentum and the energy equations. The commercial Computational Fluid Dynamics (CFD) code Fluent was used for numerical simulations based on a finite volume method. In each case, we have studied the thermal and dynamic flow parameters in the greenhouse, such as the average velocity and the average temperature. The obtained results present a good agreement with the experimental data and show a strong dependence of the air climate in the greenhouse. These results help the farmers to set up a greenhouse with materials and dimensions suitable for external conditions.

In this study, we are interested to the turbulent mixed convection in a ventilated enclosure. A heat source is placed at the middle of the enclosure that's equipped with two openings; one is located at the lower left corner and the other located in the upper right corner. The width of the opening "h" represents 1/5 of the side of the cavity. The walls of the cavity are maintained adiabatic. The temperature of the heat source Th is higher than the room temperature. The width of the heat source "D" is equal to the opening width "h" (D = h). The governing equations of turbulent mixed flow convection in the cavity are solved using finite volumes method. A model k-ε of two-equation was used for closure the equations of turbulent regimes. The Grashof number is set constant (Gr = 10 9 ) and the Reynolds number (Re) varied such that the Richardson number (Ri) takes the values : 0.01, 0.05, 0.1, 1, 2, 5, 10, 20 and 30 (Ri = Gr / Re 2 ). The effects of flow thermal, dynamic parameters, the geometry and heat source dimensions are presented and discussed.

In this paper, double diffusive natural convection in binary mixture under the effect of external magnetic field for the steady and the oscillatory state is numerically investigated. For this end, a square cavity filled with a binary mixture has been considered; the cavity is exposed to opposing solute and thermal gradients. An external uniform magnetic field is applied separately in two directions (i.e. horizontal and vertical). The following flow parameters were considered: Prandtl number Pr = 0.71, Schmidt number Sc = 3.5 and buoyancy ratio N = 0.75, 1.0, and 1.25. The finite volume method with SIMPLER Algorithm was used to solve numerically the mathematical model. The model was validated and showed good agreement with experimental results of the literature. The obtained results showed a strong dependence of the structure of thermal and solutal effect to the buoyancy ratio. The oscillatory double diffusive flow occurs for a periodic time where the phenomenon change around in each period time. A critical thermal Rayleigh number RaTCr and corresponding dominated frequency for the onset of oscillatory double diffusive convection were determined for each N and for different values of Hartman number (0, 25, 50, and 100).

A numerical study of Rayleigh-Bé nard convection in a rectangular cavity has been presented. The onset of natural convection and the transition from laminar to oscillatory convection were considered in this study. The finite volume method was used to solve numerically the governing equations of the phenomenon and the pressure-velocity coupling was matched by SIMPLER Algorithm of Patankar. This study was carried out for Rayleigh number varied from 10 3 to 10 6 in order to control the first value of critical Rayleigh number, Rac-1 corresponding the onset of convection, and that for different aspect ratios of the cavity. The threshold transition regime of laminar-oscillatory convection is depicted by the second critical Rayleigh number Rac-2. Also, the different modes of bifurcation of convection were determined and discussed.

Transient double diffusive natural convection in a square cavity is numerically investigated. The enclosure is heated and cooled along the vertical walls with thermal and solutal gradients, the two horizontal walls of the enclosure are adiabatic and impermeable, the Dufour and Soret effects are considered. The governing equations are solved by using control volume method and SIMPLER algorithm. The main focus of this work is to identify the flow regime for thermal and solutal dominated flows. The flow pattern and heat and mass transfer and the effect of various parameters are analyzed (thermal Rayleigh number, Buoyancy ratio, Soret and Dufour coefficients). Comprehensive Nusselt and Sherwood numbers data are presented as functions of the governing parameters. The results showed that both heat and mass transfer increased in the presence of Dufour coefficient, and the Soret coefficient had great effect on the flow structure.