“…Each coefficient can be expressed in terms of the nodal coordinates and the nodal values of the corresponding variable. This function, used by Omri and Nasrallah [17], Alimi et al [18] and Omri et al [19] is of the flow-oriented upwind type but difficulties signalized in [7] are not remarked.…”
SUMMARYThis paper presents a numerical model to study the laminar flows induced in confined spaces by natural convection. A control volume finite-element method (CVFEM) with equal-order meshing is employed to discretize the governing equations in the pressure-velocity formulation. In the proposed model, unknown variables are calculated in the same grid system using different specific interpolation functions without pressure correction. To manage memory storage requirements, a data storage format is developed for generated sparse banded matrices. The performance of various Krylov techniques, including Bi-CGSTAB (Bi-Conjugate Gradient STABilized) with an incomplete LU (ILU) factorization preconditioner is verified by applying it to three well-known test problems. The results are compared to those of independent numerical or theoretical solutions in literature. The iterative computer procedure is improved by using a coupled strategy, which consists of solving simultaneously the momentum and the continuity equation transformed in a pressure equation. Results show that the strategy provides useful benefits with respect to both reduction of storage requirements and central processing unit runtime.
“…Each coefficient can be expressed in terms of the nodal coordinates and the nodal values of the corresponding variable. This function, used by Omri and Nasrallah [17], Alimi et al [18] and Omri et al [19] is of the flow-oriented upwind type but difficulties signalized in [7] are not remarked.…”
SUMMARYThis paper presents a numerical model to study the laminar flows induced in confined spaces by natural convection. A control volume finite-element method (CVFEM) with equal-order meshing is employed to discretize the governing equations in the pressure-velocity formulation. In the proposed model, unknown variables are calculated in the same grid system using different specific interpolation functions without pressure correction. To manage memory storage requirements, a data storage format is developed for generated sparse banded matrices. The performance of various Krylov techniques, including Bi-CGSTAB (Bi-Conjugate Gradient STABilized) with an incomplete LU (ILU) factorization preconditioner is verified by applying it to three well-known test problems. The results are compared to those of independent numerical or theoretical solutions in literature. The iterative computer procedure is improved by using a coupled strategy, which consists of solving simultaneously the momentum and the continuity equation transformed in a pressure equation. Results show that the strategy provides useful benefits with respect to both reduction of storage requirements and central processing unit runtime.
“…(4) and (8) with same both side length (L 1 = L 2 ); led to (b 1 = b 2 ) and different azimuth and latitude angles, the total amount of transmitted solar energy (H G ) per square meter of the total surface area (L · Z) through the solar still could be obtained by Eq. (16) and is represented in Fig. 2 for inclination angles (b = b 1 = b 2 ) from 10°to 60°while the basin to cover length ratio (a = W/L = cos b) varies from 0.984 to 0.5.…”
Section: 1mentioning
confidence: 99%
“…Experimental and theoretical studies were performed for single slope solar still [1][2][3][4][5][6][7][8][9][10][11], these studies were investigated for different climate conditions, also at different periods of the year as well as all a year investigation. The performance of double slope solar still was performed experimentally and theoretically by many researches [12][13][14][15][16][17][18], their studies were concerned with the effect of inclination angle of the glass cover on its performance for different locations and orientation of the solar still.…”
This investigation represents the optimum inclination angles of the glass cover of the double slope solar still, and orientation for maximum collected solar energy that could be captured by the solar still glass cover. The results will be displayed for different latitudes (/ = 24°, / = 27.2°, / = 30°and / = 31.2°) to cover Egypt geographically. The double slope solar still has two opposite inclined surface; so it has two surfaces azimuth angles (c 1 and c 2 ) according to |c 1 | + |c 2 | = 180°, with opposite signs, these values are (c 1 = 0°and c 2 = 180°), (c 1 = 90°a nd c 2 = À90°), (c 1 = 45°and c 2 = À135°) which is equivalent to (c 1 = À45°and c 2 = 135°); consequently, the total energy is the summation of the collected energy by the two surfaces represents the double slope solar still surface area. The inclination angle (b) is changed from 10°to 60°on both sides of the glass cover to get independently the optimum inclination angles for each side that not necessary to be the same. ª 2015 Faculty of Engineering, Alexandria University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
“…Boukar and Harmim [8] experimentally investigated design parameters of an indirect vertical solar still. Omri et al [9] examined the thermal exchange by natural convection and effect of buoyancy force on flow structure. The authors provided useful information on the flow structure sensitivity to the governing parameters, the Rayleigh number and the tilt angle on the thermal exchange.…”
This paper concerned with the numerical study of thermal and mass diffusive natural convection flow inside a triangular shape solar collector using finite element method for the governing equations expressing the velocity pressure formulation along with the energy and concentration balance equations. In the solution procedure, the isothermal and isoconcentration boundary conditions are assumed at the absorber and covers of collector. Local and mean heat and mass transfer rates for the thermal Rayleigh number and Lewis number are presented. Streamlines, isotherms and isoconcentration are also presented for the aforesaid parameters. The result found in this study fully agreed with the previous published work. But this result will be profitable for the design of the collector.
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