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4 E0020 Icmsn 2018 International Journal of Structural and Civil Engineering Research Vol. 8, No. 1, February 2019 The Modern Approach for Materials Construction Design Elhadj. Benachour a Energetic laboratory in Arid Zones (ENERGARID), Departement of Sciences, Faculty of Science, University of Tahri Mohamed, Bechar, 08000, Algeria Email: benachour_elhadj @yahoo.fr Belkacem. Draoui b, Bachir. Imine c and Khadidja. Asnoune d b Energetic laboratory in Arid Zones (ENERGARID), Departement of Sciences, Faculty of Science, University of Tahri Mohamed, Bechar, 08000, Algeria cLASP Laboratory, Faculty of Mechanical Engineering, USTOran, 31000, Algeria dLaboratory of Smart Grids and Renewable Energies, TAHRI Mohammed University of Bechar, BP. 417 Bechar (08000), Algeria Email: [email protected],{ imine_b, kh_asnoune}@yahoo.fr Abstract—The simulation grant a deep insight into the construction problems but what are the most common and quantum mechanical and thermal heat transfer effects how can you avoid them?. Each building design team which determine material properties, and therefore, must complete its own due diligence on the system that computational materials design is traditionally used to works best for its building and the end user of the improve and further develop already existing materials. building, as well as the design of the exterior walls Especially when it comes to thermal transfer within building materials because it directly affects the quality thermal without forgetting the building material because the comfort. In this work the evolution of conduction convection building sector today is known to be consuming 40% of coupling through this material which represents the raw the world energy [3]. The building sector is experiencing material of the construction of the walls. Also, in this paper significant challenges in relation to the consumption of we have developed a new correlation for Controller the energy, climate change and energy poverty issues [4], average Nusselt number which gives us a prediction before there are even simulations and analyzes of vapor bubble conception walls and with Newton polynomial interpolation bundles to show the potentially erosive impact loads on method and the material optimization for a average the walls [5]. Also, it has become common in recent years Rayleigh number equal to 1.E-4. to gather data on human attitudes and behavior in Index Terms—materials, advanced materials, optimized building energy, research examples of this kind of design, convection in buildings research are found in the main journals which deal with technical aspects of energy in buildings, including Building and Environment [6–8], International review of I. INTRODUCTION mechanical engineering [9], Energy Storage [10-11], Construction and Building Materials [12-13], Energy and Cooling is one of the major concerns in building Buildings [14]. In numerical analysis, polynomial tropical houses. This problem is exacerbated by the heat interpolation is the interpolation of a given data set by the gain of the roof and the external walls, which constitutes polynomial of lowest possible degree that passes through more than 70% of the total heat gain [1]. The range of the points of the dataset. A new mathematical method is applications where heat sinks are specified as an integral developed for interpolation from a given set of data part of electronics components and circuitry has increased points in a plane and for fitting a smooth curve to the significantly in recent years. Heat sinks have typically points. This method is devised in such a way that the been used in high powered, electronic devices, such as resultant curve will pass through the given points and will stereo equipment, computing devices and appear smooth and natural. It is based on newton communications equipment, however, newer applications interpolation method. So, firstly we vary the thickness of in the automotive industry and consumer products are the building material of the outer wall four times and reshaping the way we design and manufacture heat sinks. calculate the Nusselt number aims to find a cloud point. In addition to traditional design requirements such as After, we developed new formula that helps us to know thermal performance and structural integrity, the high the exchange ratio and the Nusselt number for each volume, low cost requirements associated with newer thickness e by the Newton polynomial interpolation heat sink markets, necessitates a re-examination of the method for mean Rayleigh number equal 10.E4. Thus, it materials and methods used to manufacture heat sinks [2]. can be applicable for use in building simulators The last thing you wish to encounter are building concerning heat transfer phenomena in building physics. Manuscript received April 9, 2018; revised August 15, 2018. © 2019 Int. J. Struct. Civ. Eng. Res. 21 doi: 10.18178/ijscer.8.1.21-25 International Journal of Structural and Civil Engineering Research Vol. 8, No. 1, February 2019 II. GEOMETRIC CONFIGURATION D. Energy The idea is illustrated in the configuration shown in T T T 1 (4) Figure 1. It is a square cavity where the outer wall is U V 2T t X Y concrete, the form factor equal to A = 1, the length L = 1 cp cp and an author H = 1 (dimensionless case). This cavity is The derived equation of motion Eq. (2) over Y and the differentially heated; in addition the upper and lower equation of motion Eq. (3) by contributing to x, then, walls are adiabatic. The thickness takes four values after subtracting the two equations obtained, we obtain respectively e = L / 0, e = L / 40, e = L / 20, e = L / 10. the equations dimensionless variables in writing Helmotz This is a necessary step to obtain the Nusselt numbers in terms of vorticity and stream function formulation are corresponding to the fluid flow. Inside the cavity. See Fig. as follows: 1. T U V Pr2 Ra Pr t X Y X (5) T T 2T 2T L2 U V (6) t X Y X 2 Y 2 Cp a T 2 2 (7) X 2 Y 2 The stream function and vorticity are related to the Figure 1. Schematic of the studied configuration. velocity components by the following expressions: V U To simplify the problem, assume that: U , V and (8) • The fluid is Newtonian and incompressible. Y X X Y • The Boussinesq approximation is considered The dimensionless parameters in the equations above III. OBJECTIVES are defined as follows: x y u (9) We can express our aim for this study in the X , Y , U L L ui following points: Prediction of the wall design through numerical P T Ti t V , P 2 ,T* ,t * 2 evaluation of the convection in buildings by the ui ui Tc Ti L / a Newton polynomial interpolation method for mean Rayleigh number equal 1.E4. For solid (Concrete), we are interested only in the following heat equation: Modelling Study of the convection – conduction coupling. T 1 2T 2T ( ) Study of the effect of the distribution of the heat t a X 2 Y 2 (10) inside buildings on the convection V. PROCEDURE OF SIMULATION IV. MATHEMATICAL MODEL First, the numerical calculation was conducted using The fluid is assumed incompressible and obeys the the GAMBIT and FLUENT software. The numerical Boussinesq approximation. In these cases, continuity in procedure used in this work is that of finite volume. It two dimensions and the equations governing the flow and involves the integration of differential equations of energy is given by: mathematical model on finite control volumes for the corresponding algebraic equations. In this context, an A. Continuity analogy was used for the functions which are discretized U V by the finite difference method and integrated in the CFD 0 X Y . (1) code which is based on the finite volume method. The SIMPLE algorithm [15] was chosen for the coupling B. X-momentum speed pressure in the Navier-Stokes equations on a staggered grid. The convective terms in all equations are U U U 1 P (2) evaluated using the schema apwind first order. The U V 2U t X Y X discretization of the time term is made in a totally implicit scheme. The convergence of the solution is C. Y-momentum considered reached when the maximum relative change of all variables (u, v, w, p, t) between two successive time V V V 1 P T U V 2V g (3) is not less than 1.e4. With an aim of following well any t X Y X X variation of the fields thermal and hydrodynamic, we used a uniform grid of 14241 nodes and 14480 Elements © 2019 Int. J. Struct. Civ. Eng. Res. 22 International Journal of Structural and Civil Engineering Research Vol. 8, No. 1, February 2019 in non-stationary mode. Secondly, we developed a n Pn (x) d j E j (x) FORTRAN program to control the linear equation of j0 (15) order three. This method of interpolation was used for Where: predicting exchange coefficient of convection to optimize the design of walls in buildings Pn (x) d 0 d1 (x x0 ) d 2 (x x0 )(x x1 ) .... (16) . VI. MATHEMATICAL MODEL FOR NEWTON d n (x x0 )(x x1 )......(x xn1 ). POLYNOMIAL INTERPOLATION METHOD Pn (xi) f (xi) i 0,....,n.. Recall that for distinct points x0, x1, ..., xn, and a real (17) function f defined at these points, there is a unique Where, we shall see how to determine the coefficients polynomial interpolant pn ∈ πn. The idea of Newton (dj) 0 ≤ j ≤ n in the following section entitled the interpolation is to build up pn from the interpolant pn−1 divided differences. Divided differences for Newton for n ≥ 1. Defining the polynomial. Just as two points polynomial interpolation method determine a line, three (non-collinear) points determine a d0 Is called a zero-order divided difference.
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