APPLICATION OF DIGITAL CELLULAR RADIO FOR MOBILE LOCATION ESTIMATION IIUM Engineering Journal, Vol. 20, No. 1, 2019 Ahamdi et al. RANS K-ω SIMULATION OF 2D TURBULENT NATURAL CONVECTION IN AN ENCLOSURE WITH HEATING SOURCES MEHDI AHMADI, SEYED ALI AGHA MIRJALILY* AND SEYED AMIR ABBAS OLOOMI Department of Mechanical Engineering, Yazd Branch, Islamic Azad University, Yazd, Iran. *Corresponding author: Saa_mirjalily@iauyazd.ac.ir (Received: 13th Dec 2018; Accepted: 24th Feb 2019; Published on-line: 1st June 2019) https://doi.org/10.31436/iiumej.v20i1.1040 ABSTRACT: This study is conducted to investigate turbulent natural convection flow in an enclosure with thermal sources using the low-Reynolds number (LRN) k-ω model. This enclosure has a cold source with temperature Tc and a hot source with temperature Th as thermal sources, other walls of the enclosure are adiabatic. The aim of this study is to predict the effect of change in Rayleigh number, repositioning of cold and hot sources, and thermal sources aspect ratio on the flow field, temperature, and rate of heat transfer. To achieve this aim, the equations of continuity, momentum, energy, turbulent kinetic energy, and kinetic energy dissipation are employed in the case of 2D turbulence with constant thermo-physical properties except the density in the buoyancy term (Boussinesq approximation). To numerically solve these equations, the finite volume method and SIMPLE algorithm are used. According to the modeling results, the most optimal temperature distribution in the enclosure is seen when the hot source is below the cold source. With decreasing distance between hot and cold sources, heat transfer rate increases. The maximal heat transfer rate is derived via study of the heating sources aspect ratio. In constant positions of cold and hot sources on a wall, the heat transfer rate increases with increasing Rayleigh number (Ra=109-1011). ABSTAK: Kajian ini dijalankan bagi mengkaji perubahan semula jadi aliran perolakan dalam tempat tertutup dengan sumber haba menggunakan model k-ω nombor Reynolds- rendah (LRN). Bekas tertutup ini mempunyai dua sumber haba iaitu sumber sejuk dengan suhu Tc dan sumber panas dengan suhu Th, manakala dinding lain bekas ini adalah adiabatik. Tujuan kajian ini adalah bagi mengesan perubahan nombor Rayleigh, mengubah sumber sejuk dan panas dan nisbah sumber haba kepada kawasan aliran, suhu dan halaju perubahan haba. Bagi mencapai tujuan tersebut, persamaan sambungan, momentum, tenaga, tenaga kinetik perolakan, dan pengurangan tenaga kinetik telah dilaksanakan dalam kes perolakan 2D dengan sifat fizikal-haba berterusan (malar) kecuali isipadu terma keapungan (anggaran Boussinesq). Bagi menyelesaikan persamaan ini secara berangka, kaedah isipadu terhad dan algorithma MUDAH telah digunakan. Berdasarkan keputusan model, suhu distribusi optimal dalam bekas tertutup dilihat apabila sumber panas adalah kurang daripada sumber sejuk. Dengan pengurangan jarak antara sumber panas dan sejuk, kadar pertukaran haba meningkat. Kadar pertukaran haba maksima telah diperoleh melalui kajian nisbah aspek sumber pemanasan. Kadar pertukaran haba bertambah dengan bertambahnya nombor Rayleigh (Ra=109-1011), pada posisi tetap sumber sejuk dan panas pada dinding bekas. KEYWORDS: heat transfer; turbulent natural convection; k-ω model; enclosure 229 IIUM Engineering Journal, Vol. 20, No. 1, 2019 Ahamdi et al. 1. INTRODUCTION Many numerical and experimental studies have been conducted on natural convection flows. In the last two decades, many studies have sought to achieve quantitative data on the processes of flow convective heat transfer and its association with many applications inside enclosures [1-2]. The most important and most frequently investigated section of these convections is a rectangular enclosure filled with dry air and two vertical walls at two different temperatures [3-6]. In a rectangular enclosure with height H, heat is naturally transferred from the hot wall to the cold wall through the formation of a vortex with slow movement. The movement of the vortex is considered the engine of heat transfer from hot source to cold source. Flow intensity is expressed by Rayleigh number, Ra=gβΔTH3 /αʋ, where, H is the enclosure height, β is coefficient of thermal expansion, ΔT is temperature difference between vertical walls, and α and ʋ are thermal and molecular diffusivities of fluid. Depending on the Rayleigh number, the flow can be classified as turbulent or laminar [7-9]. A Rayleigh number of less than 108 represents laminar flow, and the transient of laminar flow to turbulent occurs at Ra=108-1010[10]. Natural convection in enclosure was first experimented by Elder [11] and then Giel and Schmidt [12]. In these experiments, water was used instead of air. Cheesewright [13] studied the mean velocity, center temperature, and turbulent variations in natural convection flow in an air-contained enclosure with temperature difference between the walls. He used a standard K-ε model with wall functions to simulate turbulent convection flow in an enclosure with a radiator. In addition, he used the wall functions to calculate K- ε but did not use them to measure velocity and temperature. The selected model made a good prediction of the average flow, which was consistent with previous studies but was weak for modeling turbulence; the Rayleigh number of the enclosure was constant in his study and was considered 3*1010 with length to height ratio of the enclosure of 1:5. Dafa Alla and Bets [6] studied natural convection flow in a high enclosure with length/height ratio of 1:14 and the Rayleigh number 8.3*105. In this experiment, a laser velocity meter was used to measure velocity and velocity variations and thermocouple to measure temperature and temperature variations. Olsen et al [14] conducted a study on natural convection flow in an air-conditioning enclosure with a small model and Rayleigh number of 1010. The length/height ratio of the enclosure was approximately 1:3. They illustrated the measured flow and temperature in the center and boundary layer. Unlike previous studies, two lateral lobes were seen in these experiments, this study was a rare study on an enclosure with virtually real dimensions. Chen [15] used different Reynolds models of stress (RMS) to calculate the natural, forced, and mixed convection flows in the enclosure. Modeling results demonstrated that the efficiency of different RMS approaches to simulate convection flow in the enclosure were equal and consistent with the mean flow derived in experimental calculations, but turbulence values were not predicted appropriately. Ince and Launder [16] studied natural convection flow in a square enclosure with hot right surface and cold left surface and upper and lower adiabatic surfaces. They managed to develop a model to resolve turbulent flow with Rayleigh numbers ranging from 106 to 1010. Hanjealic and Vasc [17] used three- equation K-ε-ɵ and four-equation V1-ε-ɵ-εɵ and low Reynolds number (LRN) to calculate turbulent convection flow in different empty and partitioned enclosures. The Rayleigh number in their studies varied between 1010 and 1012, which is compatible with Rayleigh numbers in real indoors. Mean temperature and velocity derived for these models have displayed relatively acceptable consistency with experimental values. Sigey et al. [18] 230 IIUM Engineering Journal, Vol. 20, No. 1, 2019 Ahamdi et al. used Launder and Sharma K-ε model with the wall functions and considered the Rayleigh number of the enclosure 1011 in their experiments. Their model was found to optimally predict the flow inside the enclosure; and the values of velocity and temperature derived for all regions of the enclosure were highly consistent with the experimental values. Ji [19] discussed the modelling of natural convection in air cavities using four turbulence models. Regarding the cited studies, we set the aims of the present study. The results of resolving this question can be used in induced buoyancy flows, heat transfer of free convection, and designing and assessing different technical and engineering uses especially designing the systems of central heating and air conditioning. Following the studies of these researchers, in the present paper we investigate turbulent natural convection flow in an enclosure with thermal sources using the low-Reynolds number (LRN) k-ω model. The aim of this study is to predict the effect of change in Rayleigh number, repositioning of cold and hot sources and thermal sources aspect ratio on the flow field, temperature, and rate of heat transfer that have been seen less in previous studies. The geometry of this paper is an enclosure that has a cold source with temperature Tc and a hot source with temperature Th as thermal sources that are placed on the left wall of enclosure, the other walls are adiabatic. Subsequently, to achieve the desired results, the Rayleigh number varies between 109-1011. 2. MODEL AND SIMULATION 2.1 Mathematical Model Fig. 1: The geometry of problem. In the present study, natural convection flow is studied in a 2D enclosure seen in Fig. 1. The temperatures of the cold and hot sources are Tc and Th, respectively, and other parts are assumed insulated. The aim of this study is to predict the effect of change in Rayleigh number, repositioning of cold and hot sources, and heating sources aspect ratio on the basic parameters of flow and temperature. Therefore, first, the flow field and fluid temperature in the enclosure are determined using a numerical solution, and then the Nusselt number, mean velocity, and temperature are calculated in different sections of the enclosure. To achieve this purpose, turbulent flow in the 2D enclosure is examined. The numerical solution of the question is conducted using a SIMPLE algorithm and the computer program is written using FORTRAN language. Henkes et al. [20] studied the concepts of the critical Rayleigh number of enclosures' layers using natural convection flow. The critical Rayleigh number was derived around 1011 for upper Reynolds models and approximately 109 for lower ones. If the Rayleigh number is less than 108, the flow is laminar, if the Rayleigh number is bigger than 1010, the flow is turbulent, and if the Rayleigh number is 108-1010, the flow is transient [8, 21]. Therefore, the Rayleigh number in the question of interest is 109-1011 and therefore convection flow in the enclosure is 231 IIUM Engineering Journal, Vol. 20, No. 1, 2019 Ahamdi et al. transient. Given the operating conditions of the enclosure, the indoor flow can be laminar or turbulent. This study investigates turbulent flow. 2.1.1 The Equations of Natural Convection Flow in the Enclosure Turbulent flow field in an enclosure is derived by continuity, momentum, and energy equations. To include buoyancy effects, a Boussinesq approximation was used. Air density, except for buoyancy sentence, is constant and is calculated according to the gases law, and its effects were included in the momentum equation. The enclosure's air was assumed to be incompressible and newtonian (Pr=0.71), and dynamic viscosity was calculated through the Sutherland formula. The equations governing continuity, momentum and energy can be expressed as follows [22]: 0)( j j U X (1) )T-()(- )( refiji j i jjj ji Tguu X U XX P X UU (2) )-( )( i jjj jp tu X T k XX TUC (3) Where U, P, and T represent velocity, pressure, and mean time temperature, respectively. In addition, there are number of high-ranking statements as tuuu iji , in Reynolds averaging equations, namely, Reynolds stress and turbulent heat transfer, respectively. We conducted turbulent modeling to use the equations of appropriate transfer in order to model these statements. 2.1.2 Two-Equation Model k-ω There are different turbulence models to solve turbulent flow equations. Here, a standard two-equation model k-ω was used in this study. In this model, in addition to a turbulence kinetic energy equation k, an additional differential model solves for energy dissipation. Wilcox [23] extended low Reynolds model k-ω to simulate a transient area as illustrated below. To describe the field and determine turbulence rate in a steady flow, the equations of kinetic energy and those of energy dissipation are generally as follows according to the above formulated hypotheses: (4) (5) (6) k jk t j kk j j S X K X P X ku )( )( S X K X P X u j t jj j )( )( K fCt 232 IIUM Engineering Journal, Vol. 20, No. 1, 2019 Ahamdi et al. (7) (8) Constants used in this model are as follow [23]: (9) (10) In this model, three damping functions 1,, fff k are added to k-ω equations. These functions become small in low Reynolds areas and tend to 1 in high Reynolds areas. (11) 2.1.3 Boundary Conditions Generally, boundary conditions to solve the equations are as follow: On the enclosure's walls: Temperature boundary conditions consider constant on hot and cold surfaces: hT=T cT=T For adiabatic walls: 2.2 Solution Procedure The equations that have already been derived can be used to calculate temperature field and velocity parameters. To conduct calculations in this study, the finite volume is used to discretize the partial differential equations with structural grid [24,25]. A QUICK scheme is employed for the convection terms in the momentum equations and in the thermal energy equation. The convection term in the turbulence transport equations is discretized using the hybrid upwind-central scheme. To increase the accuracy of discretization, a second order Van Leer accuracy method is used [26]. In addition, it j i x u 2 ijtk SP j t t k S T gG 2 j x )( 2 1 i j j i ij u u u u S KfC kkk 2 2C kk GS K P K fCP 11 KGK CS 3 0.1C 09.0KC 92.11C 075.02C 0.03C 3.1 9.0t 0.2k 6 1 6 025.0 t t R R f 11 7.2 1 7.2 1.0 f R R f t t 4 4 ) 8 (1 ) 8 (278.0 t t k R R f KRt 0kvu 0y2 2 6 yC 00yy T 0 T 0xx 233 IIUM Engineering Journal, Vol. 20, No. 1, 2019 Ahamdi et al. demonstrates that without using damping function Gk and using the combined method, the results will lead to solving the laminar flow in the enclosure. A SIMPLE algorithm is used for the mixed solution of velocity-pressure field, the iterative line-by-line TDMA procedure and the Strongly Implicit Procedure (SIP) are used for the pressure correction equation [27]. To ensure achievement of a steady state, an appropriate under-relaxation technique is used. Due to the use of a low Reynolds number model to solve the velocity field, it requires a sufficient number of grid points to be in the near-wall boundary layer. Special attention has thus been paid to the grid refinement, particularly for computing the buoyancy-driven enclosure flow. In fact, to achieve convergence in the solution equations in this problem, the first approximate grids to the wall should be placed in the near-wall region to resolve the wall-damping effect, this is not necessary for grids farther from the wall [28]. 2.3 Grid Study Running the prepared computer code and considering the high accuracy of solutions, especially near the walls and fluid phase boundaries that cause serious change in some parameters, it is necessary to review the effect of varying the number of grid points on the flow parameters. To achieve this purpose, an enclosure with geometrical specs H=W, H1=H5=0.125H, H2=0.2H, H3=0.25H, and H4=0.3H (Fig.1) was used and the Rayleigh number was considered 1011 and Pr=0.71. The average Nusselt number of the hot source was determined according to different numbers of the grid points (Table 1). As can be seen in Table 1, the difference between the values obtained using the 100*100 grid and the 110*110 grid are very small and negligible. Thus, a non-uniform grid of 110*110 is selected to run the program. Table 1: Average Nusselt number of hot source according to the numbers of grid points (Ra=1011) Number of nodes Average Nusselt of the hot source surfaces 50*50 149.8120 60*60 161.1375 70*70 178.0820 80*80 184.7461 90*90 188.6720 100*100 194.5231 110*110 194.5301 2.4 Validation To investigate the performance of the computer code in a 2D turbulent state, a comparison was made with two previous studies [5, 16]. In this study, a square enclosure was used with horizontal insulated walls and vertical walls with different temperatures. The cold wall was placed to the right and the hot wall was placed to the left. To solve the equation of turbulent convection flow, a low Reynolds turbulent model k-ω was used. Figures 2 and 3 illustrate the comparison between the results of this study and other studies in this regard. As observed, the obtained results are highly consistent with those of other studies. The difference is at most 1.65% for the average Nusselt number and 1.87% for vertical velocity, which are negligible. To insure the performance of the present model, in another validation we compare the present model with other turbulence models carried 234 IIUM Engineering Journal, Vol. 20, No. 1, 2019 Ahamdi et al. out by Ji [19]. As we can see in Fig. 4, the present model is in good agreement with the others in reference. As the results indicated, the present model is potent to simulate flow in the enclosure at the turbulent and transient stages. Fig. 2: Variations in the average Nusselt number of heating sources with constant temperature according to changes in Rayleigh number. Fig. 3: Variations in vertical velocity according to increase in distance from hot wall. 235 IIUM Engineering Journal, Vol. 20, No. 1, 2019 Ahamdi et al. Fig. 4: Numerical comparison between the present model and the reference models [19]. 3. RESULTS AND DISCUSSION 3.1 Turbulent Convection Flow in 2D Enclosure After the performance of the computer code was ensured and appropriate network selected, different runs were conducted at different states. All calculations for air were conducted with Pr= 0.71 and constant geometry enclosure H=W. Rayleigh number varied between 109 and 1011. In the following sections, the effects of change in Rayleigh number, heat source position, and heating sources aspect ratio on the rate of heat transfer, isothermal lines, mean velocity in the enclosure, and the maximum values of velocity parameters were investigated. 3.1.1 The Effect of Rayleigh Number In this section, we changed Rayleigh number only. Geometrical specs H=W, H1=H5=0.125H, H2=0.2H, H3=0.25H, and H4=0.3H were considered constant. We investigated the effects of changes in these conditions in any state and illustrated them. Figure 5 indicates isothermal lines and streamlines in this state for different Rayleigh numbers. As illustrated, in 2D turbulent flow inside the enclosure, there was a cold area at the bottom of the enclosure and a hot area at the top. With increasing Rayleigh number from 109 to 1011, this condition intensified such that at Rayleigh number 1011, we observed a cooling area besides the right vertical wall. In the area between cold and hot sources, we observed a large heating stress. Further examination of temperature profiles demonstrated that as the Rayleigh number increased, the flows of high and low temperatures between the heating sources mixed better, which caused a more uniform temperature profile at higher Rayleigh numbers compared to lower ones. Regarding the streamlines, as Fig. 5 illustrates, in all states, there are numerous vortices in the enclosure. Most large vortices form in the area close to hot and cold sources in the middle of the enclosure. Besides the large vortices, we observed several small vortices in the corners of the enclosure that form due to the flow separation in the area near to the wall. Next, we examined the effect of change in Rayleigh number on the heat transfer rate in terms of mean and local Nusselt numbers on the heating sources. Figures 6- 8 illustrate the heat transfer rate on hot and cold sources in terms of local and mean Nusselt numbers. As observed, with increasing Rayleigh number, local and mean Nusselt numbers increased in the enclosure. This can be explained by increased velocity parameters due to strengthened buoyancy forces. It is noteworthy (Fig. 8) that because the cold source was bigger than the hot source, its mean Nusselt number that represented the heat transfer rate was lower. To make a more accurate comparison, the results are tabulated in Table 2. In addition to the mean Nusselt numbers of hot and cold sources, the maximum parameters of velocity and mean fluid velocity shown in Table 2. Table 2: Comparison of temperature and flow parameters for different Rayleigh numbers in turbulent flow. Ra Num,h Num,c Vmean umax vmax 109 50.907 -49.38 0.0148 0.106 0.225 5*109 98.615 -74.306 0.0273 0.101 0.227 1010 110.33 -84.96 0.0281 0.0901 0.230 5*1010 138.10 -107.95 0.0284 0.0894 0.231 1011 195.53 -120.65 0.0287 0.0883 0.234 236 IIUM Engineering Journal, Vol. 20, No. 1, 2019 Ahamdi et al. Fig. 5: Isothermal lines (right) and streamlines (left) at different Rayleigh numbers. Fig. 6: The effect of changes in local Nusselt number on hot source for different Rayleigh numbers. 237 IIUM Engineering Journal, Vol. 20, No. 1, 2019 Ahamdi et al. Fig. 7: The effect of changes in the absolute local Nusselt numbers on cold source for different Rayleigh numbers. Fig. 8: The mean Nusselt number of heating sources according to changes in Rayleigh number. As shown in Table 2, with increasing Rayleigh number, maximum horizontal velocity in the enclosure (umax) increased. Due to increased Rayleigh number, this finding is attributed to the acceleration of the fluid velocity in the area between the heating sources due to mixture of cold and hot fluid flows following increased Rayleigh number that in turn causes increase in mean temperature in the enclosure. 3.1.2 Positions of Cold and Hot Sources Take into consideration the enclosure illustrated in Fig. 1. In this section, we changed the value of H4, the distance between the two sources. Other geometrical specs H1=H5, H2=0.2H, H3=0.3H, and H4=0.3H were assumed constant. In addition, Rayleigh number was considered 1011. In addition to repositioning cold and hot sources on a wall, we also placed the two sources on two opposite walls and then compared heat transfer rates in terms of Nusselt number. Fig.9 illustrates isothermal and stream lines in these states. As stream lines in this figure demonstrate, it was observed that the fluid movement was specified by cell flow in which the upward hot flow jet next to the hot source entered the downward cold source jet next to the cold source. The two flows mixed with each other in the distance between them and the hot flow transferred its heat to the cold flow.Tracing the stream lines when both sources were placed on a single wall, multiple vortices filled 238 IIUM Engineering Journal, Vol. 20, No. 1, 2019 Ahamdi et al. the entire enclosure. With decreasing distance between the heating sources, the number of vortices on the top of the enclosure increased. However, when the two heating sources were placed on two opposite walls, several big standing vortices were observed. As isothermal lines in Fig. 9 illustrate, when the distance between the two sources decreases, hot air above hot source mixes well with cold air and so, the cold source and the cold air fails to penetrate the enclosure. As a result, a more uniform temperature dissemination occurred in the enclosure. When the two sources were placed on two opposite walls, hot air above the hot source does not mix well with cold air beside the cold source and the cold air could penetrate the enclosure such that low temperature fluid on the bottom of the enclosure assembled with the high temperature fluid on the top of the enclosure. Therefore, the air temperature became less uniform compared to when the two heating sources were placed on a single wall. As illustrated in Fig.10, the rate of heat transfer from cold source to hot source was estimated in terms of mean Nusselt number. As Fig.10 shows, with increasing distance between the sources, the rate of heat transfer from heating sources into the enclosure declined, but these changes were negligible possibly due to decreased velocity parameters in the enclosure. Fig. 9: Isothermal (right) and stream (left) lines in different positions of hot and cold sources (Ra=1011). 239 IIUM Engineering Journal, Vol. 20, No. 1, 2019 Ahamdi et al. According to Fig. 11, with increasing distance between the sources, maximum horizontal velocity (umax) and maximum vertical velocity (vmax) in the enclosure decreased. This observation can be attributed to the movements of the fluid on the heating sources and the interaction of high temperature fluid with low temperature fluid in the distance between the heating sources. To make a more accurate comparison, the above results were tabulated in Table 3. In addition, Table 3 compares the heat transfer rate between hot and cold sources on two opposite walls. As it can be observed, when the heating sources were placed on two opposite walls, mean Nusselt number increased dramatically, which can be attributed to the regular vortex movement of the fluid in which fluid neighboring the hot source went upward and fluid neighboring the cold source went downward in the enclosure. Because the two heating sources were placed on two opposite walls, the two fluid flows reinforced each other, which led to increased mean velocity of fluid movement in the enclosure. With an increase in mean velocity in the enclosure, the heat transfer rate increased because of the fluid movement. Fig. 10: Changes in mean Nusselt number of hot and cold sources according to changes in distance between heating sources (Ra=1011). Fig. 11: Changes in maximum parameters of velocity in enclosure according to changes in distance between heating sources (Ra=1011). Table 3: Comparison of heat and flow parameters for different Rayleigh numbers in turbulent flow. 3.1.3 The Effect of Hot and Cold Sources Aspect Ratio Assume an enclosure illustrated in Fig. 1. In this section, the length of source is considered constant, H2=0.2H. By changing the length of the cold source, H4, we studied the effect of changes in the heating sources aspect ratio. Other geometrical specs, H3=0.3H and H1=H5, were assumed constant and the Rayleigh number was considered to be 1011. As stream lines in the graphs on the left side of Fig. 12 illustrate, the fluid movement was determined by vortex flow in which the fluid moves upward in parallel with the hot surface and moves downward in parallel with the cold surface. With the change in cold Positions of thermal sources Num,h Num,c Vmean umax vmax Placed on single wall H3=0.4H 193.08 -121.46 0.0271 0.0855 0.269 Placed on single wall H3=0.2H 195.61 -124.78 0.0286 0.0915 0.245 Placed on single wall H3=0.1H 196.98 -128.12 0.0963 0.125 0.209 Placed on two opposite walls H3=0.2H 212.04 -161.77 0.2108 0.1716 0.281 240 IIUM Engineering Journal, Vol. 20, No. 1, 2019 Ahamdi et al. and hot sources aspect ratio, no marked changes occurred in the stream lines. In all states, two large vortices were formed approximate to the heating sources and the central areas of the enclosure and multiple small vortices formed in the corners of the enclosure. As isothermal lines in the graphs on the right side of Fig.12 illustrate, with an increase in the heating sources aspect ratio, no marked changes occurred in the isothermal lines. Cold fluid that moved alongside gravity acceleration faced hot fluid that moved in the opposite direction of the gravity acceleration in the distance between the two sources such that in all states, a cold area is seen at the bottom, next to the cold source, a hot area is seen at the top, next to the hot source, and an area with uniform temperature profile in the wide central area of the enclosure. Fig. 12: Isothermal (right) and stream (left) lines in different aspect ratios of cold source to hot source (Ra=1011). 241 IIUM Engineering Journal, Vol. 20, No. 1, 2019 Ahamdi et al. Fig. 13: Changes in mean temperature according to heating sources aspect ratio (Ra=1011). The studies of changes in heating sources aspect ratio on the heat transfer rate indicated that with an increase in the ratio of the length of the cold source to that of the hot source, the heat transfer rate underwent an increasing trend, which can be attributed to the increased parameters of flow in the enclosure. It was also demonstrated that with decreasing aspect ratio, the maximum velocity parameters umax and vmax in the enclosure decreased, which in turn caused a decrease in mean temperature in the enclosure. As illustrated in Fig. 13, with increasing aspect ratio, mean dimensionless temperature in the enclosure decreased, which can be explained by the increased area of the cold source that causes a decrease in temperature in the enclosure. Table 4: The comparison of heat transfer rate and flow parameters in different heating sources aspect ratio in turbulent flow. 4. CONCLUSION Based on the calculations carried out in this research, the numerical results allow a better understanding on the influence of heating source arrangement within a turbulent natural convection flow in an enclosure. The influence on fluid flow and heat transfer was identified for the different arrangement of the heating sources within the enclosure. Some general conclusions are presented below. In constant positions of hot and cold sources on a wall, if the Rayleigh number increased, the mean Nusselt number of both heating sources, maximum flow function, and maximum velocity parameters increased. Study of different positions of hot and cold sources with constant aspects and temperature difference indicated that the dimensionless heat transfer rate increased with a decrease in the distance between the hot and cold sources on a single wall. If the two sources were placed on two opposite walls, a dramatic increase occurred in mean Nusselt number and mean temperature in the enclosure. However, because the distribution of the temperature profile is not uniform, the optimal position of the hot and cold sources is on a single wall with short distance. sources aspect ratio Ah× hm, Nu Ac× cm, Nu meanV maxu maxv H4/H2=2 42.21 -42.44 0.0314 0.205 0.298 H4/H2=1.5 38.74 -38.33 0.0296 0.165 0.278 H4/H2=1 35.56 -36.15 0.0214 0.0105 0.248 H4/H2=0.5 27.14 -28.11 0.019 0.0951 0.199 242 IIUM Engineering Journal, Vol. 20, No. 1, 2019 Ahamdi et al. Study of different heating sources aspects ratio with constant temperature difference and distance indicated that with an increase in sources aspect, the dimensionless heat transfer rate increased and mean temperature in the enclosure decreased. REFERENCES [1] Kadem S, Lachemet A,Younsi R, Kocaefe D. (2011). 3D-Transient modeling of heat and mass transfer during heat treatment of wood. International Communications in Heat and Mass Transfer, 38(6): 717-722. [2] Laguerre O, Benamara S, Remy D, Flick D. (2009). 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