American Journal of Modern Energy

American Journal o Modern Energy 2015; 1(1): 1-16 Published online June 15, 2015 (http://www.sciencepublishinggroup.com/j/ajme) doi: 10.11648/j.ajme.20150101.11 Heat Generation/Absorption Eect on Natural Convection Heat Transer in a Square Enclosure Filled with a Ethylene Glycol - Copper Nanoluid Under Magnetic Field Mohamed Bechir Ben Hamida 1, Kamel Charrada 2 1 Laboratory o Ionized Backgrounds and Reagents Studies (LEMIR), High School o Sciences and Technology o Hammam Sousse (ESSTHS), University o Sousse, Sousse, Tunisia 2 Laboratory o Ionized Backgrounds and Reagents Studies (LEMIR), Preparatory Institute or Engineering Studies o Monastir (IPEIM), University o Monastir, Monastir, Tunisia Email address: benhamida_mbechir@yahoo.r (M. B. B. Hamida) To cite this article: Mohamed Bechir Ben Hamida, Kamel Charrada. Heat Generation/Absorption Eect on Natural Convection Heat Transer in a Square Enclosure Filled with a Ethylene Glycol - Copper Nanoluid Under Magnetic Field. American Journal o Modern Energy. Vol. 1, No. 1, 2015, pp. 1-16. doi: 10.11648/j.ajme.20150101.11 Abstract: This paper examines the natural convection in a square enclosure that is illed with a nanoluid. This nanoluid with Ethylene Glycol based containing Copper nanoparticle is inluenced by a uniorm horizontal magnetic ield and uniorm heat generation or heat absorption. The enclosure is bounded by two isothermal vertical walls at dierent temperatures and by two horizontal adiabatic walls. The governing equations needed to deal this problem (mass, momentum, and energy) are solved numerically using the commercial simulation sotware COMSOL Multiphysics. In order to increase the natural convective heat transer in a square cavity, the eect o heat generation or absorption on the isothermal, streamline contours and the Nusselt number are studied when the Prandtl number is Pr = 151. Keywords: Heat Transer, Natural Convective, Square Enclosure, EG-Cu Nanoluid, Magnetic Field, Generation/Absorption, Comsol Multiphysics 1. Introduction The study o magnetohydrodynamic low when especially associated with heat transer has attracted several researchers in recent years due to its wide variety o applications in engineering areas and technology such as plasma industries, cooling o nuclear reactor, optimization o crystal growth processes, electronic package, geothermal energy extractions, solidiication o metal alloys, metallurgical applications involving casting and solar technology. The existence o an external magnetic ield is used as a control mechanism in material manuacturing industry, as the convection currents are suppressed by Lorentz orce which is produced by the magnetic ield. Rudraiah et al. [1] studied numerically the natural convection o an electrically conducting luid in the presence o a magnetic ield parallel to gravity. They have pointed out that the average Nusselt number decreases with an increase in the Hartmann, and the Nusselt number approaches one under a strong magnetic ield. Piazza and Cioalo [2] considered the buoyancy-driven magnetohydrodynamic low in a liquid-metal-illed cubic enclosure dierentially heated at two opposing vertical walls. Kandaswamy et al. [3] studied the magnetoconvection low in a enclosure with partially active vertical walls. They have considered nine dierent positions o active zone or dierent value o the Rayleigh and Hartman numbers. It has been ound that the average Nusselt number decreases with an increase o Hartman number and increases with the Rayleigh number. Also, the convection mode o heat transer is converted into a conduction mode or an enough large magnetic ield. Ghassemi et al. [4] investigated the eect o the magnetic ield on natural convection in a enclosure with two adiabatic bales. They showed that the magnetic ield had an adverse eect on the Nusselt number, particularly at low values o Rayleigh number. Pirmohammadi and Ghassemi [5] considered the eect o the magnetic ield on convection heat transer inside a tilted square enclosure. Their study showed

2 Mohamed Bechir Ben Hamida et al.: Heat Generation/Absorption Eect on Natural Convection Heat Transer in a Square Enclosure Filled with a Ethylene Glycol - Copper Nanoluid Under Magnetic Field that the heat transer mechanism and low characteristics inside the enclosure depend strongly upon both magnetic ield and inclination angle. Sathiyamoorthy and Chamkha [6] investigated natural magneto-convection o liquid Gallium in a square heated cavity. They ound that the average Nusselt number decreased nonlinearly with the Hartman number. Sivasankaran and Ho [7] studied numerically the eects o temperature dependent properties on the natural convection o water in a enclosure under the inluence o a magnetic ield. They showed that the heat transer rate decreases with an increase o the magnetic ield and inluenced by the direction o the external magnetic ield. Sarris et al [8] investigated the natural convection o an electrically conducting luid in a laterally and volumetrically heated square cavity under the inluence o a magnetic ield. They concluded that the heat transer is enhanced with increasing internal heat generation parameter, but no signiicant eect o the magnetic ield is observed due to the small range o the Hartmann numbers. Bhuvaneswari et al. [9] investigated magnetic convection in an enclosure with non--uniorm heating on both walls. They ound that the heat transer rate is increased on increasing the amplitude ratio. Kolsi et al [10] studied the eect o magnetic ield orthogonal to the isothermal walls on the unsteady natural convection in a dierentially heated cubic cavity. They observed the role o magnetic ield on the damping and laminarization o low ield. The main luids used or heat transer application are water, ethylene glycol, mineral oil or propylene glycol have a low thermal conductivity. In order to improve the heat transer perormance o inherently poor conventional heat transer base luids, the use o nanoluids is one o the most eective mechanisms which has a superior thermal conductivity compared to the base luid. Many publications, either theoretical [11,12] or experimental [13-16], use the water as base luid with several particles such as Al 2 O 3 [17, 18], Cu [19], CuO [20], TiO 2 and Ag. But, a ew research work on ethylene glycol [21-26] as base luid despite its extensive application in industrial and energy saving perspectives such as in power generation, heating and cooling processes, heat exchanger, chemical processes, electronics, transportation, automotive and others. In addition, the inluence o a heat generation in a cavity containing only base luid without nanoluids was studied by a ew researchers such as Khanaer et al. [27] and Hossain et al. [28]. Thereore, The main originality o the present study is to investigate in detail the natural convection in a square enclosure by utilizing Ethylene Glycol - Copper Nanoluid and is inluenced by a horizontally applied uniorm magnetic ield in the presence o uniorm heat generation or absorption. The physical models are solved using the commercial simulation sotware COMSOL Multiphysics. The results o the simulation are presented and discussed in the sections below. 2. Numerical Model 2.1. Simpliying Assumptions The governing equations o the numerical model are written taking into account the ollowing simpliying assumptions: The base luid Ethylene Glycol and the nanoparticles are assumed in thermal equilibrium. The nanoluid is Newtonian and incompressible. The low is considered to be steady, two-dimensional and laminar. The radiation eects are negligible. The displacement currents, induced magnetic ield, dissipation and joule heating are neglected. 2.2. Governing Equations 2.2.1. Equations o the Model in Dimensional Form The governing equations or this problem are based on the balance laws o mass, momentum and thermal energy o a steady laminar low. Taking into account the assumptions previously-mentioned, the simpliied system o equations is written in two-dimensional orm as ollows: Mass conservation equation: u v + = 0 x y u v Where u and + = 0 v are the velocities components x y in the x and the y direction, respectively. Momentum conservation equation in the x direction : Where ρ n u 2 2 u u 1 p u u + v = + µ n + 2 2 x y ρn x x y (1) (2), p and µ n are the density o nanoluid, luid pressure and the eective dynamic o the nanoluid, respectively. Momentum conservation equation in the y direction : 2 2 v v 1 p v v 2 u + v = + µ n + 2 2 + ( ρβ ) g( T Tc ) σ n n B0v x y ρn y x y (3) Where Tc is the temperature o cold wall, β is the thermal expansion coeicient, σ n is the electrical conductivity o nanoluid and B 0 is the magnetic ield strength. Energy conservation equation:

American Journal o Modern Energy 2015; 1(1): 1-16 3 2 2 T T T T q( T Tc) u + v = αn + 2 2 + x y x y ( ρcp) n (4) µ n µ = (1 ϕ) 2.5 (11) Where α n is the thermal diusivity o nanoluid and q is the heat generation or the heat absorption. The properties o the nanoluid used in this study are inspired by classical models reported in the literature [29]. σ = (1 ϕ) σ + ϕ σ (5) n p ρ = (1 ϕ) ρ + ϕ ρ (6) n p ( ρ Cp) = (1 ϕ) ( ρ Cp) + ϕ ( ρ Cp) (7) n p ( ρ β ) = (1 ϕ) ( ρ β ) + ϕ ( ρ β ) (8) n p kn αn = (9) ( ρcp) In the above equations, k is the thermal conductivity, Cp is the speciic heat and ϕ is the solid volume raction. The subscripts and p means the luid and nanoparticle, respectively. The thermal conductivity and the eective dynamic viscosity o the nanoluid can be modelled by [30, 31]. k n ( kp + 2 k ) 2 ϕ ( k kp) = k ( kp + 2 k ) + ϕ ( k kp) n (10) 2.2.2. Equations o the Model in Non-Dimensional Form The governing equations are nondimensionalized using the ollowing variables: x y ul vl T T x* =, y* =, u* =, v* =, T* = L L α α T T 2 pl p* = ρ α, Pr ν σn =, Ha = B0 L, α ρ ν n 2 3 2 g β L ( Th TC ) ql Ra = and q* = ν α α ( ρcp) Based on the presumptions above, the dimensionless governing equations can be expressed as ollows: Mass conservation equation: u* v* + = 0 x* y* Momentum conservation equation in the x direction : u u p µ u u u* * x y x x y n n h n C C, (12) 2 2 * * * n * * + v = + + 2 2 * * * αn α * * (13) Momentum conservation equation in the y direction : u v µ ( ρβ) Ra T Ha v 2 2 v* v* p* n u* u* n 2 * + * = + + Pr * Pr * 2 2 + x* y* y* αn α x* y* ρn β (14) Energy conservation equation: 2 2 T * T * αn T * T * αn T * u* + v* = + q* 2 2 + (15) x* y* α x* y* α These previous equations are solved using the commercial simulation sotware COMSOL MULTIPHYSICS. ψ ψ u* = et v* = (18) y* x* 2.3. Boundary Conditions o the Model 2.2.3. Nusselt Number Calculations The local Nusselt number on the let hot wall can be deined as : kn T * Nuy( y*) = ( ) k x* x* = 0 (16) The average Nusselt number (Nu m ) is calculated by integrating Nu y along the hot wall : Nu m 1 = Nu ( y*) dy* (17) The stream unction is determinated rom : 0 y Figure 1. Schematic diagram o the physical model.

4 Mohamed Bechir Ben Hamida et al.: Heat Generation/Absorption Eect on Natural Convection Heat Transer in a Square Enclosure Filled with a Ethylene Glycol - Copper Nanoluid Under Magnetic Field The schematic o a two-dimensional square cavity is shown in Figure 1. It is illed with an electrically conducting luid and a Ethylene Glycol - Copper nanoluid. The let and right side walls are kept at constant temperatures, TC and Th, respectively. The top and bottom suraces are assumed to be Table 1. Boundary conditions or dimensional and dimensionless orm. insulated and impermeable. A magnetic ield with uniorm strength B0 is applied in the x direction which is perpendicular to the gravity. The boundary conditions used or dimensional and dimensionless orm are summarized to the Table 1. Border Dimensional orm Dimensionless orm Condition on u Condition on v Condition on T Condition on u* Condition on v* Condition on T* 1 0 0 Th 0 0 1 2 0 0 TC 0 0 0 3 0 0 T T * 0 0 y y* 4 0 0 T y 0 0 The thermo-physical properties o base luid (Ethylene Glycol: C 2 H 6 O 2 ) [32, 25] with Copper [33] (Cu), Alumina [34] (Al 2 O 3 ), Titanium oxide (TiO 2 ) and Copper oxide (CuO) [35] are given in Table 2. Table 2. Thermo-physical properties o Ethylene Glycol and nanoparticles. T * y* Pr ρ [kg/m 3 ] Cp [J/kg.K] K [W/m.K] β 10-5 [K -1 ] α 10-5 [m 2 /s] Base luid Ethylene Glycol (C 2H 6O 2) 151 1109 2400 0.26 65 0.0214 Copper (Cu) 8933 385 401 1.67 11.7 Nano- Alumina (Al 2O 3) 3970 765 40 0.85 1.3 particles Titanium oxide (TiO 2) 4250 686.2 8.9538 0.9 0.31 Copper oxide (CuO) 6500 535.6 20 0.85 0.57 3. Validation o the Model In order to validate the present numerical method or natural convection in an enclosure, comparisons with the experimental results rom Linthorst et al. [36] are made. They measured the dimensionless y-direction velocity by means o a laser doppler velocimeter at midplane (y* = 0.5) o a enclosure illed with air. For the computational validation, the Rayleigh numbers are set to 1.3 10 5. A square cavity with a length L = 4 cm, whose upper and bottom walls are adiabatics, is chosen. The Prandtl number o the air is ixed as 0.733 while the thermal diusivity is 26.89 10 6 m 2 /s, which was deduced rom the mean temperature o luid equal to 320 K. The computational domain is divided by 51 51 uniorm grids spatially and the same grids are used or urther investigation. The igure 2 shows the dimensionless y-direction velocity according to dimensionless position x* at midplane o a cavity or Raygleigh number Ra = 1.3 10 5 between the theoretical values o our code and the values measured by Linthorst et al. [36]. From this igure, we notice the quite satisactory agreement between the calculated and measured values, thereby justiying the dierent assumptions adopted. 4. Results and Discussion In this study, the Prandtl number is assumed to be Pr = 151. The Rayleigh number (Ra), the Hartmann number (Ha), the dimensionless heat generation or absorption and the solid volume raction (Ø) are assumed to be in the ollowing ranges: 10 3 Ra 10 7, 0 Ha 80, -12 q* 12 and 0 Ø 0.06. The eect o Hartmann number and Rayleigh number on the isothermal and streamline contours, eect o magnetic ield on the Nusselt number, eect o heat generation or absorption and Rayleigh number on the isothermal and streamline contours, eect o heat generation or absorption and Hartmann number on the Nusselt number and the comparison with other nanoluids are presented and discussed. 4.1. Eect o Hartmann Number and Rayleigh Number on the Isothermal and Streamline Contours Figure 2. Comparison o dimensionless y-direction velocitiesat midplane o a enclosure or Rayleigh number Ra = 1.3 10 5. Figure 3 shows the isotherms or dierent Hartmann number (Ha = 0, 20, 40, 60 and 80) and Rayleigh number (Ra = 10 3, 10 4, 10 5, 10 6 and 10 7 ) at dimensionless heat generation q* = 2, a solid volume raction Ø = 0.05 and Prandlt number Pr = 151.

American Journal o Modern Energy 2015; 1(1): 1-16 5 Figure 3. Isotherms or dierent Hartmann number and Rayleigh number at dimensionless heat generation q* = 2 and a solid volume raction Ø = 0.05 (Ethylene Glycol - Cu nanoluid). Figure 4 shows the streamlines or dierent Hartmann number (Ha = 0, 20, 40, 60 and 80) and Rayleigh number (Ra = 10 3, 10 4, 10 5, 10 6 and 10 7 ) at dimensionless heat generation q* = 2, a solid volume raction Ø = 0.05 and Prandlt number Pr = 151.

6 Mohamed Bechir Ben Hamida et al.: Heat Generation/Absorption Eect on Natural Convection Heat Transer in a Square Enclosure Filled with a Ethylene Glycol - Copper Nanoluid Under Magnetic Field Figure 4. Streamlines or dierent Hartmann number and Rayleigh number at dimensionless heat generation q* = 2 and a solid volume raction Ø = 0.05 (Ethylene Glycol - Cu nanoluid). From these igures, we observe that that there is conduction dominated regime at low Rayleigh numbers and a convection dominated regime at high Rayleigh numbers. Indeed, or low Rayleigh number Ra = 10 3, the isotherms are parallel vertical lines with a weak clockwise circulation in the cavity. Also, we watch that the circulations strength decreases with the increasing o the Hartmann number and increases when the Rayleigh number increases. In addition, the sign o Hartmann number is opposite to the sign o Rayleigh number in source term o equation (14). So, there is an opposite eect o these two parameters on low regime and Nusselt number. At Rayleigh number Ra = 10 5, the convection mode is pronounced, the isotherms change rom horizontal to vertical when the Hartmann numbers increase. Also, the low cell becomes stronger. At higher Rayleigh number 10 7, the convection is dominant and the circulating cell becomes very strong. Also, the streamlines are crowded near the enclosure wall and the core is empty. As well as isothermals are stratiied in vertical direction except near the insulated suraces o the cavity and appear as horizontal lines in the enclosure core. 4.2. Eect o Magnetic Field on the Nusselt Number Figure 5 shows the Average Nusselt number according to the Raygleigh number (Ra = 10 3, 10 4, 10 5, 10 6 and 10 7 ) or dierent Hartmann number (Ha = 0, 20, 40, 60 and 80) at

American Journal o Modern Energy 2015; 1(1): 1-16 7 dimensionless heat generation q* = 2, a solid volume raction Ø = 0.05 and Prandlt number Pr = 151. Figure 5. Average Nusselt number according to the Raygleigh number or dierent Hartmann number at dimensionless heat generation q* = 2 and a solid volume raction Ø = 0.05 (Ethylene Glycol - Cu nanoluid). Figure 6 shows the ratio between average Nusselt number and average Nusselt number without magnetic ield Nu m /Nu m(ha=0) according to the Raygleigh number (Ra = 10 3, 10 4, 10 5, 10 6 and 10 7 ) or dierent Hartmann number (Ha = 0, 20, 40, 60 and 80) at dimensionless heat generation q* = 2, a solid volume raction Ø = 0.05 and Prandlt number Pr = 151. Figure 6. Nusselt number ratio according to the Raygleigh number or dierent Hartmann number at dimensionless heat generation q* = 2 and a solid volume raction Ø = 0.05 (Ethylene Glycol - Cu nanoluid). From these igures, we see that or constant Hartmann number, the Nusselt number increases with the increasing o the Raygleigh number. Also, or constant Rayleigh number, the Nusselt number decreases when the Hartmann number increases. In addition, due to eect o magnetic ield, there are two dierent phases when the Raygleigh number increases. The irst, the Nusselt number ratio decreases to minimum value at critical Rayleigh number depending on the Hartmann number. The second, due to the strong eect o the natural convection

8 Mohamed Bechir Ben Hamida et al.: Heat Generation/Absorption Eect on Natural Convection Heat Transer in a Square Enclosure Filled with a Ethylene Glycol - Copper Nanoluid Under Magnetic Field with respect to the eect o magnetic ield, this ratio increases. 4.3. Eect o Heat Generation or Absorption and Rayleigh Number on the Isothermal and Streamline Contours Figure 7 and 8 show the isotherms or dimensionless heat absorption, dimensionless heat generation and dierent Rayleigh at Hartmann number Ha = 40, a solid volume raction Ø = 0.05 and Prandlt number Pr = 151. Figure 9 and 10 show the streamlines or dimensionless heat absorption, dimensionless heat generation and dierent Rayleigh at Hartmann number Ha = 40 and a solid volume raction Ø = 0.05 and Prandlt number Pr = 151. Figure 7. Isotherms or q* 0 and dierent Rayleigh at Hartmann number Ha = 40 and a solid volume raction Ø = 0.05 (Ethylene Glycol - Cu nanoluid).

American Journal o Modern Energy 2015; 1(1): 1-16 9 Figure 8. Isotherms or q* > 0 and dierent Rayleigh at Hartmann number Ha = 40 and a solid volume raction Ø = 0.05 (Ethylene Glycol - Cu nanoluid).

10 Mohamed Bechir Ben Hamida et al.: Heat Generation/Absorption Eect on Natural Convection Heat Transer in a Square Enclosure Filled with a Ethylene Glycol - Copper Nanoluid Under Magnetic Field Figure 9. Streamlines or q* 0 and dierent Rayleigh at Hartmann number Ha = 40 and a solid volume raction Ø = 0.05 (Ethylene Glycol - Cu nanoluid).

American Journal o Modern Energy 2015; 1(1): 1-16 11 Figure 10. Streamlines or q* > 0 and dierent Rayleigh at Hartmann number Ha = 40 and a solid volume raction Ø = 0.05 (Ethylene Glycol - Cu nanoluid). From these igures, we see that the conduction regime is dominant with vertical isotherms or the low Rayleigh number Ra = 10 3. Also, we observed a strong clockwise circulation in the cavity or a heat sink condition (q* = - 12). But, the strength is reduced gradually when the dimensionless heat increases until high heat generation condition (q* = 12). In the latter case, we notice a higher temperature o nanoluid in the cavity which reduces the rate o heat transer, Nusselt number and the temperature gradient near the hot wall. Indeed, the two vertical walls temperature is lower than the nanoluids temperature. Thereore, the cold and hot walls receive heat rom the nanoluids and a negative Nusselt number at hot wall is ound. In addition, the low cell becomes stronger when Rayleigh number increases to 10 5 which the convection mode begins to appear. But, this low cell is reduced when the dimensionless heat q* increases. The convection mode begins to appear when Rayleigh

12 Mohamed Bechir Ben Hamida et al.: Heat Generation/Absorption Eect on Natural Convection Heat Transer in a Square Enclosure Filled with a Ethylene Glycol - Copper Nanoluid Under Magnetic Field number increased to 10 5. The low cell becomes stronger but reduces as q* increases. The convection is become dominant when the Rayleigh number reaches the value o 10 7. The circulating cell is become very strong with a neglected or small or heat generation. The temperature gradient near the cavity walls without heat sink condition is lower than that with heat sink. Indeed, we observed, in heat sink condition, that the cavity temperature is lower than the temperature in the cavity without heat sink. 4.4. Eect o Heat Generation or Absorption and Hartmann Number on the Nusselt Number 4.4.1. Eect o Heat Generation or Absorption at Constant Hartmann Number Figure 11 shows the average Nusselt number according to the Rayleigh number or dierent dimensionless both heat absorption and heat generation at Hartmann number Ha = 40 and a solid volume raction o Ø = 0.05 and Prandlt number Pr = 151. Figure 11. Average Nusselt number according to the Rayleigh number or dierent dimensionless both heat absorption and heat generation at Hartmann number Ha = 40 and a solid volume raction o Ø = 0.05 (Ethylene Glycol - Cu nanoluid). From this igure, we see that, or constant Rayleigh number, when the dimensionless heat q* decreases the Nusselt number increases and conversely. Also, or small Rayleigh number, the eect o heat generation (q* > 0) overcomes the eect o natural convection lead to small heat transer rom hot to cold wall or can causes reverse heat transer rom nanoluid to both vertical wall which has a negative Nusselt number. In other word, the eect o both heat generation or absorption is neglected when Rayleigh number increases. To study well the eect o heat generation or absorption on the Nusselt number, the Nusselt number ratio (the ratio between Nusselt number and Nusselt number without heat generation Nu m /Nu m(q*=0) according to the Rayleigh number or dierent dimensionless both heat absorption and heat generation at Hartmann number Ha = 40 and a solid volume raction o Ø = 0.05 is shown in Figure 12. Figure 12. Nusselt number ratio according to the Rayleigh number or dierent dimensionless both heat absorption and heat generation at Hartmann number Ha = 40 and a solid volume raction o Ø = 0.05 (Ethylene Glycol - Cu nanoluid).

American Journal o Modern Energy 2015; 1(1): 1-16 13 From this igure, we see that, or all Rayleigh number and the heat generation, the Nusselt number ratio is less than one but it is greater than unity or the case o heat absorption. Also, or small Rayleigh Ra = 10 3, the heat generation or absorption has a major eect on the Nusselt number ratio. This eect decreases with increasing the number o Rayleigh until his neglect at Ra = 10 7. 4.4.2. Eect o Heat Generation or Absorption at Constant Rayleigh Number Figure 13 shows the average Nusselt number according to the Hartmann number or dierent dimensionless both heat absorption and heat generation at a solid volume raction o Ø = 0.05, Rayleigh number Ra = 10 5 and Prandlt number Pr = 151. Figure 13. Average Nusselt number according to the Hartmann number or dierent dimensionless both heat absorption and heat generation at Rayleigh number Ra = 10 5 and solid volume raction o Ø = 0.05 (Ethylene Glycol - Cu nanoluid). From this igure, we always see that the Nusselt number or the case o heat source is lower than the case o heat o absorption. Also, or both heat source or heat absorption, the Nusselt number decreases by increasing the number o Hartmann. Thereore, the increasing o the magnetic ield reduces the Nusselt number. This reduction is important or the case o heat generation compared to the case o heat absorption. On the other hand, the eect o magnetic ield is small in the case o heat absorption but it is greater in the case o heat generation. Figure 14 shows the Nusselt number ratio according to the Hartmann number or dierent dimensionless both heat absorption and heat generation at a solid volume raction o Ø = 0.05, Rayleigh number Ra = 10 5 and Prandlt number Pr = 151. Figure 14. Nusselt number ratio according to the Hartmann number or dierent dimensionless both heat absorption and heat generation at Rayleigh number Ra = 10 5 and solid volume raction o Ø = 0.05 (Ethylene Glycol - Cu nanoluid). From this igure, we see that, or the situation o the heat absorption, the Nusselt number ratio is greater than unity and

14 Mohamed Bechir Ben Hamida et al.: Heat Generation/Absorption Eect on Natural Convection Heat Transer in a Square Enclosure Filled with a Ethylene Glycol - Copper Nanoluid Under Magnetic Field increases as the Hartmann number increases. Thereore, the increasing o the magnetic ield raises the Nusselt number ratio. Then, or the case o the heat generation, the Nusselt number ratio is less than unity and decreases as the Hartmann number increases. Thereore, the increasing o the magnetic ield reduces the Nusselt number ratio. 4.5. Comparison with Other Nanoluids Figure 15. Variation o the average Nusselt number Nu m according to the solid volume raction Ø at dierent nanoluids or Ra = 10 3, Ha = 40 and q* = 2. Figure 16. Variation o the average Nusselt ratio Nu m / Nu m,ethylene Glycol - cu according to the solid volume raction Ø at dierent nanoluids or Ra = 10 3, Ha = 40 and q* = 2. Figure 15 and 16 show, respectively, the variation o the average Nusselt number Nu m and the average Nusselt number ratio (Nu m / Nu m,ethylene Glycol - cu ) according to the solid volume raction (Ø = 0.01; 0.02; 0.03; 0.04; 0.05 and 0.06) at dierent nanoparticles (Cu, Al 2 O 3, CuO and TiO 2 ) or the Hartmann number Ha = 40, the Rayleigh number Ra = 10 3 and the dimensionless heat generation q* = 2. The choice o the value o Rayleigh number is justiied by the dominance o conduction phenomenon or this value. The thermophysical properties o the nanoparticles are given in Table 1. From these igures, we show that the heat transer depends strongly on the nano thermal conductivity, so Ethylene Glycol-Cu nanoluid enhances the heat transer compared with Ethylene Glycol - Al 2 O 3, Ethylene Glycol - TiO 2 and Ethylene Glycol - CuO. 5. Conclusion Natural convection o an electrically conducting luid in a square enclosure under an externally imposed uniorm horizontal magnetic ield and uniorm heat generation or absorption is investigated numerically. The two opposing side walls are dierentially heated with a dierent temperatures, whilst the loor and ceiling are thermally insulated. The coupled mass, momentum and energy equations associated are solved the commercial simulation sotware COMSOL Multiphysics. The main results obtained o the numerical analysis are as ollows : For the Hartmann number (Ha = 40) and the low Rayleigh number (Ra = 10 3 where the conduction regime is dominant ), there is a strong clockwise circulation in the cavity or a heat sink condition (q* = - 12). But, the strength is reduced gradually when the dimensionless heat increases until high heat generation condition (q* = 12). Thereore, a higher temperature o nanoluid in the cavity which reduces the rate o heat transer, Nusselt number and the temperature gradient

American Journal o Modern Energy 2015; 1(1): 1-16 15 near the hot wall For the Hartmann number (Ha = 40) and the higher Rayleigh number (Ra = 10 7 where the convection regime is dominant ), the cavity temperature is lower than the temperature in the cavity without heat sink (in heat sink condition). For the Hartmann number (Ha = 40) and constant solid volume raction (Ø = 0.05) : or small Rayleigh number, the eect o heat generation (q* > 0) overcomes the eect o natural convection lead to small heat transer rom hot to cold wall or can causes reverse heat transer rom nanoluid to both vertical wall which has a negative Nusselt number. In other word, the eect o both heat generation or absorption is neglected when Rayleigh number increases. Compared with other nanparticles, Ethylene Glycol-Cu nanoluid enhances the heat transer which depends strongly on the nano thermal conductivity or constant Hartmann number (Ha = 40) and constant Rayleigh number (Ra = 10 3 ). Nomenclature B 0 : magnetic ield strength Cp : speciic heat g : gravitational acceleration h : convection heat transer coeicient Ha : Hartmann number k : thermal conductivity L : enclosure length Nu y : local Nusselt number on the let hot wall Nu m : average Nusselt number p : luid pressure p* : dimensionless pressure Pr : Prandtl number q : heat generation/absorption q* : dimensionless heat generation/absorption Ra : Rayleigh number T : temperature, K T* : dimensionless temperature u, v : velocity components in x, y directions u*, v* : dimensionless velocity components x,y : cartesian coordinates x*, y* : dimensionless coordinates Greek symbols ρ : thermal diusivity β : thermal expansion coeicient φ : solid volume raction µ : dynamic viscosity ν : kinematic viscosity ρ : density σ : electrical conductivity Ψ : stream unction Subscripts c : cold wall : luid h : hot wall n : nanoluid p : nanoparticle Reerences [1] N, Rudraiah, R.M Barron, Venkatachalappa, M., Subbaraya, C.K, "Eect o a magnetic ield on ree convection in a rectangular cavity", Int. J. Eng. Sci, 33, 1075-1084., 1995. [2] Piazza I. D. and Cioalo M., "MHD ree convection in a liquid-metal illed cubic enclosure. I. Dierential heating", Int. J. Heat Mass Transer, 45, 1477 (2002). [3] Kandaswamy P, Sundari SM, Nithyadevi N., "Magnetoconvection in an enclosure with partially active vertical walls", Int J Heat Mass Transer, 51, 1946 54, 2008. [4] M. Ghassemi, M. Pirmohammadi, and G. A. Sheikhzadeh, "The Eect o Magnetic Field on Buoyancy-Driven Convection in a Dierentially Heated Square Cavity with Two Insulated Bales Attached", Proc. o Heat Transer Con., ASME, Florida, pp. 141 147, 2008. [5] M. Pirmohammadi and M. Ghassemi, Eect o Magnetic Field on Convection Heat Transer Inside a Tilted Square Enclosure, Int. Comm. in Heat and Mass Transer, vol. 36, pp. 776 780, 2009. [6] M. Sathiyamoorthy and A. Chamkha, Eect o Magnetic Field on Natural Convection Flow in a Liquid Gallium Filled Square Cavity or Linearly Heated Side Wall, Int. J.o Therm. Sci., vol. 49, pp. 1856-1865, 2010. [7] S. Sivasankaran, C.J. Ho, Eect o temperature dependent properties on MHD convection o water near its density maximum in a square cavity, International Journal o Thermal Sciences, 47, 1184-1194, 2008. [8] Sarris, I. E., et al., MHD Natural Convection in a Laterally and Volumetrically Heated Square Cavity, International Journal o Heat and Mass Transer, 48, 16, pp. 3443-3453, 2005. [9] Bhuvaneswari, M., Sivasankaran S., Kim, Y. J., Magneto- Convection in an Square Enclosure with Sinusoidal Temperature Distributions on Both Side Walls, Numerical Heat Transer A, 59, 3, pp. 167-184, 2011. [10] L. Kolsi, A. Abidi, M.N. Borjini, N. Daous, H. Ben Aissia, Eect o an External Magnetic Field on the 3-D Unsteady Natural Convection in a Cubical Enclosure, Numerical Heat Transer, Part A: Applications: An International Journal o Computation and Methodology, 51, 1003-1021, 2007. [11] H. F. Oztop and E. Abu-Nada, Numerical Study o Natural Convection in Partially Heated Rectangular Enclosures Filled with Nanoluids, Inter. J. Heat and Fluid Flow, 29, no. 5, 1326 1336, 2008. [12] E.B. Ogut, Heat transer o water-based nanoluids with natural convection in a inclined square enclosure, Journal o Thermal Science and Technology, 30, (1) 23 33, 2010.

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