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Journal of Molecular Liquids 223 (2016) 243–251

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Journal of Molecular Liquids journal homepage: www.elsevier.com/locate/molliq

Numerical investigation of water-alumina nanofluid natural convection heat transfer and entropy generation in a baffled L-shaped cavity T. Armaghani a, A. Kasaeipoor a, N. Alavi b, M.M. Rashidi c,⁎ a b c

Department of Engineering, Mahdishahr Branch, Islamic Azad University, Mahdishahr, Iran Department of Engineering, Booshehr Branch, Islamic Azad University, Booshehr, Iran Shanghai Key Lab of Vehicle Aerodynamics and Vehicle Thermal Management Systems, Tongji University, 4800 Cao An Rd., Jiading, Shanghai 201804, China

a r t i c l e

i n f o

Article history: Received 6 June 2016 Accepted 23 July 2016 Available online 26 July 2016 Keywords: Entropy generation L-shaped cavity Water-alumina nanofluid Natural convection Baffle

a b s t r a c t This article presents a numerical study of natural convection heat transfer and entropy generation of wateralumina nanofluid in baffled L-shaped cavity. The left vertical and bottom walls are placed in hot and constant Th temperature and the middle horizontal and right vertical walls are in cold and constant Tc temperature. The other walls are insulated. The baffle's temperature is Tc and their existence in cavity has a lot of impacts on flow behavior and it could disrupt flow order. The governing equations are solved numerically with Finite Volume Method using the SIMPLER algorithm simultaneously. The convection heat transfer results show: AR (aspect ratio) increasing enhances heat transfer. With dimensional ratio increasing, nanofluid has a greater impact on Nusselt growing. By baffle length increasing nanofluid has less impact on cooling cavity, as a result heat transfer raises. The entropy generation of mentioned parameters are also investigated and discussed. Finally, with studding the ε=Sm/Num (named thermal performance) the best AR and baffle length are introduced. © 2016 Published by Elsevier B.V.

1. Introduction Natural convection heat transfer is an important phenomena due to it's extensive application in engineering process such as electronic cooling, environment comfort, reactor insulation , solar collectors, fire control systems, etc. [1–3]. Many studies focus on application of different aspects of numerical and experimental convection heat transfer in the cavity has been accomplished. Among those initial accurate works, Davis's examine could be mentioned [4]. This researcher has solved a natural convection in a square cavity with insulated horizontal walls and vertical walls in two different and constant temperature numerically. In this paper, accurate answers has been presented using extrapolation methods and todays in natural convection problems, it is used in computer codes control. With Rayleigh number increasing, the formed vortexes in flow line diagram are strengthening. The value of maximum flow function and heat transfer rate from cavity that is expressed in terms of Nusselt number, raises with Rayleigh number increasing. In 2009, Wu and Ching [5] examined a natural convection in a square cavity containing air and a barrier on top wall. Their experiments in a situation of top wall insulated showed that baffle prevents the flow separation and vortex formation behind the barrier and the vortex flow structure depends on the location of the baffle and the top wall ⁎ Corresponding author at: ENN-Tongji Clean Energy Institute of Advanced Studies, Shanghai, China. E-mail addresses: [email protected] (T. Armaghani), [email protected] (A. Kasaeipoor), [email protected] (M.M. Rashidi).

http://dx.doi.org/10.1016/j.molliq.2016.07.103 0167-7322/© 2016 Published by Elsevier B.V.

temperature. It also showed that for a top wall insulated, ambient temperature outside of boundary layer and Nusselt number close to the corner position change by displacing baffle position and the vortex flow spread with increasing the height of the baffle. In 2003, Shi and Khodadadi [6] investigated the natural convection numerically in square cavity with a thin blade on the left wall. They showed that putting blade on the left wall alters the vortex rotation in clockwise. Also flow current increases regardless of blade length and its position for high Rayleigh numbers. Sivasankaran and Kandaswamy [7] researched on natural convection heat transfer in a cavity with heated stairs. They found that by increasing the height of stairs, average Nusselt number increases and stairs location has an important impact on fluid movement and Nusselt number. Yucel N, Ozdem [8] have done a new case study on natural convection in a partitioned square container. For this purpose, they assessed a cavity with insulated horizontal walls and side walls in two different temperature with a few stairs on the bottom wall. They concluded that the Rayleigh number changing and increase of height and number of steps, lead to significant changes in average Nusselt number. In 2009, Bahlaoui et al. [9] have accomplished a convection numerical study from a heat source inside of horizontal cavity. The cavity includes a surface radiation that is applied on the lower wall. They used air as a working fluid to cool the cavity. The results showed heat transfer increases significantly with Reynolds number raising between 200 b Re b 500 for a constant radiation coefficient. Also, it has been shown that with radiation coefficient increasing for the same Reynolds number heat transfer raises. Kandaswamy et al. [10] studied the natural convection in a square cavity with two baffles


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T. Armaghani et al. / Journal of Molecular Liquids 223 (2016) 243–251

Nomenclature Cp g k L H2 Bf Nu Num p P Pr T Tc U0 u ,v U, V x,y X, Y

specific heat, J·kg·K−1 gravitational acceleration, m·s−2 thermal conductivity, W m−1 K−1 length of cavity, m length of baffle, m dimensionless length of baffle local Nusselt number average Nusselt number of heat source fluid pressure, Pa dimensionless pressure, p/ρnf v20 Prandtl number, vf/αf temperature, K inlet flow temperature, K inlet flow velocity, m·s−1 velocity components in x, y directions, m·s−1 dimensionless velocity components, u/v0 ,v/v0 Cartesian coordinates, m Dimensionless coordinates,x/L , y/L

Greek symbols α thermal diffusivity, m2·s, k/ρ cp β thermal expansion coefficient, K−1 ϕ solid volume fraction θ dimensionless temperature, (T − Tc)/(Th − Tc) μ dynamic viscosity, N·s·m−2 ν kinematic viscosity, m2·s−1 ρ density, kg·m−3 Subscripts c cold f pure fluid h hot wall m average nf nanofluid s nanoparticle

perpendicular to each other. They concluded by increasing the length of vertical baffle, heat transfer would raise, also horizontal baffle length increasing leads to heat transfer raising when the baffle is lower than the center compartment. Altaç and Kurtul [11] studied a numerical heat transfer of a box with three walls insulated with an embedded warm baffled in the middle and the other wall in cold temperature. In this study the effects of different size and location of baffles on heat transfer and flow lines has been assessed. Furthermore, the effects of Rayleigh number between 105 to 107 and tilt angle of cavity between 0 and 90 degrees has been studied. Nag et al. [12] have investigated a square cavity whose walls are in different conditions of temperature and a horizontal blade is added to the warm wall. The blade length and it's position changes in this study and Rayleigh numbers between 103 and 106 have been studied. Two status of insulated blade and fully conductive blade have been perused. This study shows that heat transfer in a cavity with high conductive blade increases regardless of location and length of blades in cold wall and it decreases in an adiabatic blade so that the upper position of the blade the more reduction. Oosthuizen and Paul [13] have studied cavities with different thermal walls and they assessed impacts of adding a horizontal plate to the middle of cold vertical wall. They examined different relations and ratios, finally concluded that local heat transfer in top warm wall increases but it declines close to center. Frederick [14] has investigated natural convection in a square cavity with a step on the cold wall numerically. He indicated step prevents

natural convection and heat transfer in a cavity with step reduces 47% more than a simple cavity in a constant Rayleigh number. Bilgen [15] has studied a heat transfer in the cavity with thin fin on the warm wall numerically and has predicted the effect of the position and size of the fin on the heat transfer. Also, Ben-Nakhi and Chamkha [16] has evaluated the natural convection in a tilted container with two steps numerically. Vertical walls are at two different temperatures and horizontal walls are insulated. Two steps have been located on a bottom wall with the same distances. They found that flow velocity decreases with step's height increasing, As a result heat transfer declines. Also, by cavity slope increasing N 30 degrees, the average Nusselt number value decreases. In most natural convection studies, the fluid within the cavity has low conductivity coefficient that limits heat transfer rate. That's why researchers attention has been paid to the use of nano-fluid. It is expected nanoparticles addition to the base fluid enhances the conductivity and specifically heat transfer. Many researchers have suggested that by low volume fraction (1% to 5%) addition of nano-particles to the fluid, nano-fluid thermal conductivity can be increased by approximately 20% [17–19]. Although, high thermal conductivity is a promising factor, it doesn't assure the cooling capacity increasing of such a fluids. Ghasemi and Aminossadati [20] investigated the cooling process of natural convection of heat source swinging on left side of a cavity containing nanofluid numerically. In this paper, the effect of several different parameters such as Rayleigh number, location and position of the heat source, nanofluids and swinging time on cooling process performance of cavity was investigated. As a result of heat wave fluctuation, a periodic performance can be seen in fluids and thermal range. Fluctuation of generated heat wave by heat source causes not only variable yields in movement but thermal factors affect the heat source. The authors believe that the results of this study will provide useful information for electronic industry to help electronic components maintenance with generating heat fluctuation under a safe and effective operational conditions. Mahmoudi et al. [21] investigated a numerical solution for natural convection of water-copper nanofluid in a square cavity containing a horizontal thermal source on the vertical wall. They assessed parameters effect such as Rayleigh number heat source location and nanoparticles volume fraction on cavity's heat transfer. They concluded that heat source dimension is the most effective parameter on flow properties and heat transfer, So by increasing the heat source length the cavity's heat transfer rate decrease. Jou and Tzeng [22] accomplished a numerical study about heat transfer parameters in nanofluid in two dimensional cavity. They concluded that nanoparticle volume fraction increasing would raise the average rate of heat transfer. Khanafer et al. [23] studied nanoparticles role on natural convection in a two dimensional cavity of water-copper. They obtained this point that heat transfer rate increases with raising copper particles dispersion ratio in the water in any Grashof number. Sheikhzadeh et al. [24] investigated a natural convection of watercopper oxide nanofluid in a square cavity with heat and cold source on vertical walls numerically and they reported heat transfer increases with nanoparticles volume fraction and Rayleigh number raising. Santra et al. [25] studied a natural convection in a cavity containing nano-fluids numerically with assumption of non-Newtonian behavior of nanofluids. Their results showed that in some specific Rayleigh numbers with increasing volume fraction of nanoparticles heat transfer rate decreased and in another range of Rayleigh numbers heat transfer rate raises with nanoparticles volume fraction increasing. Aminossadati and Ghasemi [26] investigated a natural convection of heat source located at bottom of cavity filled with nanofluid. In this paper, the effect of Rayleigh number, location and geometry of the heater, type and volume fraction of nanoparticles on cooling performance has been assessed. The results show nanoparticles addition to pure water provide better cooling performance and this is more remarkable in small Rayleigh numbers. Nanoparticles type, length and location of thermal heater have a significant effect on heater's maximum temperature. The higher




nanoparticles volume fraction the greater average Nusselt number changes in low Rayleigh number (104) than high Rayleigh (106). AbuNada and Oztop [27] accomplished a numerical study for analyzing the effects of deviation angle of convection and heat transfer in a tilted cavity filled with water-copper nanofluid and examined nanofluid yield with regard to solid particles distribution inside of cavity. The paper concluded that the effect of cavity's slope angle in heat transfer raising in small Rayleigh numbers is negligible. They also deduced that deviation angle is a good control factor for both cavity (each cavity filled with pure material and a cavity full of nanofluid). In another article from Oztop and Abu-Nada [28] heat transfer and fluid flow have been assessed based on a buoyancy force in a cavity that it's left wall is warm and right wall is colder and the other surfaces are insulated. Calculations have been carried out for various variables such as Rayleigh numbers, the length and position of heater, the cavity's volume and nanoparticles volume fraction. With nanoparticles addition heat transfer increases in any Rayleigh number and the Nusselt number raises with heater length growing. Furthermore, the nanofluid's effect on Nusselt number growing is more significant in lower volume fraction and heat transfer rate rises by nanofluid decreasing in higher Rayleigh number. Ghasemi and Aminossadati [29] investigated a natural convection in a triangular cavity with a heat source embedded on it's vertical wall and filled with water- copper nanofluid numerically. The results show that for all solid material volume, increasing Rayleigh number leads to more thermal convection which is caused by buoyancy force intensity. It has been seen in low Rayleigh numbers that heat transfer rate increases when heat source moves upward on cavity's vertical wall. All the aforementioned studies are based on the first-law analysis. Recently, the second-law based investigations have been gained attention for studying thermal systems. Entropy generation has been used as a gauge to evaluate the performance of thermal system [30–34]. The analysis of the exergy utilization and the entropy generation has become one of the primary objectives in designing a thermal system. Bejan [35–37] focused on the different reasons behind entropy generation in applied thermal engineering. Generation of entropy destroys available work of system. Therefore it makes good engineering sense of focus on irreversibility of heat transfer and fluid friction process. There are only a very few studies that consider the second law analyzes in the presence of nanofluid as a working fluid in a engineering geometry such as cavity. Shahi et al. [38] reported entropy generation due to natural convection cooling of nanofluid in cavity. Furthermore several studies was investigated in the field of entropy [39–42]. Ellahi et al. [43] heat transfer fluid mixture flows studied through the wedge under the influence of nano-porous medium. Ellahi et al. [44] developed a mathematical model to study the natural convection boundary layer flow along an inverted cone. Investigation of correlation coefficient of friction Nusselt number heat transfer and activation parameters. Recently Chamkha et al. [19] investigated the entropy generation and natural convection of CuO-water nanofluid in C-shaped cavity under magnetic field. For the baffled L-shaped cavity, one interested question would be the optimum AR and baffle length to minimize entropy generation and allows for the best performance? Finding the optimal case and optimum design for engineering tools is very important. In present study the natural convection heat transfer and entropy generation of wateralumina nanofluid is examining in a baffled L-shaped cavity. According to conducted researches it has been found that despite the natural convection heat transfer studies of nanofluids in such cavities, the natural heat transfer of water–alumina nanofluid in a baffled cavity has not been investigated yet. Also, the effect of parameters on entropy has not been considered in these cavities. Therefore, in this paper, a numerical study of natural convection heat transfer in a baffled L-shaped cavity containing water-alumina nanofluid has been performed. The effects of parameters such as Rayleigh numbers, cavity's dimension, nanoparticles volume fraction and length of baffle on heat transfer rate and entropy generation has been investigated.

245

2. Problem description A closed L-shaped cavity with a baffle on internal horizontal wall including water-alumina nanofluid (Fig. 1) is considered. The left vertical walls are placed on warm and constant temperature of Th and the middle horizontal walls are cold in Tc. The other walls are insulated. Baffle's temperature is Tc and their existence in cavity could influence flow behavior hugely and disrupt flow order. AR = H1/L and Bf = H2/L are dimensional ratio and baffle length respectively. In current work, different parameters effects on flow field, heat transfer and also entropy generation rate are studied and discussed. 3. Mathematical formulation The problem under consideration is a two-dimensional steady flow without any energy generating and storing. Also the nanofluid is treated as a two-component mixture (base fluid + nanoparticles) with the following assumptions, • • • • • • •

Incompressible flow, No chemical reactions, Negligible external forces, Dilute mixture (ϕ ≪ 1), Negligible viscous dissipation, Negligible radiative heat transfer, Nanoparticles and base fluid are in thermal equilibrium locally.

Dimensionless applied equations (continuity, momentum and energy) with regards to application of Bvzynsk approximation are as follow [17]: ∂U ∂V þ ¼0 ∂X ∂Y

ð1Þ

" 2 # 2 μ nf ∂U ∂U ∂P ∂ U ∂ U þ þV ¼− þ U ∂X ∂Y ∂X ρnf ν f ∂X 2 ∂Y 2 " 2 # 2 ðρβÞnf μ nf ∂V ∂V ∂P ∂ V ∂ V U þ þ Ra Pr θ þV ¼− þ ρnf β f ∂X ∂Y ∂Y ρnf ν f ∂X 2 ∂Y 2

U

" 2 # 2 ∂θ ∂θ α nf ∂ θ ∂ θ þ þV ¼ α f ∂X 2 ∂Y 2 ∂X ∂Y

Fig. 1. L-shaped cavity with baffle.

ð2Þ ð3Þ

ð4Þ


246



Applied dimensionless variables in equations are as follows [17]: x y uL vL pL T−T c ; V¼ ; P¼ ; θ¼ X¼ ; Y¼ ; U¼ T h −T c L L αf αf ρnf α 2f

ð5Þ

Dimensionless numbers of Rayleigh, Prandtl are as follows too: Ra ¼

gβL3 ðTh −TC Þ ν ; Pr ¼ f αf νf αf

"

∂θ ∂X

2

þ

∂θ ∂Y "

2 #

μ nf k f Br 2 þ μ f knf ΩU 2 Sc ¼

(

∂U ∂X

2

2 ) 2 # ∂V ∂U ∂V þ þ þ ∂Y ∂Y ∂X

Sc kðΔT Þ μu2 ΔT ¼ Ec Pr; Ω ¼ and SG;c ¼ 2 2 ; Br ¼ SG;c kΔT T0 L T0

Sm ¼ ∬ Sc d∀

ð10Þ

The average Nusselt number is obtained by integrating the warm walls: i 1 hB C ∫ A Nu dY þ ∫ B Nu dX 2L

ð13Þ

ks As As þ cks Pe knf ¼ k f 1 þ kf Af kf Af

ð14Þ

ks and kf are nanofluid's conductive coefficient of water-alumina and pure fluid respectively. Water-alumina nanofluid's capacity, c = 36,000 has been proposed [49]. As d f φ ¼ Af ds 1−φ

ð15Þ

Solid nanoparticles diameter is ds = 100 nm and molecular size of water base fluid is as below:

No-slip and no-wall penetration are the hydrodynamic boundary conditions, U,V = 0. Also, the thermal boundary condition for heat source surface and top wall with cold temperature are θ = 1 and θ = 0 respectively. Temperature gradient is zero for insulated walls. The heat transfer rate is expressed in the form of Nusselt number and local Nusselt number on warm walls is defined as below [17]: ∂θ with n ¼ ðX; Y Þ ∂n n

According to Brickman equation nanofluid's effective dynamic viscosity is expressed as follow [47]:

ð8Þ

3.1. Boundary conditions

Num ¼

3970 765 40 0.85 1 × 10−10

Nanofluid's thermal conductivity is Knf and Patel et al. [48] has proposed a model for it. This model is as follow for two independent components of suspension's spherical particles.

ð9Þ

∀

Alumina nanoparticles

997.1 4179 0.613 21 0.05

μ nf ¼ μ f ð1−φÞ−2:5

where Ω , S⁎c , and Br are dimensionless temperature difference ratio, dimensionless local entropy generation and Brinkman number, respectively. As the distribution of volumetric entropy generation is obtained, it would be integrated over the whole domain to yield the global entropy generation (GEG) rate [19]:

knf kf

Pure water

ρ (kg m−3) Cp (J kg−1 K−1) k (W m−1 K−1) ×105 (K−1)β σ (m−1 Ω−1)

ð7Þ

2

Nu ¼ −

Thermo-physical properties

ð6Þ

In dimensionless forms, local entropy generation can be expressed as following [19]: Sc ¼

Table 1 Thermo-physical properties of pure water and alumina nanoparticles.

ð11Þ

d f ¼ 2Å Pe ¼

ð16Þ

us ds αf

ð17Þ

us is a rotational speed of nanoparticle: us ¼

2kb T πμ f ds

ð18Þ

2

kb = 1.3807 × 10−23 J K−1 is Boltzmann's constant. In above equations nf, f and s mention to nanofluid, water and alumina nanoparticles properties, respectively. Prandtl of pure water will be considered Pr = 6.2. Thermo-physical properties of water and alumina are shown in Table 1. 3.3. Program controlling

3.2. Nanofluid properties relations Nanofluid's density (ρnf), volume expansion coefficient (ρβ)nf, thermal capacity (ρcp)nf, thermal diffusion coefficient (αnf) and electrical conductivity (σnf) are calculated by below equations [45] and [46]. ρnf ¼ ð1−φÞρ f þ φρs ðρβÞnf ¼ ð1−φÞðρβÞ f þ φðρβÞs ρcp nf ¼ ð1−φÞ ρcp f þ φ ρcp s knf α nf ¼ ρcp nf σ nf 3ðγ−1Þφ σs ¼1þ ;γ ¼ σf σf ðγ þ 2Þ−ðγ−1Þφ

In order to geometry modeling a programming was done by FORTRAN. The Eqs. (1)–(4) were solved by using finite element method

Table 2 Current problem validation with square compartment.

ð12Þ

Ra

105

104

106

Present work Khanafer et al. [55] Barakos et al. [56] Markatos and Pericleous [57] Davis [58]

4.522 4.522 4.510 4.430 4.519

2.243 2.245 2.245 2.201 2.243

8.850 8.829 8.806 8.754 8.719




247

Fig. 3. Cavity meshing.

Fig. 2. Current programming validation of L-shaped compartment [46].

based on mentioned boundary conditions and finite volume. Algebraic equations were solved simultaneously by using SIMPLE algorithm, details are brought in reference [50]. The algorithm simple It is consisting of semi-implicit equivalences which they related each other by pressure it is in this form first they solve fast equivalences. Then after solution the speeds should classify though the cooperation equivalences reformed fast. For this reason after classification of bases at suitable frames and imposing the following conditions: Guess the pressure p⁎. Solution of momentum equivalences for calculating U⁎ & V⁎. Solving the equivalence of pressure and defining p′. Accounting the pressure amount by relation p =p⁎ + p′. Defining the amounts of U & V by application of speed reform by stared aped and p′. 6. Solving the equivalence of heat. 7. The gained amounts indicate P pressure by guess pressure by P⁎ and it repeat the operation by complete convergence.

1. 2. 3. 4. 5.

It needs mentioning the equivalence reform of pressure it has convergence condition. Therefore it is as opposing convergence it applies the following low relation. The above indexes depending on its kind are different. In this survey the indexes of speed defined as 0.5 and for pressure 0.6. Also, the below convergence criteria has been used [19]: vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u2 32 u nþ1 u δ −δn ∑ j ∑i t4 nþ1 5 ≤10−8 δ

different temperature of Tc (cold) and Th (warm) has been calculated for Pr = 0.71 and Ra = 104,105,106 and the average Nusselt number has been compared with results of different references in Table 2. It's been concluded from data comparison that derived results are acceptable with a good accuracy. Furthermore, Fig. 2 shows a programming validation of a L-shaped compartment filled with nanofluid. In this figure, average Nusselt number of a L-shaped compartment with two insulated walls and two cold and warm walls has been plotted [51]. The average Nusselt number obtained from current programming matches properly with other similar works results. It is needed to assess results independence from investigated network points and to select suitable solution network after program performance control. Then, network points effect on Nusselt number of enclosed cavity's warm walls in Rayleigh numbers, dimensional ratio, baffle length and volume fraction percentage of different nanoparticles. Some of these assessments for Ra = 10,000, AR = 0.5, Bf = 0.2, φ = 0.04 has been collected in Table 3. According to this table, it is obvious that results almost has been remained the same for networks smaller than 100 × 100. thus, the uniform mesh of 100 × 100 has been selected for program execution. Also, the cavity's meshing process has been shown in the Fig. 3. Table 4 shows time of running for different Ra (AR = 0.5, Bf = 0.2, φ = 0.04) – mode coding in computer with RAM 4.00 GB & CPU core i3 2.73 GH characteristics. 4. Results and discussion After ensuring of programming accuracy and selecting the proper mesh, we are discussing the results. In this part the effective parameters on heat transfer rate and entropy generation of baffle L-shaped cavity such as Rayleigh number, cavity's dimensional ratio, baffle length and nanoparticle volume fraction are investigated. 4.1. Rayleigh number and nanoparticle volume fraction effect assessment

ð19Þ

Which n is number of repeating and δ shows general variable of (U,V,θ). To verify programming accuracy a comparison between achieved results and other reference's results has been taken. First, the square cavity including insulated horizontal walls and vertical walls with two

In this section we are assessing the Rayleigh number effect on flow field, temperature field, entropy field, natural convection heat transfer rate and entropy. Also, it is been considered AR = 0.5 and Bf = 0.2. The flow and temperature lines and entropy field in different Rayleigh numbers for pure fluid and nanofluid φ = 0.04 has been plotted in Fig. 4. The results show by Rayleigh number increasing and as a result buoyancy forces raising, flow lines are drawn to the walls. This issue leads to flow velocity increasing close to walls [52].

Table 3 Effects of number of mesh points on average Nusselt number.

Table 4 CPU time for different Ra (AR = 0.5, Bf = 0.2, φ = 0.04).

i; j

Grid

40 × 40

60 × 60

80 × 80

100 × 100

120 × 120

Ra

103

104

105

106

Num

2.39

2.05

1.92

1.89

1.88

CPU time (second)

185

187

1155

5793


248



streamline

Ra=103

Ra=104

Ra=105

-1.28

-0.14

Ra=106

-6.54 -17.50

-0.08

-7.84

-6.54

-1.01

5.73

0 .8

21.14

-5.01

0.8 3

3

0.1 7 0.33

0.50

0.67

0 0 .5 0 .3 3

0.17

0.33

0.50 0.67 0.83

Isentropic

0.8 3

0.67

7

0 .5 0 3 0 .3 7 0 .1

0 .1

Isotherm

0.67

Fig. 4. Flow lines, temperature lines and entropy field in different Rayleigh numbers for pure fluid(—) and nanofluid φ = 0.04 (- - -).

In small Rayleigh numbers which conductivity is governing, thermal layers with parallel and vertical isothermal lines are composed in central section of cavity. By Rayleigh number increasing temperature gradient close to walls gets intense and thermal boundary layers occur close to warm and cold walls [53]. Moreover, entropy field contours show by Rayleigh number increasing, entropy lines close to walls gets more compressed. Effects of different Rayleigh number of nanofluid (φ = 0.04) on local Nusselt number has been shown in Fig. 5. In this thesis, local heat

Fig. 5. Nanofluid's different Rayleigh numbers effect (φ = 0.04) on local Nusselt.

transfer on warm wall has been plotted. In general, Results show heat transfer level increases by Raleigh number rising due to problem's buoyancy feature increasing. Also, it is seen that on top corner of cavity's warm wall this process gets inverse and conductive heat transfer gets dominant because of velocity decreasing in this section. The effect of Rayleigh number and nanoparticles volume fraction percentage on ε (ε = Sm/Num) is shown

Fig. 6. Rayleigh number and nanoparticles volume fraction percentage effect on ε (ε=Sm/ Num).




249

in Fig. 6. ε shows the thermal performance and it is introduced by Ismael et al. [54]. It is clear with nanoparticles volume fraction increasing, ε reduces and it increases when Rayleigh number raises. The best thermal performance is experienced at high nanofluid volume fraction and law Rayleigh number. 4.2. Effects of cavity's aspect ratio (AR) In this part the effects of cavity's aspect ratio at fixed Rayleigh number (Ra = 104) and baffle length (Bf = 0.2) on flow field, temperature field, natural heat transfer rate and entropy generation is investigated. The isotherm flow lines and entropy in different dimensional ratio for base fluid (pure water) and nanofluid (φ = 0.04) has been plotted in Fig. 7. The results show by cavity's dimensional ratio increasing the flow vortex in cavity gets smaller due to space decreasing. As it can be seen, by increasing the cavity's dimensional ratio isotherm lines get closer to warm wall because of fluid flow decreasing between cold and warm wall. It is expected this issue is the reason of heat transfer raising. Furthermore, entropy field contours indicate that entropy lines get denser close to walls with dimensional ratio growing. The effect of cavity's dimensional ratio and nanoparticles volume fraction percentage on entropy generation rate Sm , ⁎ = Sm/Sm , φ = 0 has been indicated in Fig. 8. Always, with nanoparticles volume fraction increasing entropy generation reduces. Also, with cavity's dimensional ratio raising the entropy generation rate decreases and with nanoparticles volume fraction increasing the effect of cavity's dimensional ratio on entropy generation rate increments. 4.3. Investigation of baffle length The effect of baffle length on mentioned items is studied and discussed at fixed Ra = 104 and AR = 0.5. The flow lines, isotherm and entropy in different lengths of baffle for base fluid and nanofluid (φ = 0.04) has been plotted in Fig. 9. Results

Straemline

AR=0.1

Fig. 8. The effect of cavity's dimensional ratio and nanoparticles volume fraction percentage on entropy generation rate Sm,⁎ =Sm/Sm,φ=0.

show by baffle length increasing the space for nanofluid flow decrease, as a result the vortex gets smaller. Cavity's baffle length increasing causes isotherm lines gets closer to warm wall and it is expected this reason increases the heat transfer. Also, entropy field contours show that baffle length increasing leads to entropy lines condensation close to walls. The effect of baffle length and cavity's dimensional ratio in nanofluid (φ = 0.04) on average Nusselt number has been represented in Fig. 10. Results show baffle length increasing causes heat transfer boosting.

AR=0.3

AR=0.5

AR=0.7

-1.28 -0.50

-5.09 -3.65 -1.01 -0.10

Isotherm

0 .1

0.

7

33

0 .1 7

0.17 0.50

0.33

0.33

0.50 0.67

0.67 0.83

0.67 0.83

Isentropic

0.83

0.50

Fig. 7. Flow lines, isotherm and entropy in different dimensional ratio for pure fluid (—) and nanofluid φ = 0.04 (- - -).

0.17 0.33 0.50 0.67 0.83



250


Bf=0.1

Bf=0.2

Bf=0.3 -1.10

-1.28 -1.61

-2.35

-1.01

-0.86

0.17

0.17

0.17

0.17

0.33

0.33

0.33

0.33

0.50

0.50

0.50

0.50

0.67

0.67

0.67

0.67

0.83

0.83

0.83

0.83

Isentropic

Isotherm

Straemline

Bf=0

Fig. 9. Flow lines, isotherm and entropy in different baffle lengths for pure fluid (—) and nanofluid φ = 0.04 (- - -).

Also, AR increasing results to Nusselt number enlarging. In case of AR = 0.7 and Bf = 0.3 heat transfer decreases due to cavity dividing into two separate cavity. The effect of baffle length and dimensional ratio in nanofluid (φ = 0.04) on ε ε = Sm/Num has been shown in Fig. 11. It can be seen that with baffle length increasing ε decrease and AR enlarging results to baffle length effect declining on ε. As a result, the optimum condition for this cavity happens in Bf = 0.2 and AR = 0.7.

5. Conclusion

Fig. 10. The effect of baffle length and cavity's dimensional ratio in nanofluid (φ = 0.04) on average Nusselt number.

Fig. 11. The effect of baffle length and dimensional ratio in nanofluid (φ = 0.04) on ε ε= Sm/Num.

In this paper the natural convection heat transfer and entropy generation of alumina-water nanofluid in baffled L-shaped cavity has been analyzed by numerical method. The governing Continuity, momentum and energy equations solved numerically by using finite difference method based on control volume and simple algorithm simultaneously. The effect of governing parameters in natural convection fluid on heat transfer rate and entropy generation has been assessed. Finally, the results have been achieved as follows:




√ Heat transfer decreases via going up towards warm wall. √ With AR increasing heat transfer boosts. √ As dimensional ratio grows nanofluid has more effect on Nusselt number increasing √ When baffle length increases nanofluid has less effect on cavity cooling √ In ϕ = 0.04, the best thermal performance is experienced at AR = 0.7 and Bf = 0.2

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