Investigation of turbulent heat transfer and nanofluid

Advanced Powder Technology 29 (2018) 273–282

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Advanced Powder Technology journal homepage: www.elsevier.com/locate/apt

Original Research Paper

Investigation of turbulent heat transfer and nanofluid flow in a double pipe heat exchanger Mohammad Hussein Bahmani a, Ghanbarali Sheikhzadeh a, Majid Zarringhalam b, Omid Ali Akbari c, Abdullah A.A.A. Alrashed d, Gholamreza Ahmadi Sheikh Shabani f, Marjan Goodarzi e,⇑ a

Department of Mechanical Engineering, University of Kashan, Kashan, Iran Young Researchers and Elite Club, South Tehran Branch, Islamic Azad University, Tehran, Iran Young Researchers and Elite Club, Khomeinishahr Branch, Islamic Azad University, Khomeinishahr, Iran d Department of Automotive and Marine Engineering Technology, College of Technological Studies, The Public Authority for Applied Education and Training, Kuwait e Sustainable Management of Natural Resources and Environment Research Group, Faculty of Environment and Labour Safety, Ton Duc Thang University, Ho Chi Minh City, Vietnam f Department of Mechanical Engineering, Khomeinishahr Branch, Islamic Azad University, Isfahan, Iran b c

a r t i c l e

i n f o

Article history: Received 27 March 2017 Received in revised form 14 August 2017 Accepted 7 November 2017 Available online 21 November 2017 Keywords: Double pipe heat exchanger Turbulent nanofluid flow Thermal efficiency Finite volume method

a b s t r a c t In present study, heat transfer and turbulent flow of water/alumina nanofluid in a parallel as well as counter flow double pipe heat exchanger have been investigated. The governing equations have been solved using an in-house FORTRAN code, based on finite volume method. Single-phase and standard ke models have been used for nanofluid and turbulent modeling, respectively. The internal fluid has been considered as hot fluid (nanofluid) and the external fluid, cold fluid (base fluid). The effects of nanoparticles volume fraction, flow direction and Reynolds number on base fluid, nanofluid and wall temperatures, thermal efficiency, Nusselt number and convection heat transfer coefficient have been studied. The results indicated that increasing the nanoparticles volume fraction or Reynolds number causes enhancement of Nusselt number and convection heat transfer coefficient. Maximum rate of average Nusselt number and thermal efficiency enhancement are 32.7% and 30%, respectively. Also, by nanoparticles volume fraction increment, the outlet temperature of fluid and wall temperature increase. Study the minimum temperature in the solid wall of heat exchangers, it can be observed that the minimum temperature in counter flow has significantly reduced, compared to parallel flow. However, by increasing Reynolds number, the slope of thermal efficiency enhancement of heat exchanger gradually tends to a constant amount. This behavior is more obvious in parallel flow heat exchangers. Therefore, using of counter flow heat exchangers is recommended in higher Reynolds numbers. Ó 2017 The Society of Powder Technology Japan. Published by Elsevier B.V. and The Society of Powder Technology Japan. All rights reserved.

1. Introduction One of the important effective factors in heat transfer of fluids is thermal conductivity of fluid. The common fluids used in industries have low capability in heat transfer. Therefore, from the industrial perspective, there is a demanded need in industries to develop, use and progress of fluids with higher heat transfer coefficients. In recent years, novel methods have been used for heat transfer enhancement and removing high heat flux. One of these methods is using nanofluids. The experimental results indicate that thermal properties of nanofluids are greater than base fluid. ⇑ Corresponding author. E-mail address: [email protected] (M. Goodarzi).

For instance, by adding almost 1–5% of nanoparticles to the base fluid, thermal conductivity increases up to 20% [1]. The amount of this enhancement depends on different factors such as shape, dimension, material and concentration of nanoparticles [2,3]. It is notable that in primary experiments, the physical and thermal properties of nanofluid has been obtained in the base temperature and specific environment. Das et al. [4] investigated the effect of temperature on nanofluid properties for the first time. This study has been done for water/Al2O3 nanofluid with volume fractions of 1 and 4% and revealed that temperature increment has noticeable influence on thermal conductivity enhancement and the reduction of dynamic viscosity. Naphon et al. [5] experimentally studied the behavior of titanium nanofluid in heat pipes. He figured out that for 10% of nanoparticles, the thermal efficiency enhances

https://doi.org/10.1016/j.apt.2017.11.013 0921-8831/Ó 2017 The Society of Powder Technology Japan. Published by Elsevier B.V. and The Society of Powder Technology Japan. All rights reserved.

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M.H. Bahmani et al. / Advanced Powder Technology 29 (2018) 273–282

Nomenclature Cp D F H K L Nu Q R Re t T Uin

heat capacity, J/kg K tube diameter, m friction factor convective heat transfer coefficient, W/m2 K thermal conductivity, W/m K tube length, m Nusselt number heat transfer, W radius of the tube, m Reynolds number distance between the internal and external tube diameter, m temperature, K inlet velocity in x directions, m/s

Greek symbols q density, kg/m3 l dynamic viscosity, Pa s e heat exchanger efficiency

up to 10.66%. Namburu et al. [6] numerically investigated the effect of properties variations on heat transfer of turbulent flow inside a pipe. They also studied the effect of nanoparticle dimension. Their results showed that in a specific Reynolds number and for a nanofluid with 6% of CuO nanoparticle, Nusselt number enhances to 36%. Chun et al. [7] experimentally studied the effect of using nanoparticles on heat transfer performance in a double pipe heat exchanger under laminar regime. They found that surface properties, volume fraction and geometrics of nanoparticles are the main factors in heat transfer improvement. Zarringhalam et al. [8] experimentally investigated the convection heat transfer coefficient of water/CuO nanofluid with different volume fractions of turbulent flow through a counter flow double pipe heat exchanger. They figured out that by increasing Reynolds number and volume fraction of nanoparticles to 2%, the convection heat transfer enhances to 57%. Zhaoa et al. [9] numerically investigated the water/Al2O3 nanofluid flow in a smooth tube under constant temperature and heat flux. Their numerical results represented that adding nanoparticles to base fluid improves the heat transfer and pressure drop of the working fluid in different Reynolds numbers and temperatures. Bagherzadeh et al. [10] numerically studied the water/CuO and water/Ag nanofluids flow inside the coiled tubes under constant temperature and heat flux in the laminar flow. They investigated thermal conductivity with four equations and figured out that the obtained results from homogeneous model are closer to the experimental results. Hashemi et al. [11] experimentally studied the heat transfer and pressure drop of oil/CuO nanofluid inside the horizontal coiled tubes under constant heat flux. Their results illustrated that the delay in thermal boundary layer formation due to existence of nanoparticles enhances the convection heat transfer coefficient. Hojjat et al. [12] experimentally studied the convection heat transfer of a non-Newtonian nanofluid (DI water/CuO, Al2O3, TiO2) inside the circular tubes in turbulent flow regime. They figured out that by increasing Peclet number, the convection heat transfer and Nusselt number enhance. Hemmat Esfe et al. [13] experimentally studied the heat transfer and pressure drop of water/doublewalled carbon nanotubes (DWCNT) nanofluid inside a double pipe heat exchanger under turbulent regime. Their findings showed 25% enhancement for convection heat transfer coefficient of nanofluid with 0.4% of nanoparticles, compared to the base fluid. Abbasian Arani and Amani [14] experimentally studied the effect of

u

nanoparticles volume fraction

Super- and Sub-scripts Av average b balk f base fluid (Distilled water) C cold eff effective H hot in inlet max maximum min minimum nf nanofluid out outlet r radius p solid nanoparticles

nanoparticles diameter of water/TiO2 nanofluid on the convection heat transfer and pressure drop inside a counter flow double pipe heat exchanger. Their results indicated that by reducing the nanoparticle diameter, Nusselt number enhances, but this enhancement is not absolute because in diameter of 20 nm, Nusselt number values are higher compared to the diameter of 10 nm. Darzi et al. [15] experimentally studied the water/Al2O3 nanofluid inside a double pipe heat exchanger. Their results depicted that adding nanoparticles to the base fluid creates impressive potential for heat transfer enhancement and thermal efficiency of heat exchanger. Chun et al. [16] investigated the convective heat transfer coefficient of oil/alumina nanofluids in different volume fractions in a double pipe heat exchanger under laminar regime. They reported that the reason of heat transfer enhancement of nanofluids is the concentration of nanoparticles in thermal boundary layer near walls and particles motion. Garoosi et al. [17] numerically studied the heat transfer performance of a heat exchanger filled with nanofluid and found that adding solid nanoparticles to the base fluid has great effect on heat transfer enhancement rate. Shahmohammadi and Beiki [18] numerically studied the heat transfer and pressure drop of c/Al2O3 nanofluid inside a shell and tube heat exchanger under turbulent regime. Their results indicated that by increasing the flow rate and number of baffles, heat transfer and pressure drop enhance. However, the increase of nanoparticles does not have a considerable influence on pressure drop intensification. EbrahimniaBajestana et al. [19] numerically and experimentally studied the water/TiO2 nanofluid inside a tube. Their results depicted that adding nanoparticles to base fluid enhances the heat transfer rate up to 21%. Other experimental and numerical studies are usually investigating a nanofluid inside simple geometrics like cavity [20], channel or microchannel [21–24], vertical annulus [25] or inside a tube or microtube [26,27]. In present study, heat transfer and turbulent fluid flow of water/alumina nanofluid in a double pipe heat exchanger are numerically investigated. In this research, effects of nanoparticles volume fraction and Reynolds number on temperature variations of base fluid, nanofluid and wall, thermal efficiency, Nusselt number and convective heat transfer coefficient has been investigated. According to the abundant application of heat exchangers in heat transfer of power plant equipment, the results of this research can be used in many industries, especially oil, gas and petrochemical industries.

275


2. Problem statement, geometrics and boundary conditions In this research, turbulent flow and heat transfer parameters of water/Al2O3 nanofluid in a double pipe heat exchanger by using finite volume method have been investigated. In this study, the heat exchanger with a long length has been modeled in which the nanofluid flow enters in fully developed condition with uniform velocity and temperature of Vin and Tin. According to axial symmetric, the problem has been modeled two-dimensionally according to Fig. 1 with symmetrical axial boundary in the bottom. According to Fig. 1a and for counter flow regime, cold fluid (distilled water) enters from right side of external pipe (Rout = 25 mm) with temperature of 285 K. In internal pipe with radius of Rin = 13 mm, the hot fluid (water/Al2O3 nanofluid) enters from left side with the temperature of 350 K, in u=0–10%. The length of tube is L = 2 m. A solid steel wall with thickness of t = 2 mm has been used between the internal and external pipe. For parallel flow case (Fig. 1b), the flow of distilled water and nanofluid with mentioned uniform temperatures and geometric conditions enter from left side. The wall of external pipe with length of L is insulated. At the center of both pipes, due to the symmetric, axis boundary condition has been used. The middle area between the internal and external areas is under the influence of coupled temperature condition. On the tube wall, no-slip boundary condition is assumed. The fluid enters uniformly to inlet section and the radiation effects are not regarded. In outlet section, the developed condition is considered. Therefore, the velocity variations and axial temperature can be considered equal to zero. In this study, the heat transfer and hydrodynamic behavior of distilled water/Al2O3 nanofluid will be investigated in 0–10% of volume fractions and at the range of Reynolds numbers between 10,000 and 100,000. The solid nanoparticles have been considered as spherical and uniform with the diameter of 30 nm. In Table 1, thermophysical properties of cooling fluid, solid nanoparticles and selected material for tube wall have been showed.

Table 1 The thermophysical properties of used materials in this research. Thermo-physical properties

Water [28]

Al2O3 [29]

Steel [30]

q (J/kg K)

997.1 4179 0.613 8.91 104

3970 765 40 –

8030 502.48 16.27 –

Cp (kg/m3) k (W/m K) m (N s/m2)

3. Governing equations 3.1. Governing equation of fluid flow In this paper, the hydrodynamic behavior and heat transfer of turbulent flow are investigated. The governing equations of flow in steady states and forced turbulent flow are continuity, momentum and energy equations which are as follows [28–30]: Continuity equation:

@ ðqui Þ ¼ 0 @X i

ð1Þ

Momentum equation:

@ @P @ @ui @uj 2 @ui ðqui uj Þ ¼ þ l þ dij @X j @X i @X j @X j @X i 3 @X j @ = = qui uj þ @X j

ð2Þ

Energy equation:

@ @ @T P u2 & E¼h þ ðui ðEq þ PÞÞ ¼ ðkeff Þ @X i @X j @X j q 2

ð3Þ

In this simulation, the standard k-e equations are used. The standard turbulence k-e model is as [31]:

(a) Counter flow

(b) Parallel flow Fig. 1. Schematic of the problem.

276


@ @ ðqkui Þ ¼ @X i @X j

lþ

lt @k þ Gk qe rk @X j

@ @ l @e e e2 þ C 1e Gk C 2e qGk ðqeui Þ ¼ lþ t @X i @X j re @X j k k @u j ¼ qu=i u=j @X i

ð4Þ

e

ð6Þ

q

In above equation, Cl is constant and equals with 0.09 and other values are respectively equal with re = 1.3, rk = 1, C2e = 1.92 and C1e = 1.44. 3.2. The governing equations for calculating the nanofluid thermophysical properties and calculated parameters In this research, water/Al2O3 nanofluid has been considered as an incompressible fluid with constant physical properties. The physical properties are calculated according to nanoparticles volume fraction in inlet temperature of fluid. Density and specific heat coefficient of nanofluid [32], ratio of nanofluid viscosity to the base fluid [33] and ratio of thermal conductivity of nanofluid to base fluid [34] are calculated by following equations:

qnf ¼ ð1 /Þqb þ /qp

ð7Þ

ðC p Þnf ¼ ð1 uÞðC p Þb þ uðC p Þp

ð8Þ

lr ¼

lnf ¼ 123u2 þ 7:3u þ 1:0 lb

knf ¼ 4:97/2 þ 2:72/ þ 1:0 kb

ð9Þ

ð10Þ

The efficiency of heat exchanger is calculated as:

e¼

Q Q max

ð11Þ

In Eq. (11), the real heat transfer is indicated with Q parameter and the maximum rate of heat transfer from a fluid to other fluid (for counter arrangement and infinitive surface) is displayed by Qmax. Each of the Q and Qmax values are respectively computed by following equations:

_ p Þf ðTf;out Tf;in Þ Q ¼ Q f ¼ ðmc _ p Þnf ðTnf;in Tnf;out Þ or Q ¼ Q nf ¼ ðmc

ð12Þ

_ p Þmin ðTnf;in Tf;in Þ Q max ¼ ðmc

ð13Þ

The amounts of local and average convection heat transfer coefficient for internal wall with radius of Rin are obtained from flowing equations:

hnf ¼

hnf ¼

knf @T @r r¼R

in

Twall Tb;nf 1 L

Z 0

ð14Þ

L

hnf dxjr¼Rin

ð16Þ

Nunf ¼

hnf ð2Rin Þ kin

ð17Þ

4. Numerical procedure

2

k

hnf ð2Rin Þ kin

ð5Þ

In above equations, Gk parameter is turbulence energy generator, rk is Prandtl number for turbulence energy and rk parameter is turbulence energy dissipated. C1e and C2e are constant and lt is turbulent viscosity which is defined as:

lt ¼ C l

Nunf ¼

ð15Þ

For calculating the average and local Nusselt number following equations can be used [35]:

Mass, momentum and energy equations are non-linear, coupled equations and should be solved according to boundary equations. These equations have been solved by developing an in-house FORTRAN code, based on finite volume method. For discretizing of equations, second order upwind approach has been utilized and for the pressure-velocity coupling, the SIMPLEC algorithm has been used. 5. Grid independency study and validation In order to verify the number of selected meshes for numerical simulation of the flow and heat transfer field, the influence of meshes numbers on the hydrodynamic and heat transfer parameters are considered simultaneously in the case of the velocity and axial static temperature, at the center of heat exchanger. For present 2-D numerical simulation, the number of rectangular grids has been changed from the 10 50 to 40 200 and has shown in Fig. 2. According to this figure, the obtained results are dependent to number of grids clearly. According to the figure and for low numbers of grids, forecasting the velocity behavior at the center of flow has maximum error. Approximately, the variations of studied parameters for 150 30 and 200 40 grids have same results. Therefore, a non-uniform grid with number of 30 150 cells has been selected for present modeling. For study the accuracy and performance of developed computer code and its results, the numerical solution procedure of present work has been compared with the experimental results of Pak and Cho [36] study for turbulent water/Al2O3 nanofluid flow inside a tube. Pak and Cho [36] studied the coefficient of friction and turbulent convective heat transfer coefficient of nanofluids. They conducted their research for Reynolds number of 104–105 and Prandtl number of 6.5–12.3 under constant heat flux in a steel tube with inner diameter of 10.66 mm and length 4.8 m. In their experiments, c-Al2O3 and TiO2 nanofluids with mean diameter of 13 nm and 27 nm are used, respectively. Also, they presented an experimental relation to calculate the Reynolds number for dispersed nanoparticles in the base fluid. Average Nusselt number has been calculated and presented against the experimental results of reference [36] in Fig. 3. In this validation, volume fraction of nanofluid was equal to 5% and the inlet temperature of carrying fluid was 285 K. The maximum observed error between calculated values and the experimental study results is about 10% which indicates an acceptable accuracy of present code. 6. Results and discussion This research has been done for investigating the effect of nanoparticles volume fraction and Reynolds number on hydrodynamic behavior and heat transfer of turbulent nanofluid flow in a double pipe heat exchanger for parallel and counter flow regimes. The inlet temperature of fluid flows inside the internal tube (nanofluid) is equal to 350 K and the inlet temperature of fluid flows inside the external tube (base fluid) is considered as 285 K. The nanofluid flow has been analyzed in six different Reynolds numbers (10,000–100,000) and for five nanoparticles volume fractions (between 0 and 10%).

277


1.10

10*50 15*75

u (m/s)

1.05

20*100

1.11

25*125

1.10

30*150

1.00

1.09

35*175 1.08

40*200

0.95

1.07

1.06 0.50

0.55

0.60

0.65

0.70

0.75

0.80

0.90

0.0

0.5

1.0

1.5

2.0

X (m)

(a) 330 10*50 15*75

328

Tstatic (K)|center line

20*100

326

25*125 330.0

30*150 329.5

324

35*175 329.0

322

40*200

328.5

328.0 0.45

320

0.0

0.50

0.55

0.5

0.60

0.65

0.70

0.75

0.80

1.0

1.5

2.0

X (m)

(b) Fig. 2. The variation of (a) nanofluid velocity and (b) static temperature at centerline of heat exchanger with different number of meshes.

6.1. Investigating the turbulent flow of nanofluid in parallel flow heat exchanger In this section, the parallel flow regime at the range of turbulent flow is investigated. In the parallel flow regime, the cold and hot fluids enter from one side (the left side) and exit from the other side. In Fig. 4, the variation of average temperature of two fluids and wall temperature along the exchanger is presented. Reynolds number is kept equal to 30,000 for the base fluid and 40,000 for nanofluid. Comparison has been done for u = 0 and u = 5%. As it can be seen form the figure, outlet temperature of distilled water (cold flow) increases and nanofluid as well as wall temperature

decrease. The purpose of using nanofluid is heating the cold fluid and according to improvement of nanofluid properties, this purpose can be obtained. By using same cold fluid and just by increasing the nanoparticles volume fraction, the outlet temperature of cold fluid enhances. The outlet temperature of nanofluid is under the influence of different factors. As it has mentioned, the thermal conductivity coefficient of nanofluid enhances and the heat capacity reduces. These two factors have direct influence on outlet temperature of nanofluid. Therefore, according to the enhancement of outlet temperature it can be said that the effect of thermal conductivity coefficient is undeniable. Another point is that variation of nanofluid temperature is more than the base fluid and this issue

278


800

190 Pak & Cho [36]. Our study.

170

600

160

500

150

400

140

300

130

200

120

100

110 14

15

16

17

18

19

=0 =0.025 =0.05 =0.075 =0.1

700

Nuave

Nuave

180

20

21

0

22

1e+4 2e+4

4e+4

Fig. 3. Nusselt number variation in nanofluid turbulent flow in comparison with experimental results of Pak and Cho [36].

Parallel flow

Tempreture (K)

340

Nanofluid (Hot)

330 320 Wall heat exchanger 310

=0 =0.05

300 Base fluid (Cold)

290 280 0.0

0.5

1.0

8e+4

1e+5

1.5

Fig. 5. The effect of nanoparticles volume fraction on the average Nusselt number in parallel flow heat exchanger.

ture. In turbulent flow, Brownian motion of particles in the base fluid enhances the amount of energy exchange in fluid. The thermal diffusion from hot to cold areas increases the temperature gradients between fluid and wall and therefore, heat transfer between fluid and wall enhances. Hence, the mechanism of heat transfer enhancement by nanofluid can be defined by considering two following aspects: First, the existence and increase of particles in the base fluid improves thermal conductivity and increases the effective surface of particles. Second, the Brownian motion of small particles accelerates the thermal diffusion and consequently, energy transferring process in the fluid. Fig. 6 describes the effect of nanoparticles volume fraction on thermal efficiency of heat exchanger. As can be seen from the figure, thermal efficiency enhances with increase of Reynolds number or nanoparticles volume fraction. According to the thermal efficiency variations, it can be said that increasing the volume fraction of nanoparticles has greater effect on this factor in comparison

360 350

6e+4

Re

Re*1000

2.0 0.105

X(m) Fig. 4. Temperature variation in the parallel flow along the exchanger.

0.095

Q/Qm

is due to the reduction of nanofluid heat capacity. Also, the enhancement of wall temperature-according to increase of thermal conductivity and decrease of nanofluid heat capacity-makes sense. Fig. 5 describes the effect of nanoparticles volume fraction on average Nusselt number. The results of this part have been studied for five nanoparticles volume fractions (0–10%) and six nanofluids Reynolds numbers among 10,000–100,000. However, Reynolds number of fluid is set equal to 30,000. According to this figure, maximum amount of average Nusselt number accomplishes in Re = 100,000 and volume fraction of u = 10% which is equal to 31.85%. It can be observed that in low Reynolds numbers, volume fraction augmentation have less influence on the Nusselt number enhancement. However, by increasing Reynolds number, this effect intensifies. The Nusselt of nanofluid depends on different factors such as thermal conductivity, heat capacity of base fluid and nanoparticles, flow pattern, nanofluid concentration, volume fraction of particles, dimensions and shape of particles and flow struc-

0.100

0.090 0.085

=0 =0.025 =0.05 =0.075 =0.1

0.080 0.075

1e+4 2e+4

4e+4

6e+4

8e+4

1e+5

Re Fig. 6. The effect of nanoparticles volume fraction on thermal efficiency in parallel flow heat exchanger.

279


360

340 330 320

Wall heat exchanger

310

=0 =0.05 Base ofluid (Cold)

290 280 0.0

0.5

1.0

1.5

2.0

X(m) Fig. 8. Temperature variation in the counter flow along the exchanger.

800

=0 =0.025 =0.05 =0.075 =0.1

700 600

Nuave

500 400 300 200 100 0

6

Nanofluid (Hot)

300

6.2. Investigating the turbulent nanofluid flow in counter flow heat exchanger Fig. 8 indicates the average temperature variation of two fluids as well as wall temperature along the exchanger wall. Reynolds number has been considered equal to 30,000 for base fluid and 40,000 for nanofluid. The analysis of temperature increment is similar to parallel flow arrangement. Such that, the differences of outlet temperature for nanofluid is more than this amount for base fluid which is due to the reduction of nanofluid heat capacity. In this case, according to counter flow arrangement, the outlet of fluid in internal and external tubes is in two sides of heat exchanger which causes the uniform distribution of temperature and higher heat exchanger efficiency. By comparing the temperature diagrams, it is specified that the increase of cold fluid temperature in counter flow arrangement is more than the parallel flow. By studying the wall temperature, it can be said that in counter flow

Counter flow

350

Tempreture (K)

with Reynolds number. In all Reynolds numbers and for each constant volume fraction, there is an obvious distinction among the diagrams. Also, in Reynolds numbers less than 60,000, the thermal efficiency factor increases significantly by Reynolds number increment. However, in Reynolds number higher than 60,000 and for each specific volume fraction, the amount of this factor reaches to a constant value and this behavior is more obvious in higher volume fractions. Fig. 7 represents thermal efficiency enhancement of heat exchanger in Reynolds number of 40,000 for different nanoparticles volume fractions. It can be seen from the figure that by increasing volume fraction of nanoparticles, thermal efficiency does not significantly change. The maximum amount of thermal efficiency enhancement accomplishes in 5% of nanoparticles volume fraction and adding more than 5% nanoparticles causes the reduction of efficiency. According to the defined equation, this behavior of thermal efficiency makes sense; as thermal efficiency is the ratio of transferred heat to maximum temperature at the same volume fraction. Therefore, there is not any direct relation between the transferred heat and the base fluid. Therefore, it is not expected that thermal efficiency enhances by increasing nanoparticles volume fraction.

1e+4 2e+4

4e+4

6e+4

8e+4

1e+5

Re 5

Fig. 9. The effect of nanoparticles volume fraction on average Nusselt number in counter flow heat exchanger.

=Q/Qmax

4 3 2 1 0

2.5

5

7.5

10

% Fig. 7. The percentage of thermal efficiency enhancement in different amounts of volume fraction of nanoparticles for parallel flow state.

heat exchanger, the maximum values of wall temperature is more than the parallel flow. Figs. 9 and 10 indicate the effect of nanoparticles volume fraction on average Nusselt number and thermal efficiency of counter flow heat exchanger, respectively. The enhancement of maximum temperature on the solid wall indicates enhancement of heat transfer rate from the hot nanofluid to the wall and this heat transfer rate augmentation is higher by increasing the volume fraction of nanoparticles. The variation of wall temperature is calculated by differencing the maximum and minimum temperatures. In this study, it can be concluded that the amount of temperature difference is more for counter flow arrangement compared to the parallel flow which indicates the enhancement of heat transfer rate between hot nanofluid and cold base fluid in counter flow arrangement. The maximum average Nusselt number augmentation is calculated in u = 10% and Re = 100,000 which is equal to 32.7%. Also, it

280


0.12

nolds numbers (high velocity of fluid), there is insufficient time for heat transferring. Therefore, thermal efficiency reduces in high Reynolds numbers. It should be noted that the effect of thermal efficiency reduction is low in industrial heat exchangers.

0.11

6.3. Bulk temperature variation of cold fluid

Q/Qm

0.10

0.09

0.08

=0 =0.025 =0.05 =0.075 =0.1

0.07

0.06 1e+4 2e+4

4e+4

6e+4

8e+4

1e+5

Re Fig. 10. Nanoparticles volume fraction influence on thermal efficiency in counter flow heat exchanger.

can be seen that in lower Reynolds numbers, an increase in nanoparticles volume fraction has less effect on Nusselt number enhancement and by increasing Reynolds number, this effect enhances. In the other words, adding nanoparticles in higher Reynolds numbers has more effect and using nanofluid in lower Reynolds numbers is not plausible. In Fig. 10, it can be seen that by increasing Reynolds number in Re < 40,000, thermal efficiency enhancement increase rapidly and in higher Reynolds numbers, the slop of efficiency enhancement reduces. In fact, the reduction of efficiency is due to the low length of studied heat exchanger and in the industrial scales, the efficiency is higher. Fig. 11 shows the thermal efficiency enhancement of heat exchanger for different nanoparticles volume fractions in Re = 40,000. It can be seen that by increasing volume fraction of nanoparticles, thermal efficiency reduces insignificantly. However, according to the low length of studied heat exchanger in high Rey-

10

=Q/Qmax

8

6

4

2

0

2.5

5

7.5

10

% Fig. 11. Percentage of thermal efficiency enhancement for counter flow state.

For investigating and comparing the heating power of cold fluid with variation of nanoparticles volume fraction, the average temperature of cold fluid in constant Reynolds numbers are compared. Fig. 12 depicted the average temperature of cold fluid in Re = 100,000 and for different volume fractions in counter flow (a) and parallel flow (b) arrangements. It can be observed from the figure that by nanoparticles volume fraction addition, the outlet temperature of cold fluid increases. In the other words, adding more nanoparticles causes increment of heating fluid temperature. According to Fig. 12a, in counter flow arrangement and for u = 10%, the average outlet temperature becomes 297.8 K which is 1.3 K more than the base fluid. Also, for parallel flow and in the same velocity, the outlet temperature reaches to 292.07 K, 1.3 K further than the base fluid. However, it should be noted that due to the experimental length of heat exchanger, this enhancement is not significant. Otherwise, -according to the slop of temperature profile- if an industrial scale heat exchanger uses, this enhancement would be impressive. Also, in a constant Reynolds number, adding nanoparticles cause nanofluid temperature enhances. At the end, multiple of these three effective factors on thermal power enhance. In the other words, adding nanoparticles causes the enhancement of thermal power. Of course, the increase of thermal power is obvious from presented results of thermal efficiency.

7. Conclusion In this research, heat transfer, thermal efficiency and temperature variations of H2O/Al2O3 nanofluid fluid in parallel and counter flow double pipe heat exchangers have been investigated numerically. The effect of solid nanoparticles volume fractions and a wide range of Reynolds numbers in turbulent regimes were studied by using a FORTRAN computer code. In all studied cases, the inlet temperature of base fluid (cold) and nanofluid (hot) are considered as constant. The important results of this investigation are: (1) The slop of convection heat transfer coefficient and Nusselt number diagrams are almost constant. (2) Adding nanoparticles in higher Reynolds numbers has more effect on convection heat transfer coefficient and Nusselt number enhancement. (3) Maximum thermal efficiency and average Nusselt number enhancement observed in counter flow regime which are equal to 30% and 32.7%, respectively. (4) When the volume fraction of nanoparticles is 10%, cold fluid outlet temperature augmentation is equal to 1.3 K and 1.1 K for the counter and parallel flow, respectively. (5) In all of the studied cases, by increasing the volume fraction, variation of nanofluid outlet and wall temperatures is more than the base fluid. (6) The maximum thermal efficiency enhancement of heat exchanger happens in nanoparticles volume fraction of 5%. Adding more nanoparticles causes the reduction of efficiency. This effect, in the heat exchangers with smaller scales is less than heat exchangers with large scales. The extension of this paper for nanofluids, according to previous studies [37–62] affords engineers a good option for micro and nano-simulation.

281


293

293

292

292 =0 =0.025 =0.05 =0.075 =0.1

Tb (K)

290

291 290

Tb (K)

291

=0 =0.025 =0.05 =0.075 =0.1

289

289

288

288

287

287

286

286 285

285 0.0

0.5

1.0

1.5

2.0

X (m)

a- Counter flow

0.0

0.5

1.0

1.5

2.0

X (m)

b- Parallel flow

Fig. 12. The effect of nanoparticles volume fraction on the distribution of cold fluid average temperature.

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