Investigating the potential impact of nanofluids on the ...

13 downloads 0 Views 2MB Size Report
of condensers and evaporators – A general approach. M.T. Nitsas *, I.P. Koronaki. Laboratory of Applied Thermodynamics, School of Mechanical Engineering ...
Applied Thermal Engineering 100 (2016) 577–585

Contents lists available at ScienceDirect

Applied Thermal Engineering j o u r n a l h o m e p a g e : w w w. e l s e v i e r. c o m / l o c a t e / a p t h e r m e n g

Research Paper

Investigating the potential impact of nanofluids on the performance of condensers and evaporators – A general approach M.T. Nitsas *, I.P. Koronaki Laboratory of Applied Thermodynamics, School of Mechanical Engineering Thermal Engineering Section, National Technical University of Athens, Heroon Polytechniou 9, Zografou Campus, 15780, Athens, Greece

H I G H L I G H T S

• • • •

A modified ε-NTU model is developed. The presence of nanoparticles enhances the heat exchanger effectiveness. The effectiveness is higher under laminar flow. The effectiveness enhancement depends on the quantity of nanoparticles.

A R T I C L E

I N F O

Article history: Received 11 November 2015 Accepted 14 February 2016 Available online 27 February 2016 Keywords: Nanofluids Nanoparticles Effectiveness Heat exchangers ε-NTU method Pressure drop Heat transfer coefficient

A B S T R A C T

In this paper, the impact of nanofluids, when used as heat transfer fluids, on heat exchangers effectiveness is examined. The method used for the analysis is a modified ε-NTU. As it is already known from literature, any heat exchanger exhibits minimum and maximum values of effectiveness when the ratio of heat capacities Cr is one and zero, respectively. In this work, the improvement of effectiveness due to nanoparticles presence is investigated in heat exchangers in which Cr is zero (evaporators and condensers). The conducted analysis is performed for both laminar and turbulent flow conditions and it adopts specific assumptions so as the extracted results and conclusions to be generalized for most of the commonly used nanoparticles. Moreover, the effect of specific capacity drop and pressure drop as nanoparticles volume concentrations increase is explored. Finally, the potential benefit of nanofluids on minimizing heat exchangers size is investigated. © 2016 Elsevier Ltd. All rights reserved.

1. Introduction Considering the performance of heat exchangers, in order to increase their effectiveness and at the same time reduce their size, nanofluids can be used as heat transfer fluids. Nanofluids is a term introduced by Choi to describe fluids (commonly water or ethylene glycol) engineered by dispersing nanometer scale structures such as particles, tubes, fibers etc. Nanofluids were firstly introduced in 1995 [1], and the progress after two decades is reflected in the research already done regarding their composition and stability [2], their superior thermophysical properties compared to those of conventional base fluids e.g. water [3–6] and their capacity to enhance heat transfer rate [7–14]. Concerning the utilization of nanofluids in HEXs both computational and experimental work has been done. Pantzali et al. [15,16] studied experimentally and numerically plate HEXs with modulated

* Corresponding author . Tel.: +30 210 772 4071; fax: +30 210 772 3670. E-mail address: [email protected] (M.T. Nitsas). http://dx.doi.org/10.1016/j.applthermaleng.2016.02.059 1359-4311/© 2016 Elsevier Ltd. All rights reserved.

surface filled with CuO-water (4% volume fraction) nanofluid. Their findings depict the dependency of nanofluids efficacy on the nature of the flow (laminar/ turbulent), the unsuitability of nanofluids in industrial applications in which turbulent conditions prevail and the enhancement of HTC due to the presence of nanoparticles. Mare [17] found experimentally that in a plate HEX, the laminar convective HTC increases in the presence of carbon and alumina nanotubes. However, this enhancement is accompanied by a significant pressure drop compared to that of the base fluid. Farajollahi [18] investigated experimentally a shell and tube HEX which used Al2O3water (0.3%–4%) and TiO2-water (0.15%–0.75%) nanofluids under turbulent flow conditions (Pe ranging between 20,000 and 60,000). It was proven that HTCs increased due to nanofluids. Huminic [19] studied numerically the performance of a double pipe helical HEX under laminar flow conditions in the presence of CuO-water and TiO2-water nanofluids. An HTC enhancement of 14% was observed while the heat transfer rate increased with the increase of the flow rate. Kabeel [20] studied under laminar flow conditions a corrugated plate HEX that used Al2O3-water nanofluid as heat transfer fluid. Through his experiments, a 13% enhancement in HTC was

578

M.T. Nitsas, I.P. Koronaki/Applied Thermal Engineering 100 (2016) 577–585

observed when the volume fraction of the nanoparticles was 4%. Nevertheless, this enhancement came along with an increase in pressure drop and a drop in the HEX’s effectiveness as Reynolds number rises. Jocar et al. [21] studied numerically a corrugated plate HEX, which utilized Al2O3-water (1%–4%) under laminar flow conditions. They concluded that heat transfer decreased slightly as the volume fraction of nanofluid increased due to the complex flow regimes of nanofluids in the 3-D geometries of plate HEXs. As concluded from the above short literature review, most of the work concerns HEXs without phase change and most researches are case dependent and concern specific types of nanofluids and conditions and the drawn conclusions cannot be generalized for all commonly used nanoparticles. This work tries to fill in partially this gap as a more general approach is attempted. We examine the impact of nanofluids as heat transfer fluids on HEX effectiveness by using the ε-NTU method. In specific, the improvement of effectiveness due to nanoparticles presence is investigated in HEXs in which the ratio of heat capacities (Cr) is zero (evaporators and condensers). The conducted analysis is performed for both laminar and turbulent fully developed flow conditions and it adopts specific assumptions so as the extracted results and conclusions to be generalized for most of the commonly used nanoparticles. Moreover, the effect of specific capacity and pressure drop as nanoparticles volume concentrations increase is explored. Finally, the potential benefit of nanofluids on minimizing condensers and evaporators size is investigated.

Table 2 γ ratio of densities for common nanoparticles and base fluids.

Al2O3 CuO SiO2 ZnO Cu

Water

EG

3.6 6.3 2.2 5.6 9.0

3.3 5.7 2.0 5.1 8.1

2.2. Specific heat Experimental studies on specific heat of nanofluids are limited [5] and the results are rather controversial. Some researchers [5,24,25] reached the conclusion that nanofluids specific heat capacity decreases as the volumetric fraction of nanoparticles dispersed into the host fluid increases while others have reached the opposite conclusion [26–28]. Literature proposes various correlations for the specific heat of nanofluids [24,26,29]. However, most of them are empirical and they have been developed for particular nanoparticles of specific diameter and temperature. Since a more general approached is attempted in this work, the correlation used for the specific heat is theoretical [30].

c p ,nf =

ϕρp c p ,p + (1 − ϕ ) ρf c p ,f ϕρp + (1 − ϕ ) ρf

(3) ρ

2. Thermophysical properties of nanofluids As mentioned above, the dispersion of nanoparticles into a base fluid is expected to change the properties (thermal conductivity, specific heat and density) of the base fluid. Below follows a presentation of the correlations chosen for the analysis and their simplification under specific assumptions.

c

p p ,p Given that φ is usually less than 5%, ϕ ρf c p ,f is assumed to be a very small quantity compared to the other term of the Eq. 3 and thus it can be neglected. This can be seen in Figs. 1 and 2 when the base fluid is water and EG, respectively. By implementing this assumption, the following expression for the specific heat is received:

c p ,nf 1 = ϕ c p ,f γ +1 1− ϕ

(4)

2.1. Density 2.3. Thermal conductivity Eastman [22] proposed the following expression for the density of nanofluids, which is practically an expression for the weighted average of the densities of nanoparticles and the base fluid with volume fraction being the weight factor.

ρnf = ϕρp + (1 − ϕ ) ρf

The asset of a nanofluid over the conventional heat transfer fluids depends mainly on its thermal conductivity. The thermal conductivity of nanofluids is strongly connected with the type, quantity, shape and size of the nanoparticle, the temperature, the tendency

(1)

Eq. 1 can be written as:

ρnf = ϕ ⋅ γ + (1 − ϕ ) ρf

(2)

In Eq. 2, γ represents the ratio of densities and for the most commonly used nanoparticles and base fluids it receives values between 2 and 9, as it can be seen from Tables 1 and 2.

Table 1 Thermophysical properties of nanoparticles [9,23] and base fluids.

Water EG Al2O3 CuO SiO2 ZnO Cu

ρ

k

Cp

Μ

996.5 1104 3600 6310 2200 5600 8933

0.613 0.256 36 17.6 1.4 13 400

4181 2740 765 550.5 745 495.2 385

0.001 1.69E-4 — — — — —

Fig. 1. Contribution of the omitted term in water nanofluids.

M.T. Nitsas, I.P. Koronaki/Applied Thermal Engineering 100 (2016) 577–585

579

Fig. 3. Ratios of thermophysical properties for different volume fractions.

Fig. 2. Contribution of the omitted term in EG nanofluids.

3. Mathematical modeling of the particles to form agglomerates and the dispersant. Despite the dependencies above, several studies have come to the same conclusion, that the addition of nanoparticles in a host fluid enhances its thermal conductivity [3,31–33]. Literature proposes correlations that take into account the Brownian motion of the particles (dynamic models) [34–37] and other correlations that do not (static models) [38,39]. The dynamic models are empirical and case dependent. Therefore, the static model of Wasp [39] is preferred to predict nanofluids thermal conductivity.

k nf k p + 2k f + 2 ⋅ ϕ ⋅ (k p − k f ) = kf k p + 2k f − ϕ ⋅ (k p − k f )

(5)

Considering that kk pf → 0 as k p  k f , it becomes independent of the type of nanoparticle, thus:

3ϕ k nf = 1+ 1− ϕ kf

(6)

2.4. Viscosity

Following Incropera [44], in HEXs where a phase change occurs, concerning one or both streams, the ratio of the heat capacities is zero and the effectiveness can be expressed as follows:

ε = 1 − exp ( −NTU )

(9)

or

NTU = − ln (1 − ε )

(10)

By expressing Eq. 9 once for the nanofluid and once for the base fluid, the ratio NTUnf/NTUf is formed. Solving the former ratio with respect to the effectiveness when nanofluids are used we get the following equation. NTU nf

ε nf = 1 − (1 − ε f ) NTU f

(11)

Considering the definition of Number of Transfer Units and assuming that the addition of nanoparticles does not change substantially the mass flow, the ratio NTUnf/NTUf can be found as follows:

NTU nf ⎛ ϕ ⎞ U = γ + 1⎟ ⋅ nf ⎠ Uf NTU f ⎜⎝ 1 − ϕ

Similar to thermal conductivity, the viscosity of the nanofluids is affected by the volumetric fraction of nanoparticles, their shape and size as well as the type of base fluid and temperature. Many research works have experimentally determined nanofluids viscosity, investigated its dependency on the aforementioned factors and proposed correlations for the viscosity calculation [30,36,40–43]. In this analysis, the model proposed by Brinkman [40] is chosen.

In order to determine the ratio of total HTCs, appearing in Eq. 12, the following procedure is implemented. For the unfinned, tubular HEXs, the overall HTC can be expressed as follows.

μnf 1 = μf (1 − ϕ )2.5

ln D A R 1 1 R 1 Df = + fA + + + ff hf A f A f U f A A hA A A A A 2π kL

(7)

(

(12)

)

(13)

Equation 7 is simplified further if we limit the volume fraction −2,5 of nanoparticles to 5% since the approximation (1 − ϕ ) ≈ 1 + 2.5ϕ for small values of φ is valid. Therefore:

Should the fouling factors and the thermal resistance of the tube walls be neglected and DA ≈ Df, the HTC without nanofluids can be written as

μnf = 1 + 2.5ϕ μf

1 1 1 = + U f h A hf

(8)

Fig. 3 depicts the variation of the properties described by Eq. 3, 5 and 7 for different particle loadings.

(14)

In Eq. 13 and 14, the subscript A refers to the stream that flows outside the tubes and changes phase and f to the base fluid in flows

580

M.T. Nitsas, I.P. Koronaki/Applied Thermal Engineering 100 (2016) 577–585

inside the tubes. The convective HTC of stream A has a constant value, which for both cases (without and with nanoparticles) can be expressed as follows.

1 1 1 = − h A U f hf

(15)

The HTC with nanofluids is expressed in the same way.

1 1 1 = + U nf h A hnf

(16)

The substitution of Eq.15 in Eq. 16 yields the ratio of HTCs that appears in Eq. 12.

U nf U ⎛h ⎞ = 1 + nf ⎜ nf − 1⎟ ⎠ Uf hnf ⎝ hf

(17)

A simpler expression for the ratio above can be reached if it is assumed that the convective thermal resistance of nanofluids is a percentage, let it be α, of the total thermal resistance. Therefore,

U nf ⎛h ⎞ = 1 + a ⋅ ⎜ nf − 1⎟ ⎝ hf ⎠ Uf

(18)

The combination of Eq.11, 12 and 18 gives the final expression for the effectiveness of the HEX when nanofluids are used. ⎛ ϕ

ε nf = 1 − (1 − ε f )⎜⎝ 1−ϕ

⎞ ⎡ ⎛ ⎛h ⎞⎞ ⎤ γ +1⎟ ⋅⎢1+⎜ a⋅⎜ nf −1⎟ ⎟ ⎥ ⎠⎠ ⎦ ⎠ ⎣ ⎝ ⎝ hf

(19)

The equation stated above can be parameterized further if the ratio of convective HTCs is expressed as a function of the nanofluid properties described earlier in this work. In order to do so, both laminar and turbulent conditions concerning the nanofluids flow need to be examined.

The laminar flow of nanofluids has been studied in a few research works while some researchers propose correlations for calculating Nusselt or/and convective HTC [15,45,46]. In this work, however, the definition of Nusselt number is used instead of using one of the proposed correlations in order to make the analysis case independent.

( )( RePr L D

1 3

)

μ 0.14 μs

≥ 2.

Therefore, the flow is fully developed in terms of both fluid dynamics and heat transfer (regarding the thermal entry length problem) and thus the Nusselt number under these conditions is equal to 3.66. This value of Nusselt number implies constant tube wall temperature, which is merely consistent with the fact that the phase change occurs under constant temperature. Then, through the definition of Nu it is formed that:

hnf k nf = hf kf

(20)

Combing together Eq.19 with Eqs. 6 and 20, the final expression is received, which links the effectiveness of the HEX before and after the addition of the nanoparticles. 3ϕ ⎞ ϕ ⎤⎛ ⎡ γ ⋅ 1+α ⋅ 1+ 1−ϕ ⎟⎠ 1−ϕ ⎥⎦ ⎜⎝

ε nf = 1 − (1 − ε f )⎢⎣

Nu = 0.023Re 0.8Pr 0.4

(22)

By expressing the Dittus–Boelter correlation once for the base fluid and once for the nanofluid, the following equation is formed through the definition of Nu.

hnf ⎛ ρnf ⎞ = hf ⎜⎝ ρf ⎟⎠

0.8

⎛μ ⎞ ⋅ ⎜ nf ⎟ ⎝ μf ⎠

−0.4

⎛c ⎞ ⋅ ⎜ nf ⎟ ⎝ cf ⎠

0.4

⎛k ⎞ ⋅ ⎜ nf ⎟ ⎝ kf ⎠

0.6

(21)

3.2. Turbulent flow conditions Under turbulent flow conditions, the correlation proposed by Dittus and Boelter is used for the calculation of the Nusselt number

(23)

The expression above implies that the mean velocity of the flow does not change whether nanoparticles are used or not. The substitution of the nanofluids properties in Eq. 23 yields the following expression for the ratio of convective heat transfer coefficients.

hnf ⎛ (γ − 1)ϕ + 1⎞ = hf ⎜⎝ 1 + 2.5ϕ ⎟⎠

0.4



(1 + 2ϕ )0.6 (1 − ϕ )0.2

(24)

Although Eq. 24 has non-integer exponents, judging by the sum of φ exponents it can be concluded that the ratio of heat transfer coefficients depends quite linearly on φ. Therefore, a simpler expression can be found through curve fitting analysis. The ratio of HTCs can be written as 1 + f(φ, γ), where f is a function of the volume fraction of nanoparticles and the ratio of densities. This function can be expressed through a linear relation as 1 + B1φ+B2γ. However, such an expression yields an R2 =0.9268. In order to achieve the maximum equivalent to Eq. 24, the ratio is written as 1 + B1φ+B2γφ+B3φ2. This approximation gives an R2 almost equal to one (0.9998) and thus the following expression is chosen for the HTC ratio.

hnf = 1 + f (ϕ , γ ) = 1 + 0.1659ϕ + 0.356γ ⋅ ϕ − 0.3466ϕ 2 hf

3.1. Laminar flow conditions

Under laminar flow conditions, it is assumed that

and thus for the convective HTC for both the base fluid and the nanofluid. A more general expression for Nusselt number was preferred for nanofluids’ flow since the majority of Nusselt number correlations proposed for nanofluids are case dependent [30,47–49].

(25)

The substitution of Eq. 25 in Eq. 19 gives the effectiveness of the HEX under turbulent flow conditions when nanoparticles are used. ⎛ ϕ

ε nf = 1 − (1 − ε f )⎝⎜ 1−ϕ

⎞ γ +1⎟ ⋅[1+a⋅f (ϕ , γ )] ⎠

(26)

3.3. Pressure drop quantification In the introduction of this work, the short review of the experimental work done on HEXs showed that the enhancement of their performance due to nanofluids is accompanied by an increase on pressure drop. The pressure losses are represented by the Darcy friction factor, which will be determined for each type of flow. As it was aimed with the effectiveness, a more general approach will be endeavored. Therefore, the variation of pressure drop due to nanofluids is investigated in comparison with the drop when only base fluid is utilized. For fully developed laminar flows, the Darcy friction factor is f = 64/Re (27) [44]. Under the assumption that the mean velocity of the flow is not affected by the addition of nanoparticles and expressing Reynolds number and substituting Eq. 2 and 8 into 27, it follows that, for fully developed laminar flow,

1 + 2.5ϕ f nf = ff (1 − ϕ ) + γ ⋅ ϕ

(28)

For the turbulent flow, the Haaland equation will be used [50] the accuracy of which is claimed to be within ±2 %, if the Reynolds number is greater than 3000 [51].

M.T. Nitsas, I.P. Koronaki/Applied Thermal Engineering 100 (2016) 577–585

⎛⎛ e ⎞ 1 = −1.8log ⎜ ⎜ D ⎟ ⎜ ⎜⎝ 3.7 ⎟⎠ f ⎝

1.11

+

581

4. Results

⎞ 6.9 ⎟ Re ⎟ ⎠

(29)

If the relative roughness of the pipe is neglected, the expression of Eq. 29 for nanofluids and base fluid through the substitution of Eq. 2 and 8 yields the following:

1 f nf = 2 ff ⎛ ⎛ (1 − ϕ ) + γ ⋅ ϕ ⎞ ⎞ ⎜⎝ 1 + f f ⋅ log ⎜⎝ 1 + 2.5ϕ ⎟⎠ ⎟⎠

(30)

3.4. Specific heat effect There is a lack of data concerning the specific heat of nanofluids and the existing ones are rather controversial. However, the majority of the researchers tend to adopt the de facto drop of specific heat when nanoparticles are added to the base fluid. In order to illustrate the effect of the specific heat drop on the HEX when nanoparticles are added, the analysis above is repeated for both flow conditions assuming this time that the specific heat does not change with the dispersion of nanoparticles and thus cp,nf = cp,f. Under this assumption, the effectiveness of the HEX filled with nanofluids is given by the following equation. ⎡ ⎛h ⎞⎤ 1+a⋅⎜ nf −1⎟ ⎥ ⎝ hf ⎠⎦

ε nf = 1 − (1 − ε f )⎢⎣

4.1. Laminar flow conditions In order to illustrate the enhancement of HEX effectiveness due to nanofluids, α and γ were assigned the values of 0.7 and 5, respectively. However, the equations above can be used for all values of α and γ mentioned earlier. Fig. 4 depicts the effectiveness of the HEX when nanofluids are utilized as a function of the effectiveness before the addition of the nanoparticles while Fig. 5 presents the benefit of the nanofluids utilizations in terms of effectiveness enhancement. As seen, a HEX with for example εf = 0.7 after the addition of the 5% nanoparticles exhibits an effectiveness enhancement of 16.5% or in absolute numbers εnf = 0.816. Through these two figures, it can be concluded that the lower the effectiveness of HEX using only base fluid, the higher the enhancement after the addition of nanoparticles. Fig. 6 examines the effect of the thermal resistance ratio on the overall enhancement of the HEX as a function of the nanoparticles loadings. A HEX of 0.7 effectiveness was chosen and the nanoparticles

(31)

Following the same procedure as before, Eq. 31 is expressed for both laminar and turbulent flow conditions. 3ϕ ⎤ ⎡ ⎧ ⎢1+a⋅ ⎥ ⎪1 − (1 − ε f )⎣ 1−ϕ ⎦, laminar flow ε nf = ⎨ ⎪⎩1 − (1 − ε f )[1+a⋅g (ϕ ,γ )], turbulent flow

(32)

where g (ϕ, γ ) = 2.073ϕ 2 + 0.825γϕ − 0.1145ϕ

3.5. Nanofluids benefit on HEX size The analysis above is done on the hypothesis that the size of the HEX is already known. The effect of the nanoparticles presence on the size of the HEX will be determined according to the nature of the flow. In order to determine how much more or less surface area is needed with the presence of nanofluids, in order to ensure the same effectiveness of HEX with and without the nanoparticles, is set that εnf = εf. The equalization of ε before and after the addition of nanoparticles implies that the NTU nf = NTU f . Therefore,

Anf c p ,nf 1 = ⋅ Af c p ,f U nf Uf

Fig. 4. HEX effectiveness for different particle volume fractions under laminar flow.

(33)

The analysis made for the HTC ratio lead to the following expression for the HEX surface ratio:

1 ⎧ ⎪ ϕ γ ⎪1 + Anf ⎪ 1 − ϕ =⎨ 1 Af ⎪ ϕ ⎪ ⎪1 + 1 − ϕ γ ⎩



1 1+ α

3ϕ 1− ϕ

, laminar flow

1 ⋅ , 1 + α ⋅ f (ϕ , γ ) turbulent flow

(34)

Fig. 5. Enhancement factor for different particle volume fractions under laminar flow.

582

M.T. Nitsas, I.P. Koronaki/Applied Thermal Engineering 100 (2016) 577–585

Fig. 6. Enhancement factor for different ratios of thermal resistance under laminar flow conditions.

Fig. 8. Enhancement factor for both types of flow.

utilized have a density ratio γ = 5. The higher values of α correspond to liquid-refrigerant condensers and evaporators. It is found that the stream that has higher convective HTC and thus contributes the most in the overall HTC exhibits the higher enhancement as the particles loading increases.

of 0.7 after the addition of 3% nanoparticles exhibits a 10.4% enhanced effectiveness under laminar flow and a 9.3% under turbulent flow.

4.2. Turbulent flow conditions The same values were adopted for α and γ as in the laminar flow. Fig. 7 shows the effectiveness before and after the addition of nanoparticles. A HEX of 0.7 effectiveness exhibits a 0.803 effectiveness when it utilizes 5% nanoparticles under turbulent flow conditions. In Fig. 8, the enhancement of the effectiveness compared to that of laminar flow is illustrated for different nanoparticles fractions. As observed from other researchers, nanoparticles contribute more in terms of HTC increase under laminar flow rather than under turbulent flow. For example a HEX with an effectiveness

The drop in pressure depends on both density and viscosity of the fluid. More specifically, these two properties have opposite effects on Reynolds number and thus on the Darcy friction factor. In order to investigate the opposite effects, the friction factor will be illustrated for different particle loadings (higher φ increases viscosity and reduce Re) and densities ratios (higher densities tend to increase Re). Fig. 9 depicts the nanofluids friction factor normalized to that of the base fluid for different values of φ and γ. It seems that nanofluids with particles of greater density lead to less pressure drop than the host fluid itself. The opposite conclusion is reached for nanoparticles of lower densities.

Fig. 7. HEX effectiveness for different particle volume fractions under turbulent flow.

Fig. 9. Friction factor ratio for laminar and turbulent flow.

4.3. Pressure drop variation

M.T. Nitsas, I.P. Koronaki/Applied Thermal Engineering 100 (2016) 577–585

Fig. 10. Specific heat effect on effectiveness under laminar flow conditions.

4.4. Specific heat effect For the investigation of specific heat effect, a HEX with εf = 0.7 is assumed. The values for α and γ are the same as before. Fig. 10 depicts the effectiveness when nanofluids are used under laminar conditions. It can be concluded that the specific heat drop leads to an increase of NTU and thus a higher effectiveness in comparison with the case in which the specific heat drop is neglected. The same conclusion can be drawn for the turbulent flow even though the enhancement factor is lower (Fig. 11). 4.5. Nanofluids benefit on HEX size The benefit of nanofluids on HEX size is determined through Eq.34. The same values for α and γ are assumed. Fig. 12 shows the variation of HEX size as a function of particles loadings for both types of flows. It can be concluded that a HEX utilizing nanofluids needs less surface so as to exhibit the same effectiveness as it does without nanoparticles.

583

Fig. 12. Nanofluids effect on HEX size for both types of flow.

5. Sensitivity analysis and discussion In order to determine which of the parameters presented above has the greatest effect on the effectiveness of condensers and evaporators when nanofluids are utilized, a sensitivity analysis (SA) is performed. When performing a sensitivity analysis (SA), the objective is to include as many properties of the involved variables as possible, expecting them to play a role, large or small, on the system’s performance. The results of this regression analysis will indicate the degree of influence of each independent variable on the dependent variable. The dependent output variable of HEX’s effectiveness depends upon quantitative variables such as the volume fraction of nanoparticles, the type of nanoparticles (expressed by the ratio of the densities γ) and the parameter α used to describe the contribution of nanofluid convective HTC hnf to the overall HTC Unf. Since in this work static models were chosen to quantify nanofluids properties, parameters such as particles diameter and temperature are not examined. So, in case a multiple regression analysis is performed on the exponent of the Eq. 17 for both laminar and turbulent conditions. The independent variables ranged as follows: φ = 0:5%, γ = 2:9 and a = 0:1. Tables 3 and 4 show the SA output statistic results after running a multiple regression on the exponent of Eq. 19. There is a lot of information that can be obtained from the contents of Table 4. In multiple regressions, if the involved independent variables are expressed in different units, or are measured in different scales, then the relative size of each coefficient has no particular importance. In order to determine the relative importance of explanatory variables and/or compare the effects of changing different variables, regression coefficients (RC) are transformed into standardized regression coefficients (SRC), also known as beta coefficients. This way, standardized variables could be measured in the comparable scale of standard deviations. An easy and simple method to calculate the SRC of an independent variable is to multiply the corresponding RC

Table 3 Regression Statistics.

Fig. 11. Specific heat effect on effectiveness under turbulent flow conditions.

Confidence level Multiple R R2 Standard error

Laminar

Turbulent

95% 0.999218544 0.998437698 0.001042564

95% 0.99969971 0.999399511 0.002213527

584

M.T. Nitsas, I.P. Koronaki/Applied Thermal Engineering 100 (2016) 577–585

Table 4 Sensitivity Analysis results. Regression coefficients

Intercept φ γ α

Standardized RC

Standard error

Laminar

Turbulent

Laminar

Turbulent

Laminar

Turbulent

0.637438485 2.318137458 0.008854988 0.029216741

0.741418483 6.934797319 0.041035354 0.068897796

0.16306975 0.09500443 0.05523700

0.528609 0.477068 0.141146

0.001215857 0.024186045 0.000158526 0.000900742

0.00258146 0.05135079 0.00033658 0.00191242

(found after running a linear regression analysis) by its standard deviation (SD) and then divide by the standard deviation of the dependent (indicator) variable [52]. This new set of values found is the set of SRC’s that are comparable to one another, with the larger coefficient pointing to the independent variable with the greater influence on the dependent variable in question. The respective degree of influence, regardless of sign, could be found by arranging SRCs in a descending order of sensitivity. Judging by the information on Table 4, it is concluded that at a confidence level of 95%, the effectiveness of evaporators and condensers is influenced mainly by the volume fraction of nanoparticles while the type nanoparticle is important also, but at a secondary significance level. The remark above can be observed for both types of flow (laminar and turbulent).

Nu Re Pr f Bi E Rf

Nusselt number [Nu = h·D/k] Reynolds number [Re = ρ·u·D/μ] Prandtl number [Pr = μ·cp/k] Darcy fiction factor Coefficients of approximation function Enhancement of heat exchanger effectiveness Fouling factor [m2K/W]

Greek characters α Thermal resistance ratio [Rconvective/Rtotal] ε Heat exchangers effectiveness μ Dynamic viscosity [Pa·s] ρ Density [kg / m3] γ Ratio of nanoparticles density over base fluid density φ Nanoparticles volumetric fraction

6. Conclusions In this work, the impact of nanofluids as heat transfer fluids on HEX effectiveness was examined. The improvement of effectiveness due to presence of nanoparticles was determined under specific assumptions. The results of the analysis can be generalized for most of the commonly used nanofluids. It was found that nanoparticles enhance the effectiveness of HEXs and the enhancement is higher under laminar flow conditions. In addition, HEXs of low effectiveness benefit more from the presence of nanoparticles. As for the specific heat drop, it was concluded that the aforementioned drop leads to an increase of NTU and thus an increase of effectiveness. Moreover, the pressure drop was investigated through the Darcy friction coefficient. In addition, the heavier nanoparticles reduce the pressure drop and under turbulent flow the pressure losses are almost equal to those without nanoparticles. Finally, the presence of nanoparticles contributes in the minimization of HEX size since the HEX utilizing nanofluids needs less surface to exhibit the same effectiveness as it does with only base fluid. Acknowledgements The authors acknowledge with appreciation the Laboratory of Applied Thermodynamics, Thermal Engineering Section, School of Mechanical Engineering, National Technical University of Athens, for the support of the work on which this paper is based. Nomenclature Latin characters Pe Peclet number [Re·Pr] Heat capacities ratio [Cmin/Cmax] Cr cp Specific heat capacity [kJ/kg·K] k Thermal conductivity [W/m·K] U Overall heat transfer coefficient [W/m2·K] h Convective heat transfer coefficient [W/m2·K] A Surface area [m2] D Diameter [m] e Absolute tube roughness [m] L Tube length [m]

Subscripts f Base fluid/ heat transfer fluid p Particle nf Nanofluid A Fluid stream that changes phase Abbreviations HEX Heat exchanger HTC Heat transfer coefficient NTU Number of Transfer Units [NTU = U·A/Cmin] References [1] S. Choi, J. Eastman, Enhancing thermal conductivity of fluids with nanoparticles, in: International Mechanical Engineering Congress and Exposition, San Francisco, CA, 1995. [2] A. Ghadimi, R. Saidur, H. Metselaar, A review of nanofluid stability properties and characterization in stationary conditions, Int. J. Heat Mass Transf. 54 (2011) 4051–4068. [3] S. Lee, S. Choi, J. Eastman, Measuring thermal conductivity of fluids containing oxide nanoparticles, ASME J. Heat Transf. 121 (1999) 280–289. [4] C. Kleinstreuer, Y. Feng, Experimental and theoretical studies of nanofluid thermal conductivity enhancement: a review, Nanoscale Res. Lett. 6 (2011). [5] R. Vajjha, D. Das, A review and analysis on influence of temperature and concentration of nanofluids on thermophysical properties, heat transfer and pumping power, Int. J. Heat Mass Transf. 55 (2012) 4063–4078. [6] S. Murshed, K. Leong, C. Yang, Thermophysical and electrokinetic properties of nanofluids – a critical review, Appl. Therm. Eng. 28 (2008) 2109–2125. [7] S. Kakaç, A. Pramuanjaroenkij, Review of convective heat transfer enhancement with nanofluids, Int. J. Heat Mass Transf. 52 (13–14) (2009) 3187–3196. [8] J. Sarkar, A critical review on convective heat transfer correlations of nanofluids, Renew. Sustain. Energy Rev. 15 (2011) 3271–3277. [9] H. Dawood, H. Mohammed, K. Munisamy, Heat transfer augmentation using nanofluids in an elliptic annulus with constant heat flux boundary condition, Case Stud. Therm. Eng. 4 (2014) 32–41. [10] H.A. Mohammed, G. Bhaskaran, N.H. Shuaib, R. Saidur, Numerical study of heat transfer enhancement of counter nanofluids flow in rectangular microchannel heat exchanger, Superlattices Microstruct. 50 (3) (2011) 215–233. [11] I. Nkurikiyimfura, Y. Wang, Z. Pan, Heat transfer enhancement by magnetic nanofluids – a review, Renew. Sustain. Energy Rev. 21 (2013) 548–561. [12] B.H. Salman, H.A. Mohammed, A.S. Kherbeet, Numerical and experimental investigation of heat transfer enhancement in a microtube using nanofluids, Int. Commun. Heat Mass Transf. 59 (2014) 88–100. [13] I. Koronaki, M. Nitsas, Heat transfer analysis of a buoyancy-induced flow of nanofluids along a vertical hot plate – effect of nanoparticle type and diameter, in: International Mechanical Engineering Congress and Exposition, Montreal, Quebec, 2014.

M.T. Nitsas, I.P. Koronaki/Applied Thermal Engineering 100 (2016) 577–585

[14] B. Salman, H. Mohammed, A. Kherbeet, Heat transfer enhancement of nanofluids flow in microtube with constant heat flux, Int. Commun. Heat Mass Transf. 39 (8) (2012) 1195–1204. [15] M. Pantzali, A. Mouza, S. Paras, Investigating the efficacy of nanofluids as coolants in plate heat exchangers (PHE), Chem. Eng. Sci. 64 (14) (2009) 3290–3300. [16] M. Pantzali, A. Kanaris, K. Antoniadis, A. Mouza, S. Paras, Effect of nanofluids on the performance of a miniature plate heat exchanger with modulated surface, Int. J. Heat Fluid Flow 30 (2009) 691–699. [17] T. Mare, S. Halelfadl, O. Sow, P. Estelle, S. Duret, F. Bazantay, Comparison of the thermal performances of two nanofluids at low temperature in a plate heat exchanger, Exp. Therm. Fluid Sci. 35 (8) (2011) 1535–1543. [18] B. Farajollahi, S. Etemad, M. Hojjat, Heat transfer of nanofluids in a shell and tube heat exchanger, Int. J. Heat Mass Transf. 53 (1–3) (2010) 12–17. [19] G. Huminic, A. Huminic, Heat transfer characteristics in double tube helical heat exchangers using nanofluids, Int. J. Heat Mass Transf. 54 (19–20) (2011) 4280–4287. [20] A. Kabeel, T.E. Maaty, Y.E. Samadony, The effect of using nano-particles on corrugated plate heat exchanger performance, Appl. Therm. Eng. 52 (2013) 221–229. [21] A. Jokar, S. O’Halloran, Heat transfer and fluid flow analysis of nanofluids in corrugated plate heat exchangers using computational fluid dynamics simulation, J. Therm. Sci. Eng. Appl. 5 (1) (2013) p. art. no. 011002. [22] J. Eastman, S. Phillpot, S. Choi, P. Keblinski, Thermal transport in nanofluids, Annu. Rev. Mater. Res. 34 (2004) 219–246. [23] O. Mahian, Performance analysis of a minichannel-based solar collector using different nanofluids, Int. Commun. Heat Mass Transf. 41 (2014) 41–46. [24] R. Vajjha, D. Das, Specific heat measurement of three nanofluids and development of new correlations, ASME J. Heat Transf. 131 (7) (2009) 1601– 1607. [25] D. Kulkarni, R. Vajjha, D. Das, D. Oliva, Application of aluminum oxide nanofluids in diesel electric generator as jacket water coolant, Appl. Therm. Eng. 28 (2008) 1774–1781. [26] D. Shin, D. Banerjee, Enhancement of specific heat capacity of high-temperature silica-nanofluids synthesized in alkali chloride salt eutectics for solar thermalenergy storage applications, Int. J. Heat Mass Transf. 54 (2011) 1064– 1070. [27] A. Starace, J. Gomez, J. Wang, S. Pradhan, G. Glatzmaier, C. Greg, Nanofluid heat capacities, J. Appl. Phys. 100 (2011) 1–5. [28] M. Ghazvini, M. Akhavan-Behabadi, E. Rasouli, M. Raisee, Heat transfer properties of nanodiamond-engine oil nanofluid in laminar flow, Heat Transfer Eng. 33 (2011) 525–532. [29] K. Khanafer, K. Vafai, A critical synthesis of thermophysical characteristics of nanofluids, Int. J. Heat Mass Transf. 54 (2011) 4410–4428. [30] B. Pak, Y. Cho, Hydrodynamic and heat transfer study of dispersed fluids with submicron metallic oxide particles, Exp. Heat Transf. 11 (1998) 151– 170. [31] M. Chandrasekar, S. Suresh, A.C. Bose, Experimental investigations and theoretical determination of thermal conductivity and viscosity of Al2O3/water nanofluid, Exp. Therm. Fluid Sci. 35 (2010) 210–216.

585

[32] C. Li, G. Peterson, The effect of particle size on the effective thermal conductivity of Al2O3–water nanofluids, J. Appl. Phys. 101 (2007) 44312–44315. [33] X. Zhang, H. Gu, M. Fujii, Effective thermal conductivity and thermal diffusivity of nanofluids containing spherical and cylindrical nanoparticles, J. Appl. Phys. 100 (2006) 1–5. [34] J. Koo, C. Kleinstreuer, A new thermal conductivity model for nanofluids, J. Nanopart. Res. 6 (6) (2004) 577–588. [35] H. Patel, T. Sundararajan, S. Das, An experimental investigation into the thermal conductivity enhancement in oxide and metallic nanofluids, J. Nanopart. Res. 12 (2010) 1015–1031. [36] R. Vajjha, D. Das, P. Namburu, Numerical study of fluid dynamic and heat transfer performance of Al2O3 and CuO nanofluids in the flat tubes of a radiator, Int. J. Heat Fluid Flow 31 (2010) 613–621. [37] C. Li, G. Peterson, Experimental investigation of temperature and volume fraction variations on the effective thermal conductivity of nanoparticle suspensions (nanofluids), J. Appl. Phys. 99 (8) (2006) 84314–84318. [38] R. Hamilton, O. Crosser, Thermal conductivity of heterogeneous two component systems, Ind. Eng. Chem. Fundamen. 1 (3) (1962) 187–191. [39] F. Wasp, Solid–Liquid Slurry Pipeline Transportation, Transactions on techniques Publications, Berlin, 1977. [40] H. Brinkman, The viscosity of concentrated suspensions and solution, J. Chem. Phys. 20 (1952) 571–581. [41] S. Maiga, S. Palm, C. Nguyen, G. Roy, N. Galanis, Heat transfer enhancement by using nanofluids in forced convection flows, Int. J. Heat Fluid Flow 26 (2005) 530–546. [42] J. Koo, C. Kleinstreuer, Laminar nanofluid flow in micro-heat sinks, Int. J. Heat Mass Transf. 48 (13) (2005) 2652–2661. [43] J. Buongiorno, Convective transport in nanofluids, ASME J. Heat Transf. 128 (2006) 240–250. [44] F. Incropera, D. Dewitt, Fundamentals of Heat and Mass Transfer, 5th ed., John Wiley & Sons, Hoboken, NJ, 2001. [45] M. Bond, Plate heat exchangers for effective heat transfer, Chem. Eng. 367 (1981) 162–167. [46] W. Focke, J. Zachariades, I. Olivier, The effect of the corrugation inclination angle on the thermohydraulic performance of plate heat exchangers, Int. J. Heat Mass Transf. 28 (1985) 1469–1479. [47] W. Duangthongsuk, S. Wongwises, An experimental study on the heat transfer performance and pressure drop of TiO2–water nanofluids flowing under a turbulent flow regime, Int. J. Heat Mass Transf. 53 (2010) 334–344. [48] R. Vajjha, D. Das, D. Kulkarni, Development of new correlations for convective heat transfer and friction factor in turbulent regime for nanofluids, Int. J. Heat Mass Transf. 53 (2010) 4607–4618. [49] S. Maiga, C. Nguyen, N. Galanis, G. Roy, T. Mare, M. Coqueux, Heat transfer enhancement in turbulent tube flow using Al2O3 nanoparticle suspension, Int. J. Numer. Methods Heat Fluid Flow 16 (3) (2006) 275–292. [50] S. Haaland, Simple and explicit formulas for the friction factor in turbulent flow, J. Fluids Eng. 103 (1983) 89–90. [51] W. Fox, P. Pritchard, A. McDonald, Introduction to Fluid Meachanics, 7th ed., John Wiley & Sons, Hoboken, NJ, 2010, p. 754. [52] J. Bring, How to standardize regression coefficients, Am. Stat. 48 (1994).