Numerical simulation of nanofluid application in a horizontal mesh heat pipe with multiple heat sources: A smart fluid for high efficiency thermal system

Accepted Manuscript Title: Numerical simulation of nanofluid application in a horizontal mesh heat pipe with multiple heat sources: A smart fluid for high efficiency thermal system Author: P.R. Mashaei, M. Shahryari, H. Fazeli, S.M. Hosseinalipour PII: DOI: Reference:

S1359-4311(16)30254-X http://dx.doi.org/doi: 10.1016/j.applthermaleng.2016.02.111 ATE 7840

To appear in:

Applied Thermal Engineering

Received date: Accepted date:

15-9-2015 27-2-2016

Please cite this article as: P.R. Mashaei, M. Shahryari, H. Fazeli, S.M. Hosseinalipour, Numerical simulation of nanofluid application in a horizontal mesh heat pipe with multiple heat sources: A smart fluid for high efficiency thermal system, Applied Thermal Engineering (2016), http://dx.doi.org/doi: 10.1016/j.applthermaleng.2016.02.111. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Numerical simulation of nanofluid application in a horizontal mesh heat pipe with multiple heat sources: A smart fluid for high efficiency thermal system P.R. Mashaei1*, M. Shahryari 2, H. Fazeli3 and S.M. Hosseinalipour4 1

Young Researchers and Elite Club, Yadegar-e-Imam Khomeini (RAH) Branch, Islamic Azad University, Tehran, Iran

2

Thermal Control Division, Communication Satellites Research Institute, Ministry of Communications and Information Technology, Tehran, Iran

3

Institute of Mechanics and Manufacturing Technology, Malek-Ashtar University of Technology, Tehran, Iran

4

School of Mechanical Engineering, Iran university of Science and technology, Tehran, Iran

*Address: Tehran-Qom highway, Yadegar Emam Complex, Tehran, Iran, P.O BOX: 3319118651 Phone: 0982155229252 Fax: 0982155229297 Email addresses: *P.R.Mashaei: [email protected] M. Shahryari: [email protected]

H.Fazeli: [email protected] S.M.Hosseinalipour: [email protected]

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Highlights     

Thermal performance of a cylindrical heat pipe using nanofluid is investigated. The use of nanoparticles decreases the wall temperature, especially on hot spots. The effect of nanofluid becomes more effective for higher imposed heat load. The use of nanfluid is more beneficial as porosity of wick structure increases. Hydrothermal features of heat pipe improve using nanoparticles with smaller size.

Abstract A numerical study is carried out to investigate the effects of aqueous Al2O3 nanofluids on the hydrothermal performance of a cylindrical heat pipe with discrete heat sources (evaporators), as high efficiency heat exchanger. The effects of heat load (Q= 14, 28, 56 and 112W) and nanoparticle volume fraction (

= 0, 2.5, 5 and 0.075%) on the temperature and velocity fields, pressure drop and thermal

performance of heat pipe are investigated. The more uniformity of wall temperature can be obtained as basefluid is replaced by nanofluid. Moreover, the higher impact of nanoparticle on the wall temperature reduction is found on the heat sources where the highest values of temperature occur and hence more heat should be removed. This useful feature of nanofluid indicates its potential as smart fluid in heat pipes. The values of velocity and pressure drop in wick structure decrease and increase, respectively, as particle volume fraction increases. The influence of nanoparticles on both thermal and hydraulic performance of heat pipe become more pronounced as porosity of wick structure and particle size, respectively, increases and decreases. Finally, the thermal-hydraulic performance of heat pipe is analyzed. It is found that the best performance occurs at

=5% and Q=112W.

Keywords: Cylindrical Heat pipe, Nanofluid, Multiple heat sources, Thermal-hydraulic performance, Pressure drop

1. Introduction Heat pipes have been extensively used for decades because of their ability to dissipate substantial amount of heat from wide range of engineering systems in a limited temperature difference. In addition, they operate without any external energy source because of their self-pumping feature. Due to positive impacts of this feature on power consumption, operating noise, and reliability

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concerns, heat pipes are known as high-efficiency and favorite heat exchanger. As the heat sources in engineering systems are often arranged in a column or row, a heat pipe with multiple heat sources is of high significance in cooling application. In such situation, each heat source acts as an evaporator and the heat source with high load is placed near condenser to obtain better temperature uniformity [1]. Despite the beneficial characteristics of heat pipes, their ability can be restricted by poor thermal properties of conventional coolant such as water, ammonia and ethylene glycol. To overcome such problem, the thermal properties of working fluids should be enhanced. Because of advanced manufacturing processes, the production of extremely tiny particle has been possible since 1990s. Based on this achievement, Choi [2] proposed a new class of nanofluid, called “nanofluid”. Nanofluid is a suspension of extremely tiny nanoparticles (10100 nm) in conventional cooling fluids. The material of these nanoparticles can be typically made of metals, oxides, carbides, or carbon nanotubes. Due to high values of thermal conductivity of solid particles and their Brownian motion, the thermal conductivity of nanofluids is considerably better than that of conventional fluids. With respect to useful features of nanofluid as a heat transfer medium, the application of nanofluids in various heat pipes has been analyzed by many researchers [3-17]. Some of these studies have been summarized by Alawi et al. [18], Sureshkumar et al. [19], and Liu and Li [20]. Shafahi et al. [3, 4] developed an analytical model to study the effect of nanoparticle on thermal performance in both cylindrical and flat-shaped heat pipes. They reported that the thermal resistance of heat pipes decreases as nanofluids is used and there is an optimum mass concentration for nanoparticles in maximizing the heat transfer limit. Alizad et al. [5] analyzed transient behavior and operational start-up characteristics of flat-shaped heat pipe at the presence of nanoparticle and established that for the same heat load a smaller size heat pipe can be used 3 Page 3 of 33

when using nanifluid. Tsai et al. [6] investigated experimentally that the size of gold nanoparticles can play an important role on the reduction of thermal resistance of vertical meshed heat pipe. An experimental study was performed by Shukla et al. [7] to evaluate the effect of cu-water and Ag-water nanofluid on the performance of a cylindrical heat pipe. Results showed that the wall temperature reduction and heat pipe efficiency enhancement are 3-27 C and 14%, respectively, as compared with heat pipe filled the base fluid. Solomon et al. [8-9] studied the thermal performance of heat pipe at the presence of Cu nanoparticles both experimentally and numerically. It is observed 40% heat transfer coefficient enhancement at evaporator section. Also, numerical results revealed that the liquid and vapor velocities of the heat pipe charged with 0.1 wt% of Cu-water nanofluid is about 20% higher when compared with that of heat pipe with DI water at the same operating conditions. Some researchers [10-12] investigated the heat transfer of thermosyphon heat pipe using nanofluids as working fluids. It was found that the volume fraction of nanofluid has a significant effect in reducing the temperature difference between condenser and evaporator. Also, the thermosyphon heat pipes using the nanofluids show better thermal performance that the thermosyphon heat pipes using distilled water. Experiments for applying CuO nanoparticles dispersed in DI water to a copper sintered wick heat pipe are carried out by Kumaresan et al. [13]. They observed a reduction in the thermal resistance and enhancement in the heat transfer coefficient and thermal conductivity of 66.1%, 29.4% and 63.5%, respectively, for 1.0 wt. % of CuO-water nanofluid at 45º tilt angle compared with heat pipe kept at horizontal position. Kole and Dey [14] evaluated experimentally the effect of Cu-distilled water nanofluid on the thermal performance of a screen mesh wick heat pipes for various inclinations. It is found that

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the average evaporator wall temperature using nanofluid is reduced in comparison with those obtained by distilled water and vertical heat pipes operate better that at other inclinations. Chen et al. [15] conducted an experimental study to investigate the thermal performance of a new type of copper wire-bonded flat heat pipe using water, ethanol and nanofluids as working fluids. Results revealed that the use of nanofluid can improve the heat transfer performance of the heat pipe and the best heat transfer performance of heat pipe is achieved at the concentration of 1.0 wt. % under different saturation temperature conditions and nanofluid types. Hung et al. [16] showed experimentally that the effect of nanoparticles on the thermal performance of heat pipes depends on their length. These authors used aqueous suspension of alumina nanoparticle with three concentrations (0.5, 1.0, and 3.0 wt. %). Kumaresan et al. [17] carried out several experiments to compare the enhancement in the thermal performance of sintered and mesh wick heat pipes. They observed that the reduction in thermal resistance of sintered wick heat pipe is 13.92% higher compared with mesh wick heat pipe under identical conditions. Due to high importance of heat pipes with discrete heat sources in cooling of electronic components, several researchers [1, 21-25] investigated these heat pipes both theoretically and experimentally. The operation of a heat pipe with two heat sources studied by Park [1] both numerically and experimentally to optimize the heat distribution of satellite equipment. The results showed that the best performance can be obtained by locating the higher heat dissipating equipment closer the condenser.

Chen and Faghri [21] studied numerically the overall

performance of heat pipe with single and multiple heat sources and reported that the vapor temperature along the heat pipe remains approximately uniform. Noh and Song [22] carried out a numerical study to predict the characteristics on the transient operation of heat pipe with multiple

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evaporators and stated that the temperatures of each heater reach to 90% of the whole temperature within 50% of whole transient time with an exponential manner. Shabgard and Faghri [23] and Aghvami and Faghri [24] carried out an analytical study for cylindrical and flat heat pipes, respectively. The various heating and cooling configurations with considering the coupling between the two-dimensional conduction in the wall, vapor flow and liquid flow in wick structure were considered by these authors. Lefevre and Lallemand [25] proposed a three dimensional analytical model to investigate velocity, pressure and temperature fields in a micro flat heat pipe with various heat sources and heat sinks. To the best of our knowledge, no studies have been found in the literature on numerical simulation of nanoparticles in heat pipes with discrete heat sources. This motivates the present study, where the main objective is to investigate the potential of nanofluid, as a smart fluid, in the performance of a cylindrical heat pipe with multiple evaporators. The numerical modeling of Gaya and Goldak [2] is modified to incorporate the presence of a nanofluid within the heat pipe. It is

hoped that the present numerical findings will motivate more researchers to perform experiment on nanofluids in the heat pipes with multiple discrete heat sources.

2. Problem description 2.1. Definition of configuration The schematic of a cylindrical heat pipe with two evaporators is shown in Fig. 1. Heat imposed at the evaporator sections results in vaporization and later pressurization of the working fluid. The vapor flows toward the condenser section. At the condenser section, the vapor is converted 6 Page 6 of 33

to liquid by removing its heat latent, and hence enters into wick structure. Finally, the working cycle of heat pipe is completed by returning liquid to evaporator sections, which is carried out by means of capillary force of the wick structure. Based on the experimental data obtained by Park [1], a more temperature uniformity can be achieved as the evaporator with higher heat load is located near the condenser. Therefore, in the present study the heat load of second evaporator (

) is considered 1.33 times than that of first evaporator (

).

2.2.Assumptions made The formulation model used in this paper is based on the following assumptions: 

For a heat pipe to function properly, meaning without occurring the dry-out and flooding phenomenon, the capillary pressure must be bigger than the summation of all pressure drops occurring throughout the liquid and vapor flow paths. Moreover, some physical limitation such as sonic and boiling limits should be considered. In the present study, therefore, it is assumed that the surface tension is great enough to provide suitable capillary pressure, the velocity of vapor dose not reach the velocity of sound and the input heat flux is sufficient to prevent occurring nucleate boiling in wick structure.



The vapor is considered to be saturated. So, a constant temperature is applied on liquidvapor interface. This assumption is correct when the heat pipe is working at the low temperature condition (Less than 400K), as used in several previous works [26-30].



The liquid flow in wick structure is considered steady state, incompressible and Newtonian.



External body forces such as gravity are negligible.

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

The cooling process of condenser section is carried out by water entering into cooling jacket from the end of heat pipe. In this situation, the wall temperature at the end of heat pipe can be considered approximately fixed and independent of heat load and particle volume fraction, as can be seen in the experimental study of Putra et al. [31], Park [1], and Sarafraz and Hormozi [32].



The nanoparticles distribution throughout the porous region is considered uniform and constant.



The nanoparticles can follow the vapor and liquid flows and are in thermal equilibrium with them.



As the pressure variation is small, the vapor temperature at the interface obtained from the Clausius-Clapeyron equation is nearly uniform. So, a uniform vapor temperature assumption is reasonably satisfactory [26]. Based on this fact, the energy equation for vapor region has not been solved in several previous studies [3-5, 27-28]. Therefore, the conservation equations of vapor flow are not considered in the present study because the heat pipe operates at low temperature. However, this assumption is not valid for hightemperature as demonstrated by Cao and Faghri [33], and the energy equation for vapor flow should be taken into account.

2.3.Governing equations Based on the assumptions described above, the basic conservation equations of mass, momentum and energy can be expressed in the following manner: Continuity equation: (1)

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Momentum equation in

(2)

direction:

(3)

Momentum equation in

direction:

(4)

Energy equation in porous medium: (5)

Energy equation in wall: (6)

in which ρ, ,

, K, k, cp and µ respectively are density, porosity, Forchheimer coefficient,

permeability, thermal conductivity, specific heat and dynamic viscosity. Furthermore, v , T and P represent velocity, temperature and pressure, respectively and subscript “nf” refers to nanofluid. The porosity of screen mesh wick ( ), Forchheimer coefficient ( ), permeability (K) and effective thermal conductivity (

) of porous medium can be calculated by following

expressions [34]: (7)

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(8)

(9)

(10)

where N,

and

are number of mesh, wire diameter and solid matrix thermal conductivity of

wick structure, respectively. 2.4. Boundary conditions To solve the conservation equations, the suitable boundary conditions corresponding to the correct operating conditions of heat pipe should be adopted, which can be written as: (11)

(12)

(13)

(14)

(15)

(16)

(17)

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(18)

Where

,

and

are heat flux, latent heat of evaporation and interfacial evaporation/

condensation mass flow rate, respectively. In addition, subscripts “e”, “a” and “c”, respectively, refer to evaporator, adiabatic and condenser sections. While the heat pipe operates at the lowtemperature conditions (Less than 400K), the temperature variation in vapor region is negligible as experimentally and theoretically addressed by several works [26-29]. Under such conditions, the working fluid can be considered as saturated vapor sate. Practically, this state can be obtained by adjusting vacuum pressure (working pressure) in the vapor region at the end of evaporator section. Generally, the Clausius-Clapeyron equation is used to calculate the vapor temperature from the saturation vapor pressure at the interface for a given reference pressure, temperature,

( where

, and

:

)

(19)

is gas constant. Because the pressure variation in the vapor region is negligible, the

vapor temperature at the interface calculated from Clausius-Clapeyron equation is approximately uniform. In the present study, the saturation (or reference) temperature has been chosen by the iterative method as follows. The first simulation is carried out by initial saturation temperature (Tsat =320K). Then, the energy equation in porous region is solved and the saturation temperature is calculated by wall temperature in the condenser section and thermal resistance model, as presented by Zhu and Vafai [27]: (20)

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in which

refers to average temperature of wall in condenser section where is in contact

with coolant. This procedure repeats until the difference of saturation temperatures obtained from two successive iterations become less than 0.1%. 2.5. Effective properties The density and specific heat of a liquid suspension of nanoparticles can be calculated as follows [35]: density: (21) Specific heat: (22) Where

is nanoparticle concentration level and subscript “ ” refers to nanoparticle.

A great number of experimental studies were carried out to investigate the dynamic viscosity of nanofluids with various types, volume fractions and diameters of nanoparticles over a wide range of temperature. Based on data presented in some of these studies [36-47], Corcione [48] concluded that the ratio of viscosity of nanofluid to that of base fluid (

) is approximately

independent of temperature and can be obtained by: (23)

in which

denote the diameter of nanoparticle. Also,

is the equivalent diameter of base fluid

molecule and calculated by

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(24) where

,

, and

are the molecular weight of the base fluid, the Avegadro number and the

mass density of the base fluid calculated at the temperature of 293K. The dynamic viscosity of base fluid,

, for distilled water depends on the temperature and given by [49] (25)

To have a more accurate results in our simulation, it is better to apply a correlation which considers the effect of temperature and particle diameter as well as particle concentration level. .Based on this perspective and using experimental data provided by different authors [36,37,5057], Corcione [48] proposed the following empirical correlation: (26)

Where

,

represent the Prandtl number and freezing point of the base fluid. Also, Re is the

nanoparticle Reynolds number which is given by: (27)

in which

is Boltzmann’s constant. In the Eq. 15, the thermal conductivity of base fluid,

,

is a function of temperature , given by [58]: (28) 3. Numerical technique and code validation A computer code in FORTRAN is developed to solve the conservation equations (1)-(6) alongside their boundary conditions using control volume. The power law scheme is applied to

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discrete energy and momentum equations. The SIMPLE procedure is used to couple pressure and velocity fields. The solution converges when the normalized residuals for all equations reach 106

. The well-known tridiagonal matrix algorithm (TDMA) technique is chosen to solve algebraic

discretized equations. To test the grid independence of numerical solution, three grid densities are investigated. The effect of grid size on wall temperature is shown in Fig. 2 for a typical case. As it can be seen, a grid density of 200x20 provides an accurate solution for typical solution. In order to verify the precision of the present numerical results, two comparisons are made between the present data and those reported in the literature experimentally. The first comparison is related to the analysis of a cylindrical with two evaporators, given by Park [1]. The working fluid is water and the length and diameter of heat pipe are 0.45m and 0.0158m, respectively. Also, the length of evaporator and adiabatic sections are chosen 0.1m and 0.5m, respectively. The heat load of 29W is imposed on each evaporator. The wall temperature distribution along heat pipe is compared with the experimental data given by Park [1], as shown in Fig. 3. It is clear that the present results are in a good agreement with those reported in ref. [1]. Due to the absence of information related to the use of nanofluid in a heat pipe with multiple heat sources, the second comparison is concerned with the experimental study of Al2O3/water in a cylindrical heat pipe with only one evaporator, presented by Putra et al. [31]. So, the present boundary conditions are considered by setting a zero heat flux on the second evaporator. The length, the outer diameter, and the inner diameter of heat pipe are 0.2m, 0.008m and 0.00 744m, respectively. The wick structure is four layers of screen mesh with a wire diameter 56.5 µm and the volume fraction of 4% is considered for this comparison. Fig. 4 shows a remarkable agreement between numerical results on the wall temperature and those provided by Ref. [31].

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4. Results and discussion To analyze the hydrothermal performance of Al2O3/water nanofluid inside a cylindrical heat pipe with two evaporators, the temperature, pressure and velocity fields throughout wick structure as main part of a heat pipe are obtained. In addition, in order to evaluate the thermal performance of heat pipe, the values of wall temperature are calculated. The effects of particle volume fraction and heat load on heat transfer rate and pressure drop are investigated. The effect of wick structure characteristics (i.e. porosity) and the particle size on the thermal performance of heat pipe is also studied. The heat load, particle volume fraction, porosity, thermal conductivity ratio and particle diameter are in the ranges of 14-112 W, 0-0.075%, 0.3-0.9 and 3-300, respectively. As the ratio of nanofluid thermal conductivity to that of base fluid is considered temperaturedependent, the variation of effective thermal conductivity along heat pipe plays significant role on thermal performance of heat pipe. Therefore, before discussing about velocity, pressure and temperature fields, the local effective thermal conductivity of wick structure using both Al2O3/water nanofluids and base fluid (i.e. water) is illustrated in Figure 5. The data are given for various particle volume fractions by fixing the heat load and wick structure characteristics. It is observed that the effective thermal conductivity of wick structure increases as the Al2O3/water nanofluids with higher particle volume fraction are used. Moreover, the variation of effective thermal conductivity is more pronounced along heat pipe while nanofluid is used instead of base fluid. This is due the fact that the temperature variation has more effect on nanofluid conductivity and thus effective conductivity of porous medium when compared to base fluid. Another important feature of Figure 5 is that in spite of lower temperature variation along heat pipe (will be explained later) for the nanofluids with higher Al2O3 nanoparticles concentration,

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they show more variation in effective conductivity. This is because the dependency of the Al2O3/water nanofluid on temperature increases as more nanoparticles are added. Figure 6 depicts the absolute values of axial velocity along wick structure for different particle volume fractions, as representative cases. As evident from this figure, the reduction in the axial velocity is observed when nanofluid is applied in heat pipe as a substitute of base fluid. Moreover, due to higher density, the axial velocity decreases as particle volume fraction increases. For both cases of base fluid and nanofluid, the maximum values of velocity occur at the adiabatic section near the condenser and axial velocity profiles become flatter in the adiabatic section located between two evaporators, where less mass flow rate exits from wick structure because of lower temperature gradient on liquid-vapor interface. In order to have a good understanding of the combined effect of nanoparticles and heat load on axial velocity, the relative maximum axial velocity profiles, referred to those calculated for base fluid, are illustrated in Figure 7. According to this figure, one can see that the particle volume fraction has a significant role on the reduction of axial velocity while the values of relative axial velocity increase slightly as heat load increases. As discussed earlier, the considerable increment of liquid velocity with particle volume fraction can be attributed to higher density. A similar result has also previously reported by Shafahi et al. [3] for a cylindrical heat pipe. According to equation (16), it is clear that the inlet and outlet velocity on liquid-vapor interface can be affected by effective thermal conductivity of wick structure. Although the increase of effective thermal conductivity can lead to high velocity, it decreases gradient temperature on liquid-vapor interface which is a reducing factor for mas flow rate in porous media. When heat load and thus temperature increases, the effective thermal conductivity of wick structure filled with nanofluids rises more considerable in comparison with the situation in which base fluid is applied. On the 16 Page 16 of 33

other hand although the temperature gradient decreases, the effect of increased thermal conductivity is more pronounced than that. This is why the relative velocity in wick structure increases as more heat load is imposed on heat pipe. In order to operate a heat pipe properly, it is necessary that capillary pressure overcomes the overall pressure drop throughout vapor and liquid regions. As the liquid pressure drop is much more than that of vapor, only pressure drop in wick structure is discussed. The liquid pressure distribution along the axial direction of porous medium is shown in Figure 8. The results are provided for different values of particle volume fractions as . Despite the reduced velocity of nanofluids may decreases the value of pressure, its increased dynamic viscosity plays dominant role on pressure field, and consequently the absolute value of pressure increases using nanofluid. Figure 9a depicts the liquid pressure drop as a function of heat load and particle volume fraction. With respect to this figure, pressure drop in the wick structure increases as volume fraction and heat load rise. While the increased viscosity is the reason of the pressure drop increment for higher volume fraction, the pressure drop increases with the augmentation in heat load because of the increased velocity. As we are also interested to quantify the pressure drop increment in comparison with base fluid, the pressure drop ratio, defined as the nanofluid pressure drop to basefluid one, is shown in Figure 9b. It is observed that as more nanoparticles are added in base fluid, higher pressure drop in wick structure occurs as compared with basefluid. Moreover, the pressure drop ratio profiles rises slightly as heal load increases. This trend can be explained by increased relative axial velocity (See figure 7). That is, for higher heat load and thus temperature, the nanofluid with each particle volume fraction flows with higher velocity as compared to base fluid under identical condition. Consequently, the pressure drop ratio increases as the nanoparticles are applied in heat pipe with higher heat load. 17 Page 17 of 33

The wall temperature variations along axial length of heat pipe are depicted in Figure 10. The results are given for different volume fraction by fixing heat load, particle diameter and porosity of wick structure. It is shown that the surface temperature decreases in evaporator and adiabatic sections as particle concentration increases. Moreover, the more temperature uniformity can be obtained as nanofluids are utilized instead of basefluid. That is, the same heat load can be transferred in lower temperature difference. Another point that can be seen in Figure 10 is that the use of nanofluid has more pronounced effect on the hot spots where the highest values of temperature occur. For example, while base fluid is applied, the maximum surface temperatures of first and second evaporators are 338.9K and 336.75K, respectively, and the minimum surface temperature of adiabatic section between two evaporators is 333K. The addition of 8% Al2O3 nanoparticle in basefluid decreases the maximum surface temperature of first and second evaporators 7.92K and 6.85K, while the minimum temperature of surface decreases 5K. This intelligent behavior of the Al2O3/water nanofluid is due to their temperature-dependent thermal conductivity which is in full accordance with what was previously observed by Mashaei et al. [59, 60] for the application of nanofluid in the cooling of discrete heat sources located in various geometries and media. Such useful feature of nanfluid may provide this possibility to apply them as a smart fluid in the application of heat pipe with discrete heat sources. As the goal of a heat pipe is to remove heat loads from heat sources, the evaporator heat transfer coefficient (EHTC) is of great significance, which is defined as the ratio of the heat flux to the difference between mean evaporator wall temperature and saturated temperature. The average ETHC (

) for a heat

pipe with two evaporators can be calculated by:

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(29)

Due to increased thermal conductivity, the use of nanofluids instead of basefluid have considerable positive effect on heat transfer rate in evaporator section, as can be seen in Figure 11a where the values of

are given for various particle volume fractions and heat loads.

Further, an increase in heat transfer rate can be observed as heat load increases. This is due the fact that nanofluids provide a better heat transfer medium in high temperature. Because of this superior characteristic, the nanofluid under study is called “smart fluid”. That is, the nanofluid is able to smartly and automatically act in a heat pipe and shows more pronounced effect on heat transfer enhancement in which more amount of heat load should be removed from system. The combined effect of volume fraction and heat load on thermal performance of evaporators sections can be more clearly understood from Figure 11b in which the relative average ETHC, referred to value calculated for base fluid, are provided as function of heat load for different various heat loads. It is shown that the particle volume fraction has more pronounced influence on heat transfer enhancement in evaporators sections compared to other sections of heat pipe. The thermal resistance in wick structure is well-known as a criterion to evaluate the thermal performance of heat pipe, which is defined:

(30) in which

and

are average wall temperate over evaporators and condenser sections,

respectively. Thermal resistance and relative thermal resistance (i.e. the ratio of nanofluid thermal resistance to that of base fluid) versus heat load are shown in Figure 12 for various particle volume fraction. According to Figure 12a, thermal resistance of wick structure and thus 19 Page 19 of 33

heat pipe decreases as heat load and particle volume fraction increases which can be attributed to temperature-dependent and increased thermal conductivity, respectively. Furthermore, it is observed from Figure 12b that all values of relative thermal resistance are less than unit which indicates the positive impact of nanofluid on the thermal performance of heat pipe. Another interesting feature of Figure 12b is that the relative thermal resistance decreases with heat load for all volume fractions. This behavior is due the fact that the nanofluid thermal conductivity is more dependent to the temperature comparing with basefluid, as can be understood by the slope of profiles in Figure 12a. The main achievement of decreased thermal resistance of heat pipe is that the same heat load can be transferred in heat pipe with the smaller heat transfer surfaces, and thus a heat transfer designer can reduce the size of heat pipe under identical conditions. The effect of nanofluid on downsizing of heat pipe is depicted in Table 1. In this table,

refers to the length of heat pipe

without using nanofluid and the results are given for various volume fractions and heat loads. It is apparent from this table that the smaller size heat pipes can be designed as particle volume fraction and heat pip increase. Moreover, the influence of volume fraction on the size reduction of heat pipe is more remarkable than that of heat load. This is because the heat load affects slightly the heat transfer only due to temperature-dependent thermal conductivity of nanofluid. In fact, no variation in in the size of the heat pipe with the temperature can be certainly seen if only thermal conductivity depends on the particle concentration level, as addressed by Shafahi et al. [3]. So far, only the effects of particle volume fraction and heat pipe on the hydrothermal performance of heat pipe have been explained. In this part of study, the effects of particle diameter and porosity of wick structure on thermal performance and pressure drop of heat pipe 20 Page 20 of 33

are discussed.

Figure 13 depicts the combined influence of nanoparticles and porosity on

relative thermal resistance and pressure drop. The particle volume fraction is chosen as 5%. One can see that the effect of nanofluid become more important as the porosity of wick structure increases. That is, the thermal resistance decreases more remarkably as nanofluids in a wick structure with higher porosity are applied. Further, the negative effect of nanofluid (i.e. increased pressure drop) is increased as the porosity of wick structure rises. This is due the fact that the porous medium contains more amount of nanofluid as the porosity and thus the number of pores increases. The effect of nanoparticle diameter on relative thermal resistance and pressure drop is illustrated in Figure 14 for a constant volume fraction (

). As it is clearly seen from this

figure, the use of nanoparticle with smaller size has more pronounced effect on the thermal performance of heat pipe at the expense of pressure drop increment. The addition of nanoparticles in base fluid can promote the thermal performance of heat pipe as well as pressure drop in wick structure. In order to have a good understanding from the effect of various parameters on both thermal and hydraulic performance of heat pipe, the thermalhydraulic performance factor is defined as follows: (31)

The value of 1/3 as the power of pressure drop ratio indicates that the thermal resistance reduction is of more important compared with pressure drop increment, as addressed by several researchers [59-61]. The effect of various parameter including heat load, particle concentration and diameter and porosity of wick structure on the thermal-hydraulic performance is shown in Fig. 15. With increasing heat load,

rises for all particle concentration, as one can see in Fig.

15a. This is due the fact that the higher heat load has more pronounced influence on the thermal 21 Page 21 of 33

resistance reduction in comparison to the increased pressure drop when nonofluid is used instead of base fluid. Another interesting point that can be seen from Fig. 15a is that there exists an optimum value for particle concentration level to present the best thermal-hydraulic performance in heat pipe. On the one hand the presence of low nanoparticles has lower effect on the thermal resistance, but on the other hand the nanofluid with higher nanoparticle concentration level increases the pressure drop considerably. Therefore, the best thermal-hydraulic performance occurs for middle particle concentration level (i.e. the porosity on

for

and

). Fig. 15b demonstrates the effect of

. It is clear that the

increase slightly as the wick

structure with higher porosity is applied. This behavior proves that although both positive and negative effects of nanofluid become more remarkable in a porous medium with higher porosity, the thermal resistance reduction, as positive effect of using nanofluid, plays more effective role. The influence of particle diameter on thermal-hydraulic performance is shown in Fig. 15c. One can see that that the addition of Al2O3 nanoparticles with smaller size in basefluid presents better performance in heat pipe. So far a heat pipe with two heat sources has been considered. In order to have more cases of numerical studies, a heat pipe with three heat sources is simulated. The effect of nanofluid on the wall temperature of such heat pipe is shown in Fig. 16. The numerical simulations are carried out for following cases: a) All heat sources are on, b) First heat source is off and remaining heat sources are on, c) Middle heat source is on and remaining heat sources are off.

One can see that, for both basefluid and nanofluid, the maximum temperature decrease as less

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number of heat sources are on. Moreover, the wall temperature decreases at the presence of nanoparticles. As we are also interested to quantify the effect of nanofluid on wall temperature, the reduced temperature is defined: (32)

The local reduced temperature for a heat pipe with three heat sources are shown in Fig. 17 for various cases. According to this figure, the best reduction occurs in which the heat sources are located. For example, while all heat sources are on, the minimum reduced temperatures related to heat sources and adiabatic parts are about 0.955 and 0.964, respectively. This proves that the role of nanofluid become more remarkable as the temperature rises. Another important point from Fig. 17 is that when the more number of heat sources are on, the reduced temperature decreases. That is, the nanofluid plays more significant role. Both these observations verify this claim that the nanofluid can be considered as a “smart” cooling fluid, meaning more heat automatically removed from heat sources at higher heat loads and temperatures. Although, it has been shown in the present study that nanofluid can be applied as smart fluid in the application of heat pipes with multiple evaporators and their positive effect on the heat transfer enhancement in these types of heat pipes has been discussed, more experimental and numerical studies are needed to be carried out in order to obtain a better knowledge for such applications of nanofluids. Moreover, as the nanoparticles distribution plays important role on the nanofluid properties and thus velocity, pressure and temperature fields, the nanofluid forced convection in porous medium can be investigated using two phase approaches. 5. Conclusion

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The present numerical study exhibits many interesting results concerning the effect of using Al2O3 nanoparticles on hydraulic and thermal performance of a cylindrical heat pipe with discrete heat sources. The following conclusions can be obtained from the present investigation. 

The temperature-dependent thermal conductivity of Al2O3-water nanofluids has a positive effect on wall temperature of heat pipe. On the heat sources, in which the highest values of wall temperature are detected and hence more heat should be removed, the thermal conductivity of nanofluid increases remarkable and a better condition for heat transfer enhancement is provided. Due to this useful feature of Al2O3-water nanofluid, it can be applied as smart fluid in a heat pipe with discreet heat sources.



Due to increased density, the axial velocity in wick structure of heat pipe decreases as base fluid is replaced by nanofluid. Furthermore, the particle volume fraction plays a significant role on relative axial velocity, reffered to values calculated for base fluid , while the values of relative axial velocity increase slightly as heat load increases.



As more nanoparticles are added in base fluid, higher pressure drop in wick structure occurs as compared with basefluid. Moreover, due to increased velocity, the pressure drop increases as more heat load is imposed on heat sources.



The use of nanofluids instead of basefluid has considerable positive effect on heat transfer rate in evaporator section. In addition, this effect becomes more pronounced in higher heat load in which more heat should be dissipated from heat sources. Thus, it is another reason why the nanoluid has been called “smart fluid” in the present study.



A significant reduction of thermal resistance is detected for heat pipe as Al2O3-water nanofluid with higher particle volume fraction is applied. Also, since the value of heat

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load increases the presence of nanoparticle plays more effective role on the reduction of thermal resistance of heat pipe 

Both positive (i.e. thermal resistance reduction) and negative (i.e. pressure drop increment) effects of using nanofluids become more significant as porosity of wick structure and nanoparticle diameter increases and decreases, respectively.



The best thermal-hydraulic performance of using Al2O3 nanoparicles in a heat pipe with discrete heat sources is found at middle particle concentration level (i.e.

) and

highest value of heat load. Further, since the wick structure with higher porosity is applied in heat pipe, the use of nanofluid plays more significant role on its thermalhydraulic performance. In addition, the use of nanoparticles with smaller size has more noticeable influence on the thermal-hydraulic performance.

Nomenclature Forchheimer coefficient

velocity vector (m/s)

specific heat (J/kg K)

coordinate system

diameter (m)

Greek Letters

diameter of wire in wick structure (m)

porosity

average evaporation heat transfer coefficient (W/m2 K)

Thermal-hydraulic parameter

latent heat of evaporation (J/Kg)

dynamic viscosity(Kg/m s)

thermal conductivity (W/m K)

density (Kg/m3)

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wick permeability (m2)

Nanoparticle volume fraction

Boltzmann’s constant

Subscripts

effective thermal conductivity in wick structure (W/m K)

average

molecule weight of the base fluid(Kg/mol)

base fluid

number of mesh in wick structure (1/m), Avogadro Number

condenser

pressure (Pa)

evaporator

Prandtl number of the base fluid

nanofluid

heat flux (W/m2)

outer

heat load (W)

particle

coordinate system

relative or ratio

radius (m), thermal resistance (K/W)

Solid matrix in wick structure

Reynolds number of nanoparticle

vapor

temperature (K)

wick-wall interface

freezing point of the base fluid(K)

wall Heat pipe wall

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Figure captions Fig. 1 A cylindrical heat pipe with two evaporators.

Saturated vapor ( )

Wick structure

Evaporator

Adiabatic

Evaporator

Wall

Adiabatic

Condenser

Fig. 2 Effect of grid density on the wall temperature distribution along heat pipe for Q=112W and φ=7.5%.

Fig. 3 Comparison of the wall temperature between present data and those obtained by Park [1] for a cylindrical heat pipe with two evaporators.

Fig. 4 Comparison of the wall temperature distribution between present simulation and experimental data [27] for water-Al2O3 nanofluid with φ=5%.

Fig. 5 Local effective thermal conductivity of wick structure for various particle concentration levels (Q=112W).

Fig. 6 Absolute values of axial velocity of liquid along the center line of wick structure (Q=112W). Fig. 7 Effect of particle concentration level and heat load on relative maximum axial velocity. Fig. 8 Liquid pressure distribution in wick structure for various particle concentration levels (Q=112W). 32 Page 32 of 33

Fig. 9 Effect of heat load and particle concentration level on: (a) pressure drop in wick structure, (b) pressure drop ratio in wick structure.

Fig. 10 Wall temperature distribution along heat pipe for various particle concentration levels (Q=112). Fig. 11 Effect of particle concentration level and heat load on: (a) average evaporation heat transfer coefficient, (b) relative average evaporation heat transfer coefficient.

Fig. 12 Effect of particle concentration level and heat load on: (a) thermal resistance, (b) relative thermal resistance

Fig. 13 Effect of porosity of porous medium on relative thermal resistance and pressure drop ratio for Q=112 and φ=5%.

Fig. 14 Effect of nanoparticle size on relative thermal resistance and pressure drop ratio for Q=112 and φ=5%.

Fig. 15 Effect of (a) nanoparticle concentration level and heat load, (b) porosity and (c) nanoparticle size on thermal-hydraulic performance.

Fig. 16 Wall temperature distribution along heat pipe with three heat sources for various particle concentration levels Fig. 17 Reduced wall temperature along heat pipe with three heat sources

Table captions Tab. 1 Effect of particle concentration and heat load on the size reduction of heat pipe

[%] 2 0.878375734 0.87259856 4 0.810937082 0.805077745 8 0.766369643 0.76080596

0.861494573 0.794297219 0.750773311

0.841969905 0.776897146 0.735198692

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