Flat heat pipes for potential application in fuel cell cooling

Applied Thermal Engineering 90 (2015) 848e857

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Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng

Research paper

Flat heat pipes for potential application in fuel cell cooling Marcos Vinício Oro*, Edson Bazzo Federal University of Santa Catarina, Mechanical Engineering Department, Laboratory of Combustion and Thermal Systems Engineering e LabCET,
polis, SC, Brazil 88040-900 Floriano

h i g h l i g h t s
Flat heat pipes as reliable alternatives for PEM fuel cells cooling.
The use of microgrooves for capillary pumping of the working fluid.
A useful tool for the design of PEMFC cooling systems.
Theoretical and experimental results of a 12 W flat heat pipe.
Heat pipes arrangement to ensure a suitable PEMFC operation.

a r t i c l e i n f o

a b s t r a c t

Article history: Received 21 January 2015 Accepted 18 July 2015 Available online 4 August 2015

A thin flat heat pipe is proposed as a reliable alternative for Proton Exchange Membrane Fuel Cell (PEMFC) cooling. The flat heat pipe includes a sealed casing with two microgrooves to provide the required capillary pumping of the working fluid. Deionized water was used as the working fluid. In this work, a numerical and experimental analysis is presented. A heat transfer model is proposed to evaluate the capillary limit, the operating temperature and the required working fluid inventory. The main goal is to cool the PEM fuel cells to ensure a suitable operation in the required temperature range between 70 and 90  C with small thermal gradient. The proposed control system consists of a set of stainless steel flat heat pipes, with 100 mm length, assembled in parallel. The tests showed that proposed heat pipe was able to dissipate up to 12 W, corresponding to 1.8 W/cm2 at evaporator section, ensuring a suitable PEMFC operation. © 2015 Elsevier Ltd. All rights reserved.

Keywords: PEMFC Fuel cell cooling Heat pipe Groove wick

1. Introduction The technical feasibility of proton exchange membrane fuel cell (PEMFC) still relies on technology solutions to solve problems associated with their operating limits. PEM fuel cells have a strong appeal in the use of automobiles, portable devices and even distributed electricity generation. Fuel cells work through an electrochemical process, converting the chemical energy of a substance into electrical energy. The PEM fuel cell is, basically, composed of two electrodes (anode and cathode) separated by an electrolyte (polymer membrane), which form the membrane electrode assembly (MEA). On the anode side hydrogen is supplied and dissociated, then the ions Hþ move through the membrane toward the cathode. Electrons flow externally through an electrical circuit up to the cathode side, where they recombine with Hþ ions and O2 to form H2O as the reaction * Corresponding author. E-mail address: [email protected] (M.V. Oro). http://dx.doi.org/10.1016/j.applthermaleng.2015.07.055 1359-4311/© 2015 Elsevier Ltd. All rights reserved.

product. In order to avoid problems related to the operation, the temperature needs to be in the range of 70e90  C, once an overheating leads to the membrane drying and corresponding collapse of the fuel cell. An existing 200 W Electrocell fuel cell in operation at LabCET was taken as reference in this work. Ten units 20 W fuel cells are combined to form the fuel cell stack. In this work, the efficiency was considered 50%. Therefore 20 W is the thermal power to be absorbed by the heat pipes in each unit cell. The stack dimensions are 55  140  170 mm. The commercial PEMFC cooling has been usually performed by forced convection of air or water. However, this technique can generate high thermal gradient inside the fuel cell, especially at high loads. Experiments have shown differences up to 23  C between the inlet and the outlet of a cooling channel and up to 10  C between channels [1]. One way to increase the performance of the cell is by reducing the temperature difference between the inlet and outlet of the cooling channels. Basically, this is achieved by managing the cooling fluid flow velocity [2e4]. The cooling

M.V. Oro, E. Bazzo / Applied Thermal Engineering 90 (2015) 848e857

Nomenclature a0 e a10 A C1, C2 d d* D1, D2 f FR H hlv k L Lx m m_ n N* P p q_ q_ el q_ th q00 r Rth Re T t u V Y

constants, Eq. (B.5) [e] cross-sectional area [m2] inner heat pipe dimensions [m] diameter [m] dimensionless diameter [e] outer heat pipe dimensions [m] friction factor [e] filling ratio [%] height [m] latent heat of vaporization [kJ/kg] thermal conductivity [W/(m K)] length [m] half-length of active area [m] mass [kg] mass flow rate [kg/s] fluid control volumes number [e] dimensionless area [e] pressure [Pa] perimeter [m] power [W] electric power [W] thermal power [W] heat flux [W/m2] radius [m] thermal resistance [K/W] Reynolds number [e] temperature [ C] wall thickness [m] velocity [m/s] volume [m3] half the spacing between heat pipes [m]

channels may be arranged in different ways, so the cell performance is maximized through the cells with higher temperature uniformity [5]. Some designs have been proposed as alternatives for conventional systems. Vasiliev and Vasiliev Jr. [6] presented several thermal management solutions, which could be applied in fuel cells of different sizes and powers. Among the proposed systems are mini and micro heat pipes, loop heat pipes, pulsating heat pipes and sorption heat pipes. The article only introduces the ability of each system. In patents applied by Faghri [7,8] there are two settings of bipolar plates for fuel cells, which utilize the heat pipe technology for thermal control, however no results were presented. Recently, a few papers have been presented with good results for different PEMFC thermal control ways. Joung et al. [9] proposed the use of a flat evaporator loop heat pipe (FELHP) comprising a bifacial wick. Two-phase heat spreaders (TPHS) have been prore et al. [10], where different TPHS types were posed by Rullie successful tested, including with longitudinal grooves. A combined system comprising a set of heat pipes coupled to a capillary pumped loop (CPL) was proposed by Silva et al. [11], using deionized water and acetone as the working fluid for heat pipes and CPL, respectively. The preliminary results reported by Oro and Bazzo [12] demonstrated the promising application of the proposed cooling system. Microgroove has demonstrated to be reliable to work under ground and microgravity applications as reported by Bazzo et al. [13], where results of CPLs with a circumferentially microgrooved

Z Z1

849

flow plates assembly thickness [m] cathode side flow plate thickness [m]

Greek symbols groove opening angle [ ] auxiliary angle [ ] efficiency [%] dynamic viscosity [Pa s] parameter for pressure drop [m2] density [kg/m3] surface tension [N/m] shear stress [N/m] contact angle [ ] ε convergence criterion [e]

a b h m j r s t q

Subscripts AA active area C condenser E evaporator f fluid F fraction h hydraulic HP heat pipe ins inscribed L liquid max maximum min minimum out outside sat saturation T total th thermal V vapour w wall

capillary evaporator were presented using water, ammonia, acetone and freon 11 as working fluids. A few papers have been reported referring to the mathematical models of heat pipes, including micro grooved heat pipes. Suman and Kumar [14] presented an analytical model developed for fluid flow and heat transfer applied to micro-heat pipes of polygonal shape. As study case, the proposed model was used in two heat pipes of different geometries, triangular and rectangular, showing among other parameters the corresponding liquid velocity, heat flux and capillary limit. Later, Suman [15] presented a discussion related to start-up and shutdown of a V-shaped micro-heat pipe, a detailed analysis of the fill charge and a sensitivity analysis of design parameters and properties of the working fluid on the transient operation. In this regard, as reported by other authors no experimental results were presented. This paper presents theoretical model and also experimental results concerning the use of mini flat heat pipes as a reliable alternative for thermal control of PEM fuel cells, at the industrial viewpoint assuring technical feasibility and expecting low manufacturing cost. 2. Theoretical analysis This section presents the geometric characteristics of the heat pipe under study, the fundamentals related to capillary limit, as well as simplifying assumptions and boundary conditions necessary for installation of the heat pipes in the flow plates used in PEMFC.

850

M.V. Oro, E. Bazzo / Applied Thermal Engineering 90 (2015) 848e857

The theoretical analysis is focused on a thin flat heat pipe proposed as alternative for cooling a PEMFC. The heat pipe has only the evaporator and condenser sections. The proposed cooling system consists of a set of stainless steel flat heat pipes, with 100 mm length, assembled in parallel at the interface between the flow plates, as shown in Fig. 1. The heat load as well as the number of heat pipes are the goals of this work in order to get a reliable system to absorb the waste heat of the PEMFC. The used domain to determine the temperature distribution in the flow plate cross section and the heat pipes arrangement along the interface are presented in Appendix A.

The dimension C2 is related to the outside diameter (dout) of the tube and the wall thickness (t) and can be obtained by C2 ¼ p(dout2t)[2(1 þ sec(a))]1. Finally, in Fig. 2(d) is shown the forces acting on the liquid control volume considered in the simulation, where t is the shear stress, P is the pressure and A is the wetted area. The areas occupied by the liquid and vapour phases, AL(x) and AV(x), are given by

2.1. Geometric parameters

AV ðxÞ ¼

Fig. 1(a) shows a fuel cell stack, where are presented the flow plates, the MEAs and the heat pipes. The flow plates are assembled between the MEAs, to supply the reactant gases. Fig. 1(b) shows the heat pipes arrangement on the PEMFC active area (polymeric membrane). The stack dimensions are DX ¼ 140 mm, DY ¼ 170 mm, and DZ ¼ 55 mm with a corresponding active area of 100 cm2 (LAA ¼ 100 mm and HAA ¼ 100 mm). The heat pipes are assembled at the horizontal orientation, in both sides, comprising the corresponding width of 140 mm, once the length of the heat pipe evaporator section is 70 mm. The HPs are arranged in pairs so that each HP is responsible for removing part of the released heat on the active area. The heat generated in the cell is absorbed by heat pipes located at the interface between the flow plates as illustrated in Fig. 2(a), where 2Y represents the distance between two heat pipes (HP). The parameter Z is the flow plates assembly thickness. A grid for finite difference calculations is represented in the detail, which was chosen because of the symmetry conditions and it is used to find the right number of heat pipes required to keep the temperatures below 90  C within an acceptable range. The heat flux (q00 ) is received by the fins and led through the flow plates to the HPs. Here, D1 and D2 represent the height and halfwidth of the proposed heat pipe, respectively. The domain of one heat pipe groove considered in the model is shown in Fig. 2(b), 00 where LC is the condenser length, LE is the evaporator length, qE 00 the heat flux input on the groove, and qC the heat flux output. Fig. 2(b) even shows the meniscus radius along the groove when the HP is operating. The HP triangular proposed geometry is shown in Fig. 2(c) where LT is the total length, obtained by LT ¼ LC þ LE. The main groove geometrical parameters are shown in Fig. 2(c), where a is the groove opening, q is the contact angle between the liquid and the tube wall, b is an auxiliary angle used in the simulation (b ¼ 180 e a e 2q), C1 represents the inner height, C2 the inner half-width of the proposed heat pipe and r(x) is the meniscus radius as a function of the heat pipe position.

The liquid and vapour perimeters can be determined by Eqs. (3) and (4), respectively. Then, the hydraulic diameter dh is obtained by Eq. (5), where the subscript k represents liquid (L) or vapour (V) phase.




AL ðxÞ ¼ rðxÞ2

cos2 ða=2Þ pb sinðbÞ  þ tanða=2Þ 360 2



C22 tanðaÞ  AL ðxÞ 2



pL ðxÞ ¼ rðxÞ

pb 2 þ 180 tanða=2Þ


pV ðxÞ ¼ C2 1 þ dh;k ðxÞ ¼

(2)




 1 pb 2 þ rðxÞ  cosðaÞ 180 tanða=2Þ

4Ak ðxÞ ; pk ðxÞ

(1)

k ¼ L; V

(3)

(4)

(5)

The meniscus radius, r(x), is affected by liquid and vapour pressure changes along the groove. At x ¼ 0 meniscus radius assumes its maximum value,


sinð90 þ a=2Þ rmax ¼ rðx ¼ 0Þ ¼ C2 tanða=2Þ sinð90  a=2  qÞ

(6)

2.2. Heat transfer analysis along the groove The phase change in the evaporator section is consequence of power input. Fig. 2(b) presents this behaviour into one groove (half heat pipe cross section). In this work two axial grooves are responsible by the liquid pumping. The hydrodynamic problem associated is solved under the following considerations: (i) onedimensional model; (ii) fully developed incompressible laminar flow; (iii) constant properties; (iv) steady state operation; (v) gravitational effects neglected; (vi) viscous dissipation neglected; (vii) zero contact angle; (viii) saturated liquid and vapour phases at operating temperature and (ix) heat flux uniformly distributed along the condenser and evaporator sections. Fig. 2(d) shows the forces acting on the liquid control volume with length Dx. No interaction was considered at the liquid/vapour

Fig. 1. a) Representation of the heat pipes installed in the stack; b) Heat pipes arrangement on the active area.

M.V. Oro, E. Bazzo / Applied Thermal Engineering 90 (2015) 848e857

Cathode

Z1 D1

Anode z

A

y

HP

2Y

q”

C

LE

Condenser x q”C A z

D2

q”

B

LC

HP

851

Evaporator B

q”E

C

Y

Vapour Δy

Fin

Flow channel

Liquid A-A

Δz

Flow plates

B-B

Z

(a)

C-C

(b)

D1 C1

θ

LT D2 C2

β r(x)

PAx τA

α

PAx+Δx

Δx

(c)

( d)

Fig. 2. a) Heat pipes arrangement and numerical heat transfer domain; b) Heat transfer and meniscus behaviour along the grooves; c) Triangular proposed geometry; d) Force balance on the liquid control volume.

interface because of the low flow velocities. Therefore, the force balance for both phases is written as follows:

equation is obtained for both phases, as well as for both sections, the condenser and evaporator, as follows

dðPAÞ ¼ tp dx

  2m ðfReÞ q_ j ; DPk;j;i ¼  k 2 k rk Ak hlv k;j Lj dh;k

(7)

where P is the pressure, A is the cross-sectional area (Eqs. (1) and (2)), p is the wetted perimeter (Eqs. (3) and (4)), and t is the fluid shear stress. In this work it was assumed both vapour pressure, PV, and liquid pressure, PL, change along the heat pipe length. From the mass conservation

m_ L ¼ m_ V ¼

8 > > > <

q_ x LC hlv

if 0  x  LC

> q_ > > : ðL  xÞ LE hlv T

(8) if LC < x  LT

where m_ is the mass flow rate of the fluid, hlv is the latent heat of vaporization and q_ represents the inlet/outlet power applied on the groove. Subscripts L and V represent the liquid and vapour phases, respectively. The fluid velocity (u) and shear stress (t) are given by:

uk ¼

m_ k ; rk Ak

tk ¼

  mk ðfReÞk m_ ; rA k 2dh;k

k ¼ L; V

(9)

k ¼ L; V

(10)

where r represents the density, m the dynamic viscosity and fRe the groove friction factor x Reynolds number of the fluid. Both fluid phases are divided into n control volumes along the x axis. A sufficiently high value of n is used and it can be assumed in each phase control volume the pressure is the only variable. Replacing Eqs. (10) and (5) in Eq. (7),

  dPk 2m ðfReÞk m_ ¼ k2 ; rA k dx d

k ¼ L; V

(11)

h;k

Equation (11) is integrated from i to i þ 1, such that a general

k ¼ L; V; j ¼ C; E; i ¼ 1::n (12)

where the subscript k represents the liquid (L) or vapour (V) phases, j represents the condenser (C) or evaporator (E) sections. The parameter j is shown in the Table 1. Equations (1) to (5) are used for the Eq. (12) solution. The groove friction factor x Reynolds number fRe was estimated for each control volume, following the model proposed by Etemad and Bakhtiari [16], as presented in Appendix B. The problem was solved considering the following boundary condition:

  PV ðx ¼ 0Þ ¼ Psat Tf

(13)

where Psat is the saturation pressure at the working fluid temperature, Tf. The meniscus radius, r(x), is affected by liquid and vapour pressure changes, and, using the YoungeLaplace equation, in order to maintain the balance between the phases

PV ðxÞ  PL ðxÞ ¼

s cosðqÞ rðxÞ

(14)

where s is the surface tension of the fluid. Heat pipes operation limits have been extensively studied for different working fluids and applications. The capillary structure, Table 1 Parameter j used in each control volume i of Eq. (11). k (phase)

j (section)

L L V

C E C, E

j x2iþ1 x2i 2

LT ðxiþ1  xi Þ  jL;j

! x2iþ1 x2i 2

852

M.V. Oro, E. Bazzo / Applied Thermal Engineering 90 (2015) 848e857

the operating condition and the working fluid have an important influence on the heat pipe performance. In this work, considering water as the working fluid and for temperatures in the range from 60 to 90  C, the governing equations are constrained by the capillary limitation. At this point the capillary pressure is not sufficient to overcome the pressure drop experienced by the working fluid, then the liquid supply to the evaporator becomes insufficient, reaching the dryout [17]. Here, boiling, sonic, viscous and entrainment limits are not relevant. Theoretical model was simulated considering the meniscus radius assumes a minimum value at the evaporator end (x ¼ LT), such as the dryout condition occurs when

rmin ¼ 0:01 mm

(15)

The simulation was performed starting with a low power input, using the Engineering Equation Solver (EES) software, making use of the boundary conditions (6), (13), (14) and (15). Equation (12) is iteratively solved for the n control volumes as shown in Fig. 2(d) and the corresponding vapour control volumes. As the heat pipe _ The is composed of two grooves, the total heat transfer is q_ T ¼ 2q. working fluid properties are calculated for different temperatures, also using the EES software. The inventory plays an important influence on the heat pipe performance and it is estimated by

mT ¼ mL þ mV ¼ rL VL þ rV VV

(16)

where VL is the liquid volume and VV is the vapour volume, given by

Vk ¼

n X i¼1

Vk;i ¼

n X

Ak;i Dx;

k ¼ L; V

(17)

i¼1

Special care was taken to fill the required amount of working fluid inside the heat pipe in order to allow a better comparison between the theoretical and experimental data. As expected, it has been observed along the tests, the operating temperature changes according to the power inputs, but also changes to the working fluid inventory. The higher the working fluid inventory the higher the operating temperature of the heat pipe. This particular behaviour is under investigation. 3. Experimental setup The heat pipes were assembled using stainless steel tubes (316L) with 3 mm O.D. and 0.25 mm wall thickness, moulded as shown in Fig. 3, such that two axial micro-grooves provide the required capillary pumping force for the working fluid. The total length is 100 mm. The condenser and the evaporator lengths are 30 and 70 mm, respectively. Fig. 3(a) shows a photography of one heat pipe manufactured and Fig. 3(b) a photography of the corresponding cross-section concerning different samples analysed, using a microscope Leica DM 4000-M (X16). A set of heat pipes was assembled and tested using deionized water as the working fluid. Before loading the working fluid, an ultrasonic cleaner Odontobras 2840D and a vacuum pump Edwards E2M18 were used for cleaning and evacuating the tubes, assuring the quality of the heat pipes. An amount of 52 mL of water was used as fluid inventory, somewhat about 20% of the inner total volume of the heat pipe, which was determined by weighing the empty and fully loaded heat pipe. The experimental apparatus consisted of a computer connected to a data acquisition system Agilent 34970A and seven thermocouples Omega T-type for temperature reading (Fig. 4(a)). The thermocouples were fixed along the HP surface, two at the condenser section and five at the evaporator section. To facilitate

Fig. 3. Heat pipe photographs: a) Perspective; b) Cross-section (Optical microscopy X16).

attachment of the thermocouples and the electric heater, a copper tube was mounted externally to the evaporator. The volume between the copper tube and the outer surface of the heat pipe (stainless steel) was filled with tin. Holes were made through copper and tin to insert thermocouples as shown in Fig. 4(b), which were fixed with silicone. A resistance heating wire (constantan wire) was coiled externally to the copper tube to heat the evaporator. The supplied power has been controlled by a power source Agilent N6700B. A standard cooler was assembled on the condenser section, typically designed for cooling microprocessors. The evaporator section was insulated with fibreglass and expanded polymer layers. A set of heat pipes was tested in a horizontal position in order to study performance and maximum heat transport capacity at working temperatures below 90  C. The horizontal alignment was obtained with the aid of a bubble level. The tests were performed by applying power inputs from 2 to 14 W with 2 W steps. The temperature measurements were collected by the acquisition system every 2 s. The expanded measurement uncertainties were estimated with 95% confidence interval [18]. The power input uncertainty associated was estimated as ± 0.2 W. The temperature uncertainty was evaluated taking into account the uncertainty of the thermocouples and data acquisition system, about ± 0.6  C. 4. Results and discussion As presented, a fluid hydrodynamic analysis and a twodimensional heat transfer model were performed to estimate the heat pipe behaviour under different operating conditions. Experiments were also carried out to evaluate the heat pipe thermal behaviour, using water as the working fluid. 4.1. Theoretical results A hydrodynamic analysis was performed by solving the equations (1) to (17), subject to the following input data: LC ¼ 30 mm, LE ¼ 70 mm, dout ¼ 3.0 mm, t ¼ 0.25 mm, q ¼ 0 , a ¼ 30 , n ¼ 100 and Tf ¼ 80  C. According to the proposed geometry C1 ¼ 1.05 mm and C2 ¼ 1.82 mm (see Fig. 2(c)). Consequently, rmax ¼ 0.49 mm (Eq. (6)). The theoretical model was simulated considering the meniscus radius assumes a minimum value, rmin ¼ 0.01 mm at the end of the evaporator (x ¼ 100 mm), in case of maximum power input. The heat pipe capillary limit is about 11.6 W, corresponding to a capillary pumping pressure close to 13 kPa, as shown in Fig. 5. The found results regarding liquid and vapour pressures, meniscus radius, hydraulic diameter, velocity as well as groove friction factor x Reynolds number fRe are presented in Figs. 6e10 for operating temperature of 80  C at a maximum power input condition of 11.6 W. The pressure distribution of both phases along the heat pipe is presented in Fig. 6. As expected the vapour pressure drop is negligible. However, an interesting behaviour was found in case of

M.V. Oro, E. Bazzo / Applied Thermal Engineering 90 (2015) 848e857

Condenser

Evaporator

853

A

Computer Heat pipe

A

B

Copper Tin Stainless steel

Acquisition system

Aperture for thermocouple

Heat pipe Power source

DETAIL B

SECTION A-A

Thermocouple

(a)

(b)

Fig. 4. a) Schematic overview of the experimental system; b) Thermocouple assembly.

liquid pressure drop, presenting a strong decrease at the end of the evaporator. The meniscus recedes causing a strong decrease of the cross-sectional area and, consequently, the capillary pumping pressure increases up to a limit, about 13 kPa, as shown in Fig. 5. The difference between the vapour pressure and the liquid pressure provides the capillary pumping pressure, Pcap. Fig. 7 shows the meniscus radius decreasing along the groove because of the progressive liquid pressure drop up to the end of the evaporator section. The corresponding hydraulic diameter behaviour is shown in Fig. 8. The non-linear behaviour is a consequence of the groove geometry. Fig. 9 shows the velocities profiles along the HP. Because of the physical properties and again groove geometry, a strong non-linear behaviour is observed showing vapour velocities of two orders of magnitude higher than liquid velocities. As expected the maximum vapour velocity occurs at the interface between the evaporator and condenser sections (x ¼ 30 mm), about 12 m/s, corresponding to a Mach number equal to 0.03. The liquid velocity in turn increases progressively until the end of the evaporator, where as a consequence of the imposed boundary condition it falls to zero (uL ¼ 0 m/ s at x ¼ 100 mm). The fluid groove friction factor x Reynolds number fRe behaviour is shown on Fig. 10. The found results are in agreement with technical literature, which provides 13.3 for an equilateral triangle and 16 for a circle. Here the liquid channel is similar to an isosceles triangle, changing only in its size along the groove, and so resulting fReL close to 13.2. Differently the vapour channel varies from the shape of a circle at x ¼ 0 (fReV ¼ 15.8) to the shape of an isosceles

14

Condenser

triangle at x ¼ LT, (fReV ¼ 12.9). Further considerations are presented in Appendix B. In addition of the operating temperature of 80  C, results are also presented for operating temperatures equal to 40, 60 and 100  C for capillary limit condition. As shown in Fig. 11, although a similar behaviour and just small changes are observed in the meniscus radius along the groove, the heat load capacity falls significantly, from 11.6 W (at 80  C) to 4.2 W (at 40  C). FR means the corresponding filling ratio of the working fluid, here considered as the volumetric fraction of the fluid inventory inside the heat pipe at room temperature. FR was calculated as the fraction between the liquid volume (VL) of the working fluid and the inner total volume of the heat pipe. It is a theoretical result, which means different fluids inventories, enough to fit every particular case. The found values in the range of 16e20 % were considered to load a set of heat pipes with working fluid for tests in the laboratory. However, it was considered FR ¼ 20%, in order to avoid the dryout due to the capillary limit condition on the PEMFC operating temperature. 4.2. Experimental results Tests were also performed in order to check the heat load capacity and wall temperatures along a set of heat pipes at horizontal position. As mentioned in Section 1, the temperature needs to be in the range of 70e90  C, once an overheating leads to the membrane drying and corresponding collapse of the fuel cell. The obtained results correspond to a heat pipe loaded with deionized water at filling ratio of 20% (52 mL), which was

Evaporator

50

qT=11.6 [W]

12

46

8

P [kPa]

Pcap [kPa]

10

6

42

Condenser

Evaporator qT=11.6 [W]

PV PL

38

4 34

2 0 0

20

40 60 x [mm]

Fig. 5. Capillary pressure along the HP.

80

100

30 0

20

60 40 x [mm]

Fig. 6. Pressure behaviour along the HP.

80

100

854

M.V. Oro, E. Bazzo / Applied Thermal Engineering 90 (2015) 848e857

Condenser

Evaporator

17

qT=11.6 [W]

0.4

16

0.3

15

Condenser

0.2

14

0.1

13

0 0

qT=11.6 [W] fReV fReL

20

40 60 x [mm]

80

12 0

100

0,5

Condenser

60 40 x [mm]

20

Fig. 7. Meniscus radius behaviour along the HP.

80

100

Fig. 10. fRe behaviour along the HP.

0.5

Evaporator qT=11.6 [W]

0,2

Evaporator . C; FR = 19.7 %; qT = 16.4 W 100 °C; . 80 °C; FR = 18.7 %; qT = 11.6 W . 60 °C; FR = 17.6 %; qT = 7.4 W . 40 °C; FR = 16.3 %; qT = 4.2 W

0.3

r [mm]

0,3

Condenser

0.4

0,4 dh;L [mm]

Evaporator

fRe

r [mm]

0.5

Tf

0.2 0.1

0,1 0 0

20

40 60 x [mm]

80

0 0

100

20

40 60 x [mm]

80

100

Fig. 8. Liquid hydraulic diameter along the HP.

Fig. 11. Temperature influence over the meniscus radius in the capillary limit condition.

chosen because it is slightly above the capillary limit estimated. The corresponding heat pipe thermal behaviour is presented in Figs. 12 and 13, for different power inputs, from 2 up to 14 W, where q_ is the power input, TC1 and TC2 the condenser wall temperatures

and TE1, TE3 and TE5 the evaporator wall temperatures. Therefore, power inputs were applied in steps of 2 W, remaining about 20 min on each level, sufficient to reach the steady state. In order to meet the fuel cell requirement, the maximum power input must be about

qT=11.6 [W]

10

0.10

8

uv 0.08 uL

6

0.06

4

0.04 0.02

2 0 0

20

40 60 x [mm]

80

Fig. 9. Velocities profiles along the HP.

100

20

80

16

60

12

40

8

0.12

0 100

20 0 0

q 20

40

60 80 t [min]

TC2 TC1 100

q [W]

Evaporator

Tw [°C]

Condenser

uL [m/s]

uv [m/s]

12

TE5 TE3 4 TE1 0 120 140

Fig. 12. HP experimental thermal behaviour for different power inputs along the time.

M.V. Oro, E. Bazzo / Applied Thermal Engineering 90 (2015) 848e857

100

Condenser

Evaporator

Tw [°C]

80 60 40

14W 12W 10W 8W

6W 4W 2W

20 0 0

20

40 60 x [mm]

80

100

Fig. 13. Measured temperature along the HP wall.

12 W. The room temperature was measured about 26  C during the tests. Fig. 13 shows the wall temperature distribution along the heat pipe, showing small changing along the evaporator section, which is recommended to ensure good fuel cell performance. The thermal resistance is 3.5 K/W for 12 W, here representing _ where DT is the difference the heat pipe performance, Rth ¼ DT=q, between the average temperatures of the evaporator and condenser sections (DT ¼ T E  T C ). It is in good agreement with results reported by Moon et al. [19]. From the experimental data, it can be stated the heat pipe is able to dissipate up to 12 W considering the fuel cell operating temperature. As mentioned in Section 1, at least two heat pipes would be required to remove the amount of 20 W but not sufficient to ensure a maximum temperature difference of 2  C. Hence, four heat pipes were considered such as DTmax ¼ 1.2  C. As shown in Fig. A2, the heat pipes were assembled every 50 mm (2Y ¼ 50 mm), and so providing a desired temperature gradient within the PEMFC. 5. Conclusions A thin flat heat pipe was proposed and analysed as a reliable alternative for proton exchange membrane fuel cell cooling. Power inputs up to 12 W (corresponding to 1.8 W/cm2 at evaporator section) was measured using deionized water as the working fluid. Tests with the proposed heat pipe were considered successful, meeting the required heat dissipation and operating temperature for PEMFC. The proposed theoretical model was useful in designing the flat heat pipe and its integration as a PEMFC cooling system. Acknowledgements ~o de AperfeiçoaThe authors acknowledge CAPES (Coordenaça mento de Pessoal de Nível Superior) and CNPq (Conselho Nacional
gico) for financial support de Desenvolvimento Científico e Tecnolo of the experimental works and also scholarship. Appendix A. Temperature distribution in the flow plate The used domain to determine the temperature distribution in the flow plate cross section and the heat pipes arrangement along the flow plates interface is proposed as shown by the detail in Fig. 2(a), where the hatched area represents the flow plate, D1 the HP height, D2 the HP half-width and q00 the heat flux generated in the cell. The white region corresponds to the half

855

heat pipe cross section (HP). The heat pipe is assumed as a heat sink at constant temperature boundary condition (Tw). The gas channels are treated as a solid with properties equal to those of the flow plate. The heat transfer problem associated with the physical model is solved under the following assumptions: (i) steady-state conditions; (ii) two-dimensional conduction; (iii) constant properties; (iv) zero internal heat generation; (v) heat pipe temperature equal to the heat pipe wall temperature (Tw); (vi) flow plates gas flow channels with equal properties to those of the flow plates; (vii) adiabatic condition at (y ¼ 0, z) and (y ¼ Y, z) due the symmetry condition; (viii) flow channels with length equal to the fin. The governing equation and the boundary conditions are presented in Fig. A1. Temperature distribution in the flow plates domain was simulated by finite difference method using the explicit formulation. Simulation was performed using the MATLAB software. The initial guess for each T(i,j) was the heat pipe wall temperature, Tw. A convergence criterion (ε) was applied to each grid point, T(i,j), wherein ε  j(Tit e Tit1)/T it1j. It was used a uniform grid spacing at the internal grid nodes, and a half spacing at the boundaries. By varying Y the maximum temperature difference on the flow plates (DTmax) is obtained. Then, the heat pipes are arranged according to the temperature difference considered acceptable in the fuel cell design. An important feature of fuel cells is the electricity generation area, which is basically the area of the polymeric membrane, also called the active area (Aactive). As shown in Fig. 1(b) Aactive ¼ HAA LAA. The heat flux generated from the cell is a function of the thermal power that needs to be removed from the cell and of the active area, 00 i.e. q ¼ q_ th =Aactive . The thermal power is directly associated with the electrochemical efficiency (h). In other words, the energy of the fuel not converted into electricity is converted into heat loss. Therefore q_ th ¼ ð1  hÞq_ el , where q_ el is the electric power generated by the cell. Each heat pipe is responsible for a thermal power fraction that 00 needs to be removed from the cell, q_ HP ¼ q AF , where AF is a fraction of the fuel cell active area, AF ¼ 2Y Lx, as shown in Fig. 1(b), wherein Lx ¼ 0.5LAA. The HPs are assembled in pairs resulting in 2, 4, 6 and so on. To estimate the heat pipe arrangement and the temperature distribution, the following conditions were used: Tw ¼ 80  C, D1 ¼ 2 mm, 2D2 ¼ 4 mm, Z ¼ 5 mm, Z1 ¼ 2 mm, k ¼ 100 W/(m K) (flow plates thermal conductivity), h ¼ 50%, q_ el ¼ 20 W, Aactive ¼ 100 cm2, Dy ¼ Dz ¼ 0.0625 mm, ε  108, flow channel and fin length equal to 1 mm. The PEMFC in operation in the laboratory has an active area with HAA ¼ LAA ¼ 100 mm. The needed thermal power to be removed is equal to generated electric power due the efficiency considered, then the respective heat flux q00 ¼ 0.2 W/cm2 needs to be removed from fuel cell inside. As shown in Fig. A2, seven values of Y were simulated from 10 to 50 mm, where the limits correspond to 10 and 2 HPs, respectively. From the viewpoint of thermal waste, the higher the power which support the heat pipes, the higher spacing between them and thus the smaller the amount of heat pipes needed to remove heat from the cell. From the viewpoint of flow plate temperature, if the HP withstands high power, the limiting factor will be the thermal gradient acceptable to ensure good performance to the cell, and thus, an amount of heat pipes larger than necessary must be used. This work considered acceptable DTmax ¼ 2  C, which corresponds to Y ¼ 32.5 mm. However, taking the number of heat pipes, the closest half spacing is Y ¼ 25 mm (four HPs), which results in DTmax ¼ 1.2  C. Fig. A3 shows the isothermal fields using four and six heat pipes, taking into account the computational grid which had to increase Y to 26 and 18 mm, respectively.

Appendix B. The friction factor x Reynolds number The friction factor x Reynolds number (fRe) was estimated as proposed by Ref. [16]. This model was chosen because it has good agreement with literature data for various geometric shapes, at relatively low errors, less than 10%. As shown in Fig. B1 circles are inscribed along the liquid and vapour cross-section, providing the corresponding diameters. Once that the liquid moves from the condenser toward the evaporator the meniscus radius recedes from rmax to rmin, as shown in Fig. 6. So the liquid inscribed diameter (dins;L) reduces to a minimum. On the other side, the vapour inscribed diameter (dins;V) is constant. Hence, the inscribed diameters are given by.

dins;L ¼

2

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi SðS  ABÞðS  ACÞðS  BCÞ S

(B.1)

where S ¼ 0.5(ABþACþBC).

dins;V ¼ 2rmax Fig. A1. Flow plates domain and boundary conditions.

(B.2)

So, two dimensionless parameters are defined:

d;k ¼

dh;k ; dins;k

k ¼ L; V

(B.3)

N;k ¼

Ak ; Adh;k

k ¼ L; V

(B.4)

where AL and dh;k are provided by Eqs. (1) and (5), respectively. Adh;k is the area based on the hydraulic diameter. Equation (2) provides the half part of the heat pipe vapour core. Therefore, taking account the whole vapour core, here AV is twice the Eq. (2). Then, the product fRe is provided by

fRe ¼ a0 þ a1 d þ a2 d2* þ a3 d3* þ a4 d4* þ a5 d5* þ a6 N þ a7 N*2 þ a8 N*3 þ a9 N*4 þ a10 N*5 (B.5) Fig. A2. Y influence on the flow plates temperature and the HP thermal requirement.

Fig. A3. Isothermal fields of the flow plate domain considering: a) four heat pipes; b) six heat pipes.

M.V. Oro, E. Bazzo / Applied Thermal Engineering 90 (2015) 848e857

where the constants are a0 ¼ 28.48854; a1 ¼ 268.72899; a2 ¼ 476.29475; a3 ¼ 396.33079; a4 ¼ 155.13995; a5 ¼ 23.37618; a6 ¼ 21.00613; a7 ¼ 10.62318; a8 ¼ 2.51512; a9 ¼ 0.27889 e a10 ¼ 0.01167.

Fig. B1. Inscribed diameter representation within the heat pipe.

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