Thermal coupling of PEM fuel cell and metal hydride hydrogen storage using heat pipes

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Thermal coupling of PEM fuel cell and metal hydride hydrogen storage using heat pipes Anggito P. Tetuko*, Bahman Shabani, John Andrews School of Engineering, RMIT University, Melbourne, Australia

article info

abstract

Article history:

This paper presents a mathematical model to study opportunities for simultaneous passive

Received 4 November 2015

thermal management of an integrated PEM fuel cell and metal hydrogen (MH) storage

Received in revised form

system by thermal bridging of these two components, using heat pipes. The thermal

27 December 2015

coupling arrangement is expected to be promising, because, as more power is drawn from

Accepted 30 December 2015

the PEMFC, more heat is generated that can be used to enhance the rate of release of

Available online 29 January 2016

hydrogen from the MH storage. Heat pipes can provide an effective passive thermal bridge for this purpose on account of their high thermal conductivity, and thus avoid parasitic

Keywords:

energy penalties associated with active methods of cooling. The main components

PEM fuel cell

modelled analytically in MATLAB in this study are the PEMFC, heat pipes, and MH

Metal hydride hydrogen storage

hydrogen storage. This simulation has been used to size the heat pipe system needed for

Heat pipes

thermal coupling of a 500 W PEMFC and MH storage canisters. The performance

Passive cooling

improvement of the MH system after receiving the fuel cell heat, and the cooling capacity

Thermal management

of the MH system to be used as heat sink for thermal management of the fuel cell stack, has been studied. The MH canisters used to supply hydrogen to this stack each had the maximum supply capability of 2.5 slpm at 25
C, while the fuel cell demand was 7.2 slpm at its rated power (500 W). The results show that just under 20% of the total cooling load of the stack (i.e. ~880 W) at its maximum power point is demanded by the MH canisters (~170 W) to achieve the required hydrogen discharge rate of 7.2 slpm at 35
C provided the MH canisters are thermally well insulated. Copyright © 2016, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.

Introduction Proton Exchange Membrane Fuel cell (PEMFC) is a device in which hydrogen (as fuel) and oxygen (can be from air) react electrochemically and the result of this reaction is the generation of electricity, heat, and water [1]. Although the efficiency of a PEMFC in generating electricity is relatively high

(up to 55% based on high heating value of hydrogen), still substantial amount of heat is generated as by-product that must to be effectively removed from the fuel cell in order to maintain its temperature at a desirable level [2e4]. PEMFCs usually operate at a relatively low temperatures, usually in the range of ~60e80
C [2], that makes this type of fuel cell a suitable option for many stationary and mobile applications where particularly quick start-up is essential [5e7]. The heat

* Corresponding author. School of Engineering, RMIT University, Plenty Road, Bundoora East, Victoria 3083, Australia. E-mail addresses: [email protected] (A.P. Tetuko), [email protected] (B. Shabani), [email protected] (J. Andrews). http://dx.doi.org/10.1016/j.ijhydene.2015.12.194 0360-3199/Copyright © 2016, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.

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generated during the operation of PEM fuel cells can be extracted and used in a range of heating applications (e.g. hot water supply, space heating, or heating up the inlet reactants in cold climate conditions) together with the power generated by the fuel cell [2,8e11]. In many applications, a metal hydride (MH) hydrogen storage is used to supply hydrogen to the fuel cell. Obtaining a sufficient release rate of hydrogen from the MH storage system at normal ambient temperatures (e.g. 20e30
C) to supply the PEM fuel cell at its maximum power point is often a technical challenge [12e14]. The simple solution of oversizing the MH storage system to achieve the required rate of hydrogen release is undesirable economically. Heating up the MHs and operating them at a higher range of temperature (i.e. above normal ambient temperatures) can increase the hydrogen release rate of the MHs quite considerably [15]. This behaviour can guide us toward a more advanced solution to the above-mentioned problem: using the heat normally rejected from the fuel cell to raise the temperature of the MH storage system and enhance its hydrogen release rate [14,16,17]. The heat from the fuel cell can effectively be transferred to MH storages using heat pipes, as suggested previously by some researchers [18e20]. Heat pipes have a very high equivalent thermal conductivity and can transfer a large amount of heat from the fuel cell to the MH storage with no additional pumping power required. In turn, heat pipes come with other advantages such as simplicity and lower maintenance costs because of having no moving parts in their structure, while they can provide an excellent temperature controlling mechanism compare to many other passive cooling methods [21]. This is due to the fact that they operate based on a set equilibrium pressure and the boiling point (at this set pressure) of a certain liquid used in the heat pipe. Heat pipe solutions have also been suggested and studied before for thermal management of MHs, i.e. in order to reduce the charging/discharging time and to enhance the exothermic/endothermic reaction between the hydrogen molecules and metal powder [22e24]. However, although heat pipe solution has been used before for thermal management of MHs and PEM fuel cell separately, the possibility of thermal coupling of a PEM fuel cell and MH hydrogen storage using heat pipes has not been studied before. While thermal coupling of a PEM fuel cell and MH hydrogen storage system has been investigated before by several researchers [13,25,26], all these earlier studies employed active heat transfer methods such as water and air circulation, all involving parasitic energy consumption. This paper focuses on a mathematical modelling to describe and study the performance of the novel arrangement of simultaneous cooling of PEM fuel cells and heating a metal hydride hydrogen storage using a passive heat pipe system for heat transfer. The following section focuses on reviewing literature on the possibility of using heat pipes for PEMFC cooling and also thermal management of MHs, including previous research on active thermal coupling of PEMFC and MHs. Next section focuses on a mathematical model developed as part of this study is described, and a case study of a PEMFC and a MH hydrogen storage being thermally coupled using heat pipes is reviewed by applying the created model.

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Finally, last section provides some conclusions and recommendation for further studies.

Opportunities for thermal coupling of metal hydride hydrogen storage and PEM fuel cells An overview As already discussed in the introduction part due to inefficiencies associated the fuel cell, part of the energy content of hydrogen appears in the form of heat [2]. Thus, a proper cooling system is required in order to maintain the stacks temperature at a desired level that is ~60e80
C for PEMFCs [27e29] or up to 100
C in some high temperature PEMFCs [30]. In general fuel cell cooling can be done using either passive methods (e.g. heat spreader or heat pipes) [19] or active methods (e.g. liquid cooling, fan, and forced air cooling) [31] depending on the size and operating condition of the fuel cell. Liquid cooling is generally employed in high power PEMFCs (e.g. above 5 kW), such as those used in automotive applications [4]. In some fuel cell applications, MH systems are used to store and supply hydrogen to the fuel cell. A MH hydrogen storage unit includes a canister filled with special metal alloys (M) that can form weak bonds with hydrogen (H), at usually not a very high pressure (e.g. 10e40 bar). In other words MH stores hydrogen gas in atomic form as a chemical combination called MH. These weak bonds can be broken by applying heat (mostly absorbed from atmosphere at normal ambient temperatures) while the MH is exposed to low atmospheric pressure. The charging and discharging are exothermic and endothermic reactions respectively; hence, proper thermal management of MHs can improve their hydrogen absorption and desorption performance. In particular applying heat to enhance the discharge characteristics of MH (i.e. through external or internal heat transfer to the MH canisters) has been practiced, studied, and demonstrated by many researchers before [25,32e35]. A MATLAB/Simulink model that was developed by Hyeong Cho et al., 2013 [36] analysed the effect of an external water channel temperature to enhance the hydrogen discharging flow rate in a MH canister (i.e. with the capacity of storing 1.43 kg of hydrogen). The test was performed for 10,000 s at the initial pressure of 10 bar using different water temperature with the variations of 20, 30, and 40
C. The hydrogen discharging rates of 0.2, 0.4, and 0.6 kg/h were achieved, respectively using those temperature variations. Based on the results, the authors confirmed that a higher water circulation temperature facilitates a higher hydrogen discharging flow rate. The heat can be transferred to a MH canister using two methods: internal and external [37]. Example of internal heat transfer arrangement is that practiced by Mellouli et al., 2007 [16] who equipped a metal hydride reactor with a spiral type heat exchanger to provide more heat transfer area. Also in another case study a capillary tube bundle heat exchanger with a large heat transfer surface inside the metal hydride hydrogen storage was used by Linder et al., 2010 [38]. In both

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cases significant reduction in charging/discharging times were reported by the researchers. Dhaou et al., 2011 [39] also used a finned spiral heat exchanger and analysed the effect on the charging/discharging process in MH hydrogen storage (1 kg of LaNi5). The charging process was conducted at the temperature of 20
C and the pressure of 10 bar and the discharging process was conducted at 40
C and 0.1 bar for 4000 s. The experiments were varying the hot and cold water in shell side and tube side with a mass flow rates in the range of 7e13 g/s; according to the authors, the increase of the flow rate did not have a considerable effect on the hydrogen charging and discharging performance of the MH canister. The results also showed that charging and discharging process reached a stable hydrogen concentration at a H/M ratio of 4.5 and 1.5, respectively. Other examples can be found in Forde et al., 2009 [13] and Urbanczyk et al., 2011 [40] that used a U-shaped cooling tube and a helical coil tube inserted to the MHs for better kinetics of absorption and desorption to utilize the full hydrogen storage capacity to be utilised in the PEMFC. As for external heat transfer methods, mainly arrangements such as using fluid (air or gas) to transfer heat (i.e. through convection) can be found in the literature (e.g. Ref. [41]); or in a different case the outer surface of a metal hydride storage was covered by fins to increase heat transfer area [42]. Lototskyy et al., 2015 [43] developed a system that consists of the low temperature fuel cell (LT PEMFC) and MH hydrogen storage (mixed with 1 wt % of thermally expanded graphite). The MH canister (1.4 wt % of hydrogen) performance test was conducted at the pressure of 20e80 bar for charging and at the pressure of 1e15 bar for discharging. The charging/discharging performance could also be increased by applying water (20e40
C) for heating/cooling the MH canister. The authors found that by using a canister (12.2 kg of MH) that consist of an internal heat exchanger, a maximum flow rate of 20 slpm (capacity of 1900 nl) can be achieved at a discharging pressure of 1 bar. As briefly mentioned before, the heat generated by the PEMFC can be used to enhance the hydrogen release rate from a MH hydrogen storage system that is used to supply hydrogen to the FC. Previous and mainly experimental studies on simultaneous thermal management of fuel cells and MHs can be found in several articles, such as those by Jiang et al., 2005 [44], Wilson, et al., 2007 [25], Pfeifer, et al., 2009 [26] and Ungethum, et al., 2014 [45]. In these studies the heat generated by the PEMFC was directed toward the MHs via heat exchangers with the purpose of increasing the temperature of MHs and hence their equilibrium pressure and their hydrogen desorption rates. An innovative design for thermal coupling of MH and PEMFC, was presented by Lee et al., 2013 [46] where a MH was inserted in a hollow cylindrical PEM fuel cell for cell phone or laptop applications. With this arrangement a higher power density was reached compare to a system without an integrated metal hydride storage. Yiotis et al., 2015 [47] used COMSOL to model a thermal coupling arrangement between a MH canister (sodium alanate) with the weight of 2.43 kg and a high temperature 240-W fuel cell (HT PEMFC). The heat was transferred from the water inside a cooling jacket surrounding the HT PEMFC to a heating jacket surrounding the MH canister that reached steady state

in 10 min for 120 min operation. The purpose of this method was to maintain the MH canister temperature at 120
C and achieve an acceptable hydrogen discharge rate to be supplied to the HT PEMFC. The model confirmed that at the MH condition of 25 bar and 120
C, the hydrogen discharging value reached 224 nl/h. A similar model was also developed in MATLAB/Simulink by Khaitan et al., 2012 [48]. The heat generated by the PEMFC (800 cells with a maximum power of 80 kW) was assumed to be collected by the cooling water and passed to the MH container in order to maintain the PEMFC temperature below 80
C while heating up the MH canister to achieve a higher hydrogen discharging rate. The model confirmed that only 20% of the total cooling load of the PEMFC was enough to be used in the MH canister for achieving the hydrogen discharging optimum performance condition. The results show that at the condition of 5 bar and 57
C, the 14 MH canisters could continuously discharge 120 kg of hydrogen in 15 h. Similarly a 5-kW PEMFC and 4 MH canisters (3 kg of hydrogen with the total MH mass of 190 kg each) for mobile light tower application was also experimentally developed by Song et al., 2014 [49]. The PEMFC was cooled using air through an external heat exchanger. The hot air was then used for heating up the water circulated around a MH canister for enhancing its hydrogen discharging rate. According to the reported results at the condition of 20.7 bar and 50
C, the hydrogen discharging rate of 3.45 g/minute (0.86 g/minute each canister) could be achieved. The results also confirmed that again 20% of the heat from the PEMFC is sufficient for enhancing the hydrogen discharging rate in the MH canister to a desirable level needed by the fuel cell. Guizzi et al., 2009 [50] analysed a similar thermal coupling arrangement of a 1.5-kW, 60-cells PEMFC (hybridised with batteries and supercapacitors in this case) and a MH hydrogen storage. The MH canister used in this study had store 156 g of hydrogen while its total MH mass was 13 kg. The canister could be charged and discharged at 5 bar and 25
C; however, the hydrogen discharging rate was not sufficient to meet the fuel cell demand in this condition for an electric wheelchair application. The results confirmed that the thermal coupling between the fuel cell and MH was of help to enhance the MH hydrogen discharging rate to an acceptable level suitable for this application. Rizzi et al., 2015 [51] used water as a coolant for collecting the heat from a PEMFC and then the hot cooling water (i.e. at 67
C) flew through the heating jacket of a MH and helped maintain the temperature of the MH canister at 60
C. Copper fins (i.e. for increasing the heat transfer area) were attached to the outer surface of the MH canister used in this study. The results showed that the system could generate an average power of 760 W while the heated canister could discharge 2.67 nl/min of hydrogen (16 nl/min for 6 canisters) coping with the fuel cell demand for hydrogen.

Passive thermal coupling of PEMFCs and MHs using heat pipes Heat pipes were used before to cool electronics for many years. There are several types of heat pipes available for cooling applications, including thermosyphon, capillary heat

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pipe (CHP), loop heat pipe (LHP), pulsating heat pipe (PHP) and micro heat pipe (mHP). Vasiliev and Vasiliev Jr., 2008 [52e54] presented a review of heat pipe types to be used as the cooling media in fuel cell applications, such as micro/mini heat pipe (<10 W), loop heat pipe (10e100 W) and pulsating heat pipe (>100 W). Faghri and Guo, 2008 [19,55,56] experimentally tested micro heat pipes where heat pipes were inserted and bonded in the bipolar plates. The design could give smaller thermal gradient and much less volume and weight in the fuel cell stack; however, it suggested challenges related to the fabrication and the sealing process of the bipolar plates. Oro and Bazzo, 2015 [57] proposed using thin flat heat pipes (triangle shape) with an original diameter of 3 mm and total length of 100 mm (condenser length of 30 mm and evaporator length of 70 mm) to be used for PEMFC cooling. They developed a heat transfer model and experimentally investigated the heat pipes capillary limit (i.e. each capable of removing 12 W of heat) for operating temperatures between 70
C and 90
C. This work was only about testing the heat pipes without inserting them into a real PEMFC. Clement and Wang, 2013 [58] analysed the possibility of employing pulsating heat pipe (PHP) for use in PEMFC cooling applications. The PHP used in their study had a length of 468 mm and width of 147 mm with a diameter of 3.175 mm. The results confirmed that one PHP (15 turns) was able to dissipate the heat in the range of 100 We120 W and the author suggested that the PHP could be implemented in a PEMFC with an active area of 200 cm2. The application of loop heat pipes in fuel cell was analysed by Silva et al., 2012 for operating temperature range of 70e90
C [20]. Another heat pipe application for Unitised Regenerative Fuel Cells URFCs was investigated by Burke and Jakupca, 2005 [18], where a loop heat pipe was coiled around the outer surface of a pressurised hydrogen and oxygen cylinders to dissipate the waste heat from the system. In this arrangement the hydrogen and oxygen cylinders were used as heat sinks, connected to the condenser side of the heat pipes; with no intention to improve the performance of the hydrogen storage system. Research on the numerical modelling of heat pipes used for high temperature PEMFC cooling can be also found in the studies. The example of this is Firat et al., 2012 [59] and Supra et al., 2013 [60] that assumed the heat pipes to be solid rods with a high thermal conductivity (1600e40,000 W/m.K). They concluded that the heat pipes can be used for high temperature PEMFC cooling because of better thermal distribution and sufficient cooling and lower temperature values (150
C) that can be achieved in the cooling plates. On the other hand, with the view of enhancing hydrogen charge/discharge rates of MHs, heat pipes have also been limitedly studied theoretically and experimentally for thermal management of MHs. Chung et al., 2013 [23] analysed a MH hydrogen storage system (295 g LaNi5) with one embedded heat pipe with heat removal capacity of 60 W. Water bath was used for heating and cooling the MHs. For the absorption, the water bath was set to 20
C. On the other hand, for the desorption, the water bath was set to 50
C. The absorption and desorption time was reported to be improved by more than 50% and 44% respectively. Liu et al., 2014 [24] who validated their numerical model using Chung et al., 2013 [23] experimental results also conducted a parametric study on thermal management of MHs

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using heat pipes. According to the results of their study, more heat pipes with a smaller diameter proved to be more effective than fewer heat pipes with a larger diameter and heat removal capacity. The simulation results showed that the heat pipes arrangement can significantly affect their effectiveness in improving the hydrogen absorption time. Another numerical model developed by Boo et al., 2009 [22] used two different types of MHs thermal management: 8 brine tubes (6.35 outer diameter and 1 m effective length) and 16 heat pipes with the same dimension. The results of the numerical study conducted by Boo et al. showed that the heat pipes were far more effective than the brine tubes for improving the charging at 10
C and the discharging process at 80
C. The results show that the heat pipes and the brine tubes reached steady temperature during both charging and discharging in 500 s and 2000 s respectively. The investigation on the performance enhancement of a MH canister (1.3 wt%) was also conducted by Chung et al., 2015 [61] where one heat pipe with maximum removal performance of 70 W was inserted in the MH canister. Computational fluid dynamics (CFD) was used to investigate the case numerically before validating the results experimentally. The model confirmed the effectiveness of heat pipes to increase the heat transfer to MH canister (reaching 50
C) and change the distribution of temperature, hydrogen content and the equilibrium pressure. While the use of heat pipes for thermal management of each individual of MHs and PEMFC were limitedly studied or practiced in the past, the opportunities for thermal coupling of these two, using heat pipes, were not found to be investigated before. As discussed earlier, while the heat generated by the fuel cell has to be continuously removed from the PEMFC (i.e. to avoid the cells' overheating), this heat can be directed towards MHs, fully or in part, to enhance their hydrogen release rate that is most needed particularly when higher power rates are drawn from the PEMFC. This thermal coupling arrangement is expected to be promising and have the potential of regulating itself. This is because as more power is drawn from the PEMFC, the stack demands for higher rate of hydrogen flow; this is the time that the stack generates heat at higher rate and this coincides with the period that MHs demand for more heat to supply higher rates of hydrogen to the PEMFC. Heat pipes can thermally bridge MHs and a PEMFC, and due to their high thermal conductivities, using active methods of cooling and the parasitic energies associated with them can be avoided. Due to the possibility of omitting moving parts (e.g. fans) with heat pipes, they are of low maintenance that supports the economics of the systems. A possible schematic design for thermal coupling of PEMFC and MHs using heat pipes is shown schematically in Fig. 1.

Thermal coupling of PEMFCs and MHs using heat pipes: a mathematical model Modelling approach An overview The main components modelled analytically in MATLAB for this study are the PEMFC, heat pipe, and MH systems. The overall model was then used to size the heat pipe system

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Fig. 1 e Schematic demonstration of thermal coupling arrangement between PEMFC and metal hydride canisters using heat pipes.

needed for thermal coupling of PEMFC and MHs, study the performance improvement of the MH system after receiving the fuel cell heat, and the cooling capacity of the MH system to be used as heat sink for thermal management of the PEMFC stack. The model is expected to help narrow down the design options that would work in practice. First, the modelling will be used to estimate the performance of the fuel cell in heat and power generation and estimate the cooling load that can be extracted from the fuel cell. Another key objective of the model was also studying the hydrogen discharge performance of MHs with and without applying the heat extracted from the PEMFC. The model is though able to calculate how much heat has to be directed to the MHs in order to achieve desired flow rates of hydrogen at any operating points of the PEMFC. The heat pipe model can help size and specify the specifications of the heat pipe system required for this thermal bridging.

Mathematical modelling of PEMFCs The main purpose of modelling the fuel cell is to calculate the amount of heat generated by the stack at any operating point. This will then provide an indication of the stack's cooling load (i.e. that is part of the total heat generated) to be collected by the heat pipes at that operating point and made available to the MHs. The maximum open circuit voltage (Eo) can be calculated using the Nernst equations (ENernst). Then, in order to calculate the actual output voltage of the fuel cell (Vout), the losses including activation losses, Vact, ohmic losses, Vohmic, and mass transport losses, Vconc has to be deducted from this maximum open circuit voltage [1,62]: Eo ¼

Dgf 2F

(1) 1

ENersnt

RT PH2 PO2 2 ln ¼ Eo þ 2F PH2 O

! (2)

Vact ¼

  RT i ln 2aF io

(3)

Vohmic ¼ ir

(4)

  i Vconc ¼ aL ik ln 1  iL

(5)

Vout ¼ ENersnt þ Vact þ Vohmic þ Vconc

(6)

where Dgf is the Gibbs free energy change (J/mol); F is Faraday constant (96,485 C); R is universal gas constant (8.314 J/mol.K); T is temperature (K); PH2 is partial pressure of hydrogen (atm); PO2 is partial pressure of oxygen (atm); PH2O is partial pressure of water (atm); i is current density (A/cm2); io is exchange current density (A/cm2); il is limiting current density (A/cm2); r is internal resistance (Ohm-cm2); and aL is charge transfer coefficient. The power generated by the PEMFC (Pout) can be calculated as below [1,62]: Pout ¼ Ncell Vout iAcell

(7)

where Ncell is number of cells; Vout is output voltage (Volt); and Acell is effective cell area (m2). The fuel cell heat generation rate (Q, Watt) can be then calculated using the following equation by considering; the fuel cell current density (i), effective area of each cell (Acell), and actual voltage (Vout) of each cell, and the number of cells in the stack (Ncell). The value of the voltage is 1.48 V if the water product is in liquid form and 1.25 V is used if in vapour form [1,62]. It is hard to specify what portion of the water generated in the fuel cell appears in vapour form and what percentage gets through the Gas Diffuser Layer (GDL) of the fuel cell in liquid form. However, generally the operating pressures and temperatures of the fuel cell suggest this water to be evaporated at the point of generation. Hence, while in Equation (8), the HHV of hydrogen is used for calculating the total heat generated by the fuel cell, the Equation (9) (that is based on the

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LHV of hydrogen) can be used to estimate the cooling load of the stack (i.e. available heat to be collected by the cooling system) assuming that normally the water generated by the stack appears in vapour form [1]. Q ¼ Ncell iAcell ð1:48  Vout Þ

(8)

Q ¼ Ncell iAcell ð1:25  Vout Þ

(9)

Mathematical modelling of metal hydride hydrogen storage The model allows determining the effect of temperature and heat transfer (i.e. from the PEMFC) on the hydrogen discharge rate of the MHs. As discussed earlier hydrogen atoms can react with metals alloys reversibly to form metal hydrides as shown by Equation (10) [63e65]. x Me þ H2 4Me Hx þ Qreact 2

DH DS  RT R

(11)

(12)

where Cd is the desorption constant (s1); Ed is the activation energy for desorption (J/mol); T is the absolute temperature of MHs (K); R is the universal gas constant (8.314 J/mol.K); Peqd is the equilibrium pressure for desorption (Pa); rs is the density of metal hydride desorbed (kg/m3); and remp is the density of metal hydride alloy when all the hydrogen gas is desorbed (kg/ m3). Since the absorption and desorption reactions are exothermic and endothermic processes respectively, an appropriate thermal management of MHs can improve their performance in charging and discharging modes [12]. Assuming a well-insulated MH canister, the heat demanded by the MH (QMH) is calculated as below [13]: QMH ¼ Qreact þ QH2

(14)

QH2 ¼ md hg

(15)

where md is the mass flow rate of hydrogen leaving the reactor to be used by the fuel cell (kg/s) (i.e. the value is negative for hydrogen desorption and positive for hydrogen absorption); Dh is the enthalpy change of reaction (J/kg); and hg is the enthalpy of the hydrogen gas (J/kg) discharged from the MH. The mass flow rate demanded by the PEMFC can be calculated using the fuel cell modelling and through using the following equation by considering a hydrogen utilisation factor of 0.95 [1].  mFC ¼ 1:05  108

Pout Vout

 0:95

(16)

Mathematical modelling of heat pipes

where DH is enthalpy change of metal hydride (J/mol); DS is entropy change of metal hydride (J/mol.K); T absolute temperature of the hydride (K); and R is the universal gas constant (8.314 J/mol.K). The hydrogen mass desorbed per unit time and volume in MHs can be calculated using the following equation [72e76]:    Ed Pg  Peqd  rs remp md ¼ Cd exp  RT Peqd

Qreact ¼ md Dh

(10)

where, Me represents metal or alloy materials; H is hydrogen atom; MeHx is the metal hydride, x is the ratio of hydrogen atoms to metal or alloys, and Qreact is the heat released or absorbed during the hydrogen absorption and desorption reactions respectively. In this reaction, the metal hydride entropy change is low compared to the metals or alloys and the hydrogen (gas phase) [64]. The equilibrium pressure, P, is closely related to the absolute temperature of the metal hydride, T [66e69] as shown in Van't Hoff equation below [42,70,71]: lnPeq ¼

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(13)

where Qreact, as introduced earlier, is the amount of heat required in the chemical gas solid reaction; QH2 is the heat transferred out of the reactor with the hydrogen gas. Qreact and QH2 are calculated using the following equations [13,77]:

The heat pipes now have to be designed by considering key parameters including material (container and wick structure), working fluid, pressure difference inside the heat pipes and heat removal capability, in order to direct enough heat from the fuel cell stack towards MHs and accordingly achieve required hydrogen mass flow rates at any operating points supplied by the MHs. It is important to note that the study of heat transfer details between the evaporator side of the heat pipes and the cooling plates of the PEMFC and also the condenser side of the heat pipes and the body of the MHs, and the associated thermal resistances will remain outside the scope of this modelling exercise. However, this is worth being looked into separately at any individual cases to ensure that heat pipes transfer the fuel cell heat effectively and help create a uniform temperature distribution across each individual cooling plate. However, this analytical modelling provides an indication of the minimum number of heat pipes required to be embedded in each cooling plates. This number may increase in each individual cases depending on the way that the heat pipes come in contact with the MH canisters outer surface (condenser side) and the PEMFC's cooling plates (evaporator side). In the mathematical modelling of heat pipes, the pressure losses, the heat dissipation capability and the overall thermal resistance of heat pipes are the key parameters to be taken into consideration. To check the validity of the mathematical model used in this research, the heat pipes' performance characteristics suggested by the model were compared with the real performance data (i.e. provided by the manufacturer) of some commercially-available heat pipes that will be further discussed. Heat pipes can work properly when the maximum capillary pumping pressure, DPcmax, (Pa), is higher than the pressure losses in heat pipe regions, including the liquid pressure, DPL (Pa), the vapour pressure, DPV (Pa), and the pressure effect of the gravitational force DPG (Pa). The liquid pressure is the driving force to return the liquid back from the condenser section to the evaporator section of the heat pipe and the vapour pressure is that for the vapour to flow from the evaporator to the condenser side. On the other hand the pressure due to the gravitational head can be zero, positive or negative, depending on the inclination of the heat pipe [78,79]. The

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inclination angle will affect the temperature difference between evaporator and the condenser section of the heat pipe as suggested by Loh et al., 2005. The heat pipe orientation against the gravity will have higher temperature difference and lower thermal conductivity. To overcome this problem, sintered metal powder wick structure will be used that have better capillary affect compared to the mesh and groove types [80]. The pressure balance in the heat pipe is required to be as below: DPc±DPG > DPL þ DPv

(17)

In heat pipes, the capillary pressure difference is very important to ensure that the water from the condenser can flow back to the evaporator. Capillary effect has an important role in the rise or fall of liquid in a small-diameter tube that is linked to physical properties of surface tension as well as cohesive and adhesive forces. Those properties are related to the contact angle between the liquid and the surface that needs to be considered when designing the heat pipes, especially at the wick structure regions where the capillary phenomena occur [81]. The wick structure can use various materials such as stainless steel, ceramic or composite and with different physical structures, such as screen. For non-wetting liquids, the contact angle is greater than 90
(hydrophobic) and for wetting ones, it is less than 90
(hydrophilic) [82]. In order to achieve better performance of the capillary effect to transfer the liquid from the evaporator to the condenser section, the hydrophilic type of wick structure is used [83,84]. The maximum capillary pressure happens when the contact angle of the wick structure zero as shown in Young's equation that affect the surface tension of the liquid used inside the heat pipe [85]. The capillary limitation (DPcmax) in the heat pipe can be expressed by the following equation: DPcmax ¼

2s rp

(18)

where s is surface tension (N/m); and rp is pore radius of the wick (m). The fluid flow energy loss (i.e. pressure drop) when moving through the wick structure can be calculated using Darcy equation [81,86]: DPL ¼

mL Leff m KrL A

(19)

where mL is liquid dynamic viscosity (kg/m.s); Leff is effective length ¼ Ladiabatic þ (Levaporator þ Lcondenser)/2, (m); m is mass flow rate (kg/s), rL is liquid density (kg/m3), A is surface area (m2), and K is permeability (m2). The permeability describes how easily a fluid can move through the porous material. Thus it is related to the connectedness of the void spaces and the pore size of the material [86]. Another important consideration in designing heat pipes is the pressure difference in the vapour section that can be explained using the Poiseulle law. This pressure difference drives the vapour flow from the evaporator to the condenser. The Poiseulle law considers the fluid to be Newtonian and flown in a laminar condition as a result of above-mentioned pressure difference where the fluid resistance depends on

the viscosity and the density [81,87]. The Poiseulle law is defined as follows: DPV ¼

128mV Leff m pD4 rV

(20)

where mv is vapour dynamics viscosity (kg/ms); L is effective length (m); m is mass flow rate (kg/s); D is heat pipe inner diameter (m); and rV is vapour density (kg/m3). The gravitational pressure can be calculated using the following equation for a heat pipe inclined at angle q DPG ¼ rL gLeff sinq

(21)

where rL is liquid density (kg/m3); g is gravity (m/s2); Leff is effective length (m) and; q is the angle between the axis of the heat pipe and the horizontal plane. As discussed earlier in this section as shown in Equation (18), capillary phenomenon is quite an important effect utilised by the heat pipes for maintaining the circulation of the fluid between the condenser and evaporator sides. This is what guarantees the effectiveness of heat pipes in transferring heat between the evaporator and condenser. Hence the maximum heat transfer rate in heat pipes (QHP) would be limited by the extent of this capillary effect and can be calculated using the following equation [88]: QHP ¼

    rL shfg A:K 2 rL gLeff sinq ± Leff rp mL s

(22)

where rL is liquid density (kg/m3); s is surface tension (N/m); hfg is latent heat of vaporization (J/kg); mL is liquid dynamic viscosity (kg/ m.s); A is surface area (m2); K is permeability (m2); Leff is effective length (m); rp is pore radius of the wick (m); g is gravity (m/s2); and q is the angle between the axis of the heat pipe and the horizontal. This equation is based on the fact that the heat dissipation process in a heat pipe can continue until the net capillary forces generated by the vapoureliquid interfaces can overcome the other pressure losses described earlier [79,89].

Thermal coupling of MHs and PEMFCs using heat pipes The mathematical models of the main components of the thermal coupling system have been integrated into a single overall system model. This system model allows investigation of the feasibility of thermal coupling arrangement between MHs and PEMFC using heat pipes. The model is used to match the hydrogen usage rate in PEMFC and the hydrogen discharge rate in MHs by suggesting the number of heat pipes required for this thermal arrangement. The mathematical model can also provide indications on the number of cooling plates to be used in PEMFC; however, this needs to be accurately determined by running a numerical analysis and considering some other design targets (e.g. uniform distribution of temperature across the stack). The systematic approach for integrating the mathematical models of the main components (i.e. PEMFC, MHs and heat pipes) is shown in the flowchart shown by Fig. 2.

A case study Results of PEM fuel cell modelling The performance characteristics of a 500 W BCS PEMFC have been used in this case study. The cell is designed with 32 cells,

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an active area of 64 cm2 and the operating temperature of 65
C. Table 1 [62,90] shows the values that have been used in modelling this 500-W PEMFC. The fuel cell model (Equations 19) is used to calculate the cooling load to be dissipated fully or in part by the heat pipes (depending on the heat demand by the MHs). This is the heat that can be transferred to the MHs in order to enhance their hydrogen discharge rate. Fig. 3a shows the polarisation curve (i.e. that is used to determine the fuel cell cooling load) of the fuel cell suggested by the model, and compares it with that the experimental data [2]. Fig. 3b also shows the total heat generated by the PEMFC as well as the portion of it that has to be collected as cooling load in order to maintain its operating temperature in the range of 60e80
C (i.e. specifically 65
C in this case). As expected and also suggested by the polarisation curve of the fuel cell (Fig. 3a), the heat generated by the fuel cell increases as the value of current density and the power output of the fuel cell increase. As discussed earlier, this behaviour resonates very well with increasing demand of hydrogen from the MH at higher power operating points of the fuel cell: the fuel cell demands for more hydrogen at higher current densities and this is the time that also more heat is available from the fuel cell to enhance the hydrogen release rate of MHs. Considering the original design of the BCS fuel cell used in this case study, the same five cooling plates used in this design have also been used in the model for inserting the heat pipes in them. As Fig. 3b is suggesting, these heat pipes are supposed to remove the maximum 880 W of heat from the stack and directing that to the MHs. This is actually the maximum cooling load of the fuel cell to be considered when designing the heat pipe system (e.g. the type of heat pipes, geometry, and the number of heat pipes).

Table 1 e The properties to be used in PEMFC model [62,90]. Properties R F T Acell Ncell r a k

Ideal gas constant Faraday Constant Temperature of the cell Active area in single cell Number of cells Internal resistance Charge transfer coefficient Mass transport constant

Value

Unit

8.314 96,485 65 64 32 0.3 0.1 1.1

J/molK C (Coulomb)
C cm2 e Ohm.cm2 e e

The recommended maximum power, to be drawn from the fuel cell, is specified by the manufacturer to be 500 W. According to the manufacturer at this operating point a hydrogen flow rate of 7.2 slpm (considering a hydrogen utilisation factor of 0.95) has to be supplied to the fuel cell. This value is a key consideration for the design of MHs to make sure that the hydrogen storage system can supply the fuel cell hydrogen demand at its maximum power point.

Metal hydride hydrogen storage system The MH hydrogen storage system, used in this case study comprises five commercially-available MH canisters each with a capacity of 660 sl of hydrogen (~61 g), chosen to supply a total of around ~5e6 kWh of electricity at an average fuel cell electrical energy efficiency of 40e45%. Each of these canisters has a diameter of 75 mm, a length of 380 mm and the total weight of 6100 g. LaNi5 was considered as the material used inside the storage. The properties of LaNi5 are available in the literature [68,91] as provided in Table 2 (obtained from Refs. [42,68]). The maximum hydrogen discharging rate can be

Fig. 2 e The flowchart of the mathematical modelling of thermal coupling arrangement between a PEMFC and MHs using heat pipes.

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1

1200

600

Fuel cell heat generation (model)

0.8

400

0.7

300

0.6

200 Output voltage (model) Output voltage (experimental) Output power (model) Output power (experimental)

0.5

0.4 0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

1000

800

Heat (Watt)

500

Output power (Watt)

Output voltage (Volt)

Fuel cell cooling load (model)

0.9

600

400

100 200

0.4

0.45

0 0.5

Current density (A/cm2)

0

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

Current density (A/cm2)

a.

b.

Fig. 3 e a. Output voltage and output power as a function of current density in 500 W PEMFC at the operating temperature of 65
C. b. Generated heat and cooling load as a function of current density in 500 W PEMFC at the operating temperature of 65
C.

calculated using Equation (12) by considering the desorption constant (Cd), the activation energy for desorption (Ed), the equilibrium pressure for desorption (Peqd), and the MH temperature. The total discharge rate at ambient temperature (25
C), suggested by the manufacturer is about 2.5 slpm (i.e. less than 0.5 slpm per canister). This discharge rate can even be less if the ambient temperature drops down to let's say 10
C. The maximum hydrogen discharge rate is already far from what is demanded by the stack, that is 7.2 slpm at 500 W (i.e. the rated power of the fuel cell). Here is where the heat extracted from the stack is transferred to the MH canisters, through heat pipes, to enhance the hydrogen flow rate from the canister. It is important to note that the scenario of this case study is based on the point that the exciting hydrogen storage capacity (305 g) is enough for this case and increasing this capacity to achieve a higher hydrogen flow rate is not desirable. Hence, the ideal solution would be increasing the hydrogen discharge rate (e.g. through heating up the MHs) while keeping the total storage capacity constant (i.e. 5  61 g of hydrogen). As suggested by Fig. 4, the discharge rate of MHs is affected by their average temperature. At 35
C (308 K) and 34 W of supplied heat, this rate increases to 1.44 slpm per canister (that is, 7.2 slpm for the five canisters) from only 0.5 slpm at 25
C (2.5 slpm total). The temperature of the MH increases as

Table 2 e The properties of LaNi5 material used by the model [42,68]. Properties DH DS Cd Ed

Enthalpy Entropy Desorption constant Activation energy for desorption

Value

Unit

31.8 0.11 9.57 15,473

kJ/mol kJ/mol.K S1 J/mol

the result of the heat transferred from the fuel cell through heat pipes (assuming that they are thermally well insulated and not losing heat to the atmosphere). It is noteworthy that the temperature assumed for this calculation is the average temperature of metal powder in the canister, while in practice the metal powder would be expected to experience some temperature gradients. The heat supplied by the fuel cell would then change the equilibrium pressure, where higher MH temperatures lead to higher equilibrium pressures (Peq) and is not only applied to gradient temperature condition.

Heat pipes system The heat dissipation capability of the heat pipe system is calculated using Equation (22) and considering the diameter, pressed thickness and effective length of the heat pipe, as well as the wick structure material and type, and the working fluid used in the heat pipe. As described in heat pipes section, the heat dissipation as a function of the effective length in different original diameter of 4, 5 and 6 mm and a pressed thickness of 2 mm is presented in Fig. 5. The graph shows that the heat dissipation capability is decreasing as the effective length of the heat pipe increases. Also if larger diameter is used, higher heat dissipation capability will be achieved. This is because larger diameter will increase the heat transfer area and help decrease the liquid pressure drop inside the heat pipe. In heat pipes, higher pressed thickness will also result in higher dissipation capacity again due to larger heat transfer area. Hence, the geometry of the design (e.g. the thickness of cooling plates, the distance between the FC and MHs, etc.) can play important roles in the design of the heat pipe system for this thermal coupling arrangement. Fig. 5 also compares the performance of the commercially available heat pipes used in the case study (i.e. presented in this section), obtained from the model, with that supplied by the manufacturer. Results are very close to those suggested by the manufacturer, with

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4

3.5

90 Heat demanded by one canister of MH, 660 sl (model) Hydrogen flow rate in one canister of MH, 660 sl (model)

3 60 2.5

2

45

1.5 30 1

Heat demanded by the MH (Watt)

Hydrogen flow rate in MH (slpm)

75

15 0.5

0 295

300

305

310

315

320

325

330

335

0 340

Temperature of MH (K) Fig. 4 e Hydrogen flow rate and heat demanded for desorption as a function of MH temperature (particularly, 35
C) of LaNi5 material in one canister (660 sl) to be coupled with 500 W PEMFC.

100 Model, original diameter of 4 mm Model, original diameter of 5 mm Model, original diameter of 6 mm Manufacturer, original diameter of 4 mm Manufacturer, original diameter of 5 mm Manufacturer, original diameter of 6 mm

Heat dissipation capability (Watt)

90 80 70 60 50 40 30 20 10 0 0

0.05

0.1

0.15 0.2 Effective length (m)

0.25

0.3

0.35

Fig. 5 e Heat transfer capacity in a copper heat pipe (screen wick) as a function of effective length and pressed thickness of 2 mm with different original diameter of 4, 5, and 6 mm (model and manufacturer specification).

maximum of 5% of error that is confirming the reliability of the mathematical model used to represent the performance of the heat pipe in the overall thermal coupling arrangement model created in MATLAB. The heat pipes have to be designed and arranged to be capable of transferring out the desired amount of heat generated in the PEMFC to the MHs. The heat pipes with an original diameter of 6 mm, a pressed thickness

of 2 mm and with different effective length of 220 mm (MH canister no 1, 3, and 5) and 280 mm (MH canister no 2 and 4) were chosen for this case study as shown in Fig. 1 (schematically) and Fig. 6. Each of these heat pipes can dissipate a maximum heat of 25 W and 20 W respectively (Fig. 5). As discussed before, it was assumed that the cooling load in the 500 W PEMFC can be transferred to the MHs (partly or in full

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depending on the demand dictated by the MHs) using the heat pipes with minimum overall thermal resistance. Based on the PEMFC calculation for the 500 W stack used in this case study, the maximum cooling load to be removed from the stack is 880 W. Therefore, with five cooling plates used in the stack, in order to dissipate 34 W of heat through each cooling plate (170 W for five cooling plates in total) to be transferred to MH canister, 2 heat pipes were used in each MH canister (i.e. 10 heat pipes in total for five cooling plates). However, in practice more number of heat pipes are expected to be required, taking into account the contact resistances and the round shape of the condenser section.

Thermal coupling of PEMFCs and MHs: results and discussion As already discussed in MH section, each MH canister needs 34 W (assuming an ideal thermal insulation covering the canister) of heat to reach 35
C in order to supply hydrogen at the rate of 1.44 slpm (or 170 W in total for five canisters to reach 7.2 slpm). 7.2 slpm is what the fuel cell requires at its maximum power point of operation (i.e. 500 W). The amount of heat generated by the PEMFC is much higher than that demanded by the MHs. Thus, some of the generated heat has to be removed using other means such as forced convection from the body of the FC or through exposing the MHs to the atmosphere (i.e. no thermal insulation might be needed), in order to maintain the optimum temperature of the PEMFC. The best design measure in this case can be decided and determined on case by case basis. It is important to note that the thermal insulations around the MH canisters are not perfect: assuming 0.03 W/m.K of thermal conductivity for the insulation material and a thickness of 10 mm and a minimum 25
C ambient temperature, 3.8 W heat can be lost through the body of the MH (already at 35
C) that increases the heat removal capacity of each canister from 34 W to 37.8 W. Considering the fact the thermal resistance between the heat pipes and each of cooling plates and MH bodies were note taken into consideration, the heat removal capacity of the heat pipes chosen for this case study (i.e. on each cooling plates) can be less than 50 W (that was calculated for an ideal heat transfer condition). Obviously the gap has to be still removed in a controlled condition from the body of the fuel cell. The comparison of the hydrogen flow rate with and without using the PEMFC heat is presented in Fig. 7a. According to Fig. 7b, only 170 W of the total 880 W cooling load supplied by the fuel cell at its maximum power point (500 W) is

required by the MHs for their total hydrogen discharge rate to be reached to 7.2 slpm (assuming some heat loses through the thermally insulated MHs). As mentioned before this is the flow rate of hydrogen required by the FC at this operating point. By supplying this heat to the MHs, the maximum hydrogen flow rate of each canister will increase from 0.5 slpm (2.5 slpm for five canisters) at an assumed ambient temperature (i.e. 25
C) to 1.44 slpm (7.2 slpm for five canisters) at 35
C.

Conclusions A mathematical model simulating the thermal coupling of a PEM fuel cell and a metal hydride hydrogen storage using heat pipes has been presented. The innovative idea of thermal coupling the PEMFC and MHs using heat pipes offers opportunities for cost reduction, performance enhancement, and compactness. The main parts of this thermal coupling arrangement were modelled separately and the sub-models were merged so that the overall performance of this thermal coupling arrangement could be investigated. The modelling process were started by analytically calculating the performance of the PEMFC so that the cooling load of the fuel cell in each operating point could be calculated. The cooling load of the PEMFC model were then used as an input to the MH model at certain temperature conditions. The MH model was used to calculate how the MH hydrogen discharge rate can be enhanced while they receive heat from the fuel cell. The model was employed to conduct a case study based on a 500 W PEMFC in the context of such a thermal coupling arrangement. The metal hydride storage used in this case study was based on LaNi5 material. The model was able to suggest the minimum number of heat pipes to be used for thermal bridging between the fuel cell and MH hydrogen canisters. The results of this case study suggested that 880 W of cooling load was available to be extracted from the fuel cell at its maximum power point of operation. According to the results of the model, 170 W of this heat was enough to increase the hydrogen release rate of the MHs from 2.5 slpm (at 25
C ambient temperature) to 7.2 slpm, enough to meet the fuel cell demand at its rated power (i.e. 500 W). It is important to note that the hydrogen storage capacity of the MHs were assumed to be enough for its application and remained to be a design constrain (i.e. 305 g for five bottles). That is why increasing the hydrogen storage capacity was not seen as a solution to increase the maximum hydrogen discharging rate. The rest of

Total length of 315 mm and effective length of 220 mm

Condenser section

Adiabatic section

Evaporator section

Fig. 6 e A copper heat pipe (screen wick), original diameter of 6 mm, pressed thickness of 2 mm and an effective length of 220 mm and heat removal capacity of 25 W.

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900 800

8

700

170 W of heat demanded by 5 MH canisters (supplied by the fuel cell through heat pipes)

6 5 4

880 W of cooling load from the PEMFC

600

Heat (Watt)

Hydrogen flow rate (slpm)

7

1

500 400 300

3 2

Cooling load by the fuel cell (model) Heat demanded by the MHs, 5 canisters (model)

75W of heat absorbed from the surrounding atmosphere by 5 MH canisters

200 100

0 1 2 3 MH heat absorption from the surrounding ambient (1), MH after adding heat (2) and fuel cell consumption (3)

a.

0 0

1

2

3 4 5 Hydrogen flow rate (slpm)

6

7

8

b.

Fig. 7 e a. Hydrogen flow rate comparison (without heat and after adding heat) in five MH canisters; and 500 W PEMFC consumption at maximum power operating point b. Hydrogen flow rate vs the cooling load of the 500 W PEMFC and the heat demanded by five 660-sl MH canisters.

the PEMFC cooling load thus has to be removed using a separate cooling arrangement, that has not been discussed within the scope of this study. In practice, the MH will only absorb the amount of heat demanded for hydrogen discharging process and can be limited by connecting the suitable number of heat pipes in the system.

[8]

[9]

Acknowledgements [10]

The authors of this article would like to thank the Indonesia Endowment Fund for Education (LPDP) for a PhD scholarship to Anggito P Tetuko.

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