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ABSTRACT
To investigate the effects of varying assisted heating methods on the proton exchange membrane fuel cell (PEMFC) stack in extremely low-temperature conditions, a quasi-two-dimensional dynamic model is developed. This model considers the effect of cooling channels on cold starts and has been verified by experimental data. The limited self-start ability of an adiabatic PEMFC is tested, and the result shows that the PEMFC cannot start successfully from −40°C. Then, the effects of resistance wire heating and recycled coolant heating methods on the PEMFC stack are analyzed at −40°C. For the resistance wire heating method, due to the limitation of thermal conductivity, higher heating power can hardly raise the temperature of the middle cells in the stack. Furthermore, only stacks with fewer than 6 cells can start successfully. For the recycled coolant heating method, the heat can be effectively transferred to the internal zone of the stack through the coolant. The maximum temperature difference in the stack is decreased (from 32.43°C to 7.64°C, 308.6 mW cm−2) with higher coolant flow rates. However, higher heating power is needed to achieve a successful cold start (205.8 mW cm−2 under 0.01 m s−1, 308.6 mW cm−2 under 0.05 m s−1). In summary, the recycled coolant heating method is more suitable for the cold start of the stack at −40°C.
Nomenclature
| a | = | water activity |
| A | = | area (m2) |
| ASR | = | resistance of the cell (Ω m2) |
| c | = | mole concentration (mol m−3) |
| CP | = | specific heat capacity (J kg−1 K−1) |
| D | = | diffusion coefficient (m2 s−1) |
| EW | = | equivalent weight of the membrane (kg kmol−1) |
| F | = | Faraday’s constant (C mol−1) |
| h | = | latent heat (J kg−1); convective heat transfer coefficient (W m−2 K−1) |
| I | = | current density (A m−2) |
| i | = | electrochemical reaction rate (A m−3) |
| k | = | thermal conductivity (W m−1 K−1) |
| K | = | permeability (m2) |
| L | = | total length of single cell (m) |
| W | = | width of channel; width of coolant channel (m) |
| M | = | number of nodes along the channel |
| N | = | cell numbers in the stack |
| n | = | moles of electrons production per mole of reactant consumption |
| nd | = | electro-osmotic coefficient |
| p | = | pressure (Pa) |
| pc | = | capillary pressure (Pa) |
| R | = | ideal gas constant (J K−1 mol−1) |
| RH | = | relative humidity (%) |
| s | = | volume fraction |
| S | = | source term (mol m−3 s−1) |
| Sh | = | Sherwood number |
| ST | = | stoichiometric ratio |
| T | = | temperature (K) |
| t | = | time (s) |
| V | = | voltage (V); volume (m−3) |
| x, y | = | coordinate position (m) |
| Yi | = | molar fraction of species i |
| Greek letters | = | |
| α | = | transfer coefficient |
| δ | = | thickness (m) |
| ε | = | porosity |
| θ | = | contact angle |
| λ | = | membrane water content |
| μ | = | dynamic viscosity (kg m-1 s-1) |
| ρ | = | density (kg m-3) |
| ζ | = | gas-liquid velocity ratio |
| ω | = | ionomer volume fraction |
| Superscript and subscript | = | |
| 0 | = | standard condition |
| a | = | anode |
| act | = | activation loss |
| ave | = | average |
| c | = | cathode |
| conc | = | concentration loss |
| cond | = | condensation |
| control | = | control volume |
| cool | = | coolant |
| CC | = | coolant channel |
| eff | = | effective |
| eq | = | equilibrium |
| freeze | = | freezing temperature |
| fusn | = | fusion |
| g | = | gas |
| H2 | = | hydrogen |
| H2O | = | water |
| ice | = | ice |
| in | = | inlet |
| lim | = | limit |
| lq | = | super-cooled (liquid) water |
| nf | = | nonfrozen |
| nernst | = | Nernst |
| nmw | = | nonfrozen membrane water |
| ohmic | = | ohmic loss |
| out | = | outlet |
| O2 | = | oxygen |
| per | = | permeate |
| reac | = | reaction |
| ref | = | reference state |
| sat | = | saturation state |
| surr | = | surroundings |
| total | = | total |
| vp | = | vapor |
| i-l | = | between ice and liquid water |
| l-n | = | between liquid water and non-frozen membrane water |
| n-v | = | between non-frozen membrane water and vapor |
| v-l | = | between vapor and liquid water |
Acknowledgements
This research is supported by the National Key Research and Development Program of China (Grant No. 2022YFE0103100), National Natural Science Foundation of China (Grant No. 52176196), Natural Science Foundation of Tianjin (China) for Distinguished Young Scholars (Grant No. 18JCJQJC46700), and “Research and development project of key technologies of basic simulation software for the automotive industry” fund of China Automotive Technology&Research Center Co. Ltd (ZX20220002).
Disclosure statement
No potential conflict of interest was reported by the authors.
Supplementary Material
Supplemental data for this article can be accessed online at https://doi.org/10.1080/15435075.2022.2163590