# Thermal and flow analysis in a proton exchange membrane fuel cell

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## Abstract

The effects of anode, cathode, and cooling channels for a Proton Exchange Membrane Fuel Cell (PEMFC) on flow fields have been investigated numerically. Continuous open-faced fluid flow channels formed in the surface of the bipolar plates traverse the central area of the plate surface in a plurality of passes such as a serpentine manner. The pressure distributions and velocity profiles of the hydrogen, air and water channels on bipolar plates of the PEMFC are analyzed using a two-dimensional simulation. The conservation equations of mass, momentum, and energy in the three-dimensional flow solver are modified to include electro-chemical characteristics of the fuel cell. In our three-dimensional numerical simulations, the operation of electro-chemical in Membrane Electrolyte Assembly (MEA) is assumed to be steady-state, involving multi-species. Supplied gases are consumed by chemical reaction. The distributions of oxygen and hydrogen concentration with constant humidity are calculated. The concentration of hydrogen is the highest at the center region of the active area, while the concentration of oxygen is the highest at the inlet region. The flow and thermal profiles are evaluated to determine the flow patterns of gas supplied and cooling plates for an optimal fuel cell stack design.

## Key Words

PEMFC Flow-Field Single Cell Pressure Distribution Temperature Profile Concentration Distribution## Nomenclature

*A*The pre-exponential factor

- \(\bar C_p \)
Mean constant pressure specific heat [

**J/kg-K**]- \(\bar C_p^0 \)
Reference constant pressure specific heat [J/kg-K]

- \(\bar C\)
Mean constant volume specific heat

*D*_{m}Molecular diffusivity [m

^{2}/s]*e*Internal energy [W/m

^{2}]*E*_{a}Activation energy for the reaction

*F*_{h,j}Diffusional thermal energy flux in direction

*X*_{j}[W/m^{2}]*F*_{m,j}Diffusional flux component in direction

*X*_{j}*h*Static enthalpy [J/kg]

*K*_{i}Porosity [m

^{3}/m^{3}]*H*_{m}Heat of formation [J/kg]

*k*Thermal conductivity [W/nvK.]

*m*Mass [kg]

*m*_{m}Mass fraction of mixture constituent

*m*Mass flow rate [kg/s]

*M*Molecular weight

*n*Number of cell

*P*Piezometric pressure [Pa]

*P*_{e}Total power in the stack [Watts]

*Q*Heating rate [Watts]

*S*_{m}Mass source

- S
_{h} Energy source

*S*_{i}Momentum source

*T*Temperature [K]

*T*_{o}Reference temperature [K]

*U*_{i}Superficial velocity [m/s]

*U*_{j}Absolute fluid velocity [m/s]

- \(\bar u_j \)
Relative velocity in fluid local coordinate frame [m/s]

*U*_{a}Fraction of the air usage

*U*_{h}Fraction of the hydrogen usage

*V*_{c}Cell voltage [V]

*X*_{j}Cartesian coordinate frame

## Greek symbols

- ρ
Density [kg/m

^{3}]- β
Temperature exponent

- β
_{i} Permeability

- μ
Viscosity [N-s/m

^{2}]- τ
_{ij} Viscous stress tensor [N/m

^{2}]- ξ
_{j} Orthotropic direction

- Π
Product of all constituents

- Σ
Summation over all mixture constituents

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