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Heat and Mass Transfer in Fuel Cells and Stacks

  • S. B. BealeEmail author
  • S. Zhang
  • M. Andersson
  • R. T. Nishida
  • J. G. Pharoah
  • W. Lehnert
Chapter
  • 159 Downloads

Abstract

A review is presented of the evolution of heat and mass transfer in modern fuel cells, and the role of computational fluid dynamics in the prediction of their performance. Both polymer electrolyte and solid oxide fuel cells are considered. The mathematical details of the mass transfer driving force and the transferred substance state, as well as the distributed resistance analogy, are derived. It is shown how the transferred substance state may be used to prescribe generalised convection–diffusion boundary conditions (inlet/outlet/wall). The combination of the mass transfer driving force and the application of the distributed resistance analogy concept to fuel cell stack models are explained in detail. In addition to the governing equations for thermofluids, the mathematical modelling of fuel cells requires additional thermodynamic, electrochemical kinetic and electric considerations to be taken into account (physicochemical hydrodynamics). Moreover, the results of original research conducted over two decades and culminating in very recent results are presented and explained. This work is research-in-motion and some future possibilities are outlined in the conclusion.

Keywords

Fuel cells Computational fluid dynamics Heat transfer Mass transfer Distributed resistance analogy 

Nomenclature

A

Cell area, m2

b

Blowing parameter

B

Spalding number

C

Source term coefficient, [units of solved variable]

c

Specific heat, J/(kg K)

Dh

Hydraulic diameter, m

E

Nernst potential, V

Eact

Activation energy, J/mol

F

Faraday’s constant, 96,485 C/mol

F

Distributed resistance, kg/(m2 s)

f

Friction factor

g

Mass transfer coefficient, kg/(m2 s)

g*

Zero-flux mass transfer coefficient, kg/(m2 s)

H

Height, m

Hfg

Heat of evaporation, J/mol

h

Heat transfer coefficient, W/(m2 K)

\(i^{{\prime \prime }}\)

Current density, A/m2

\(i_{0}^{{\prime \prime }}\)

Exchange current density, A/m2

\(j^{{\prime \prime }}\)

Diffusion flux, kg/(m2 s)

kR

Reaction rate, m/s

L

Length, m

M

Molecular weight, kg/mol

\(\dot{m}^{{\prime \prime }}\)

Mass flux, kg/(m2 s)

P

Péclet number

p

Pressure, N/m2

Q

Reaction quotient, [arbitrary]

R

Universal gas constant, 8.31446 J/(mol K)

R

Resistance, Ohm m2

Re

Reynolds number

r

Volume fraction

\(\dot{S}\)

Source term, [units of solved variable] × kg/s

\(\dot{S}^{{\prime \prime }}\)

Source term, [units of solved variable] × kg/(m2 s)

s

Saturation

Sh

Sherwood number

T

Temperature, K

t

Time, s

\({\user2{U}}\)

Superficial velocity, m/s

\({\user2{u}}\)

Interstitial velocity, m/s

u

Velocity, m/s

V

Cell voltage, V, source term value, kg/s

x

Displacement, m, mole fraction

y

Mass fraction

z

Charge number

Greek Letters

α

Charge transfer coefficient, volumetric heat transfer coefficient W/(m3 K)

Γ

Exchange coefficient, kg/(m s)

γ

Reaction order

δ

Cell half-width, m

η

Overpotential, V

κ

Permeability, m2

μ

Dynamic viscosity, kg/(m s)

ν

Kinematic viscosity, m2/s

ρ

Density, kg/m3

τ

Tortuosity

Φ

Polarisation

Subscripts

b

Bulk

e

Electrode

eff

Effective

g

Gas

H2

Hydrogen

H2O

Water

int

Interface

l

Liquid

O2

Oxygen

NB

Neighbour value

t

Transformed substance state

P

Nodal value

w

Wall

0

Ambient, external

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Copyright information

© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.Forschungszentrum Jülich GmbH, Institute of Energy and Climate ResearchJülichGermany
  2. 2.Mechanical and Materials Engineering, Queen’s UniversityKingstonCanada
  3. 3.Department of Energy SciencesLund UniversityLundSweden
  4. 4.Department of EngineeringUniversity of CambridgeCambridgeUK
  5. 5.Modeling in Electrochemical Process Engineering, RWTH Aachen UniversityAachenGermany
  6. 6.JARA-HPCJülichGermany

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