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Bond Graph Modelling of a Solid Oxide Fuel Cell

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Bond Graph Modelling of Engineering Systems

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Abstract

Fuel cells are environmentally friendly futuristic power sources. They involve multiple energy domains and hence bond graph method is suitable for their modelling. A true bond graph model of a solid oxide fuel cell is presented in this chapter. This model is based on the concepts of network thermodynamics , in which the couplings between the various energy domains are represented in a unified manner. The simulations indicate that the model captures all the essential dynamics of the fuel cell and therefore is useful for control theoretic analysis.

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Abbreviations

A c :

Effective cell area (m2)

c p, c v :

Specific heat capacity at constant pressure and volume (J kg−1 K−1)

E :

Activation energy (J mol−1)

F :

Faraday’s constant (C mol−1)

G :

Gibbs free energy (J)

h :

Specific enthalpy (J kg−1)

H :

Enthalpy (J)

i :

Current (A)

K :

Valve coefficient (m s)

m :

Mass (kg)

\(\dot {m}\) :

Mass flow rate (kg s−1)

M :

Molar mass (g)

n :

Number of moles (mol)

n e :

Number of electrons participating in the reaction

p :

Pressure (N m−2)

R :

Specific gas constant (J kg−1 K−1)

R:

Universal gas constant (J mol−1 K−1)

s :

Specific entropy (J kg−1 K−1)

S :

Entropy (J K−1)

\(\dot {S}\) :

Entropy flow rate (J K−1 s −1)

T :

Temperature (K)

u :

Specific internal energy (J kg−1)

U :

Internal energy (J)

v :

Specific volume (m3 kg−1)

V :

Volume (m3)

\(\dot {V}\) :

Volume flow rate (m3 s−1)

w :

Mass fraction

x :

Valve stem position (m)

ν :

Stoichiometric coefficient

η :

Over-voltage (V)

μ :

Chemical potential (J kg−1)

ψ :

Pre-exponential coefficient (A m−2)

ξ :

Reaction advancement coordinate (mol)

\(\zeta_\mathrm{f} ,\zeta_\mathrm{o} \) :

Fuel and oxygen utilisations

β :

Charge transfer coefficient

λ :

Convection heat trans. coefficient (J m−2 s−1 K−1)

ai:

Anode side inlet

an:

Anode

ao:

Anode side outlet

act:

Activation

AS:

Air source

b:

Bulk

ca:

Cathode

ci:

Cathode side inlet

co:

Cathode side outlet

conc:

Concentration

d:

Downstream side

ENV:

Environment

gen:

Generated

H:

Hydrogen gas

HS:

Hydrogen source

I1:

Interconnect on anode side

I2:

Interconnect on cathode side

L:

Limiting

M:

Membrane electrode assembly

N:

Nitrogen gas

ohm:

Ohmic

O:

Oxygen gas

PL:

Polarisation losses

r:

Reaction

TPB:

Triple phase boundary

u:

Upstream side

W:

Water vapour

i:

Inlet

o:

Outlet

r:

Reaction

ref:

Reference state

0:

Initial state

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Acknowledgments

The first author would like to acknowledge Prof. Moses Tadé, Dean of Engineering, Curtin University of Technology, for kindly permitting him to write this chapter during his stay as a research associate at the University.

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Authors and Affiliations

  1. Department of Chemical Engineering, Curtin University of Technology, Perth, WA, 6845, Australia

    P. Vijay

  2. Department of Mechanical Engineering, Indian Institute of Technology, Kharagpur, India

    A.K. Samantaray & A. Mukherjee

Authors
  1. P. Vijay
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  2. A.K. Samantaray
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  3. A. Mukherjee
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Corresponding author

Correspondence to P. Vijay .

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Editors and Affiliations

  1. of Applied Sciences, Bonn-Rhein-Sieg University, Sankt Augustin, 53754, Germany

    Wolfgang Borutzky

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Vijay, P., Samantaray, A., Mukherjee, A. (2011). Bond Graph Modelling of a Solid Oxide Fuel Cell. In: Borutzky, W. (eds) Bond Graph Modelling of Engineering Systems. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-9368-7_10

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  • DOI: https://doi.org/10.1007/978-1-4419-9368-7_10

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  • Online ISBN: 978-1-4419-9368-7

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