The thermal transport phenomena and mechanical effects due to thermal-inertia loading during start-up/shut-down operations in a 3D proton exchange membrane fuel cell (PEMFC) stack in a subfreezing environment are studied in this paper. Under the protection of a specific heat insulator, we investigate the time consumption problem due to thermal transport during the heating-startup/cooling-shutdown processes in order to find a way to normally restart PEMFC stack without regard to the electrochemical reaction. On the other hand, the mechanical effects due to thermal-inertia loading are illustrated as well for PEMFC stack in subfreezing environment. In the numerical simulations, we design a combined finite element/upwind finite-volume discretization to approximate the thermal transport equation for different cases of thermal transport process and a finite element approximation to solve the displacement fields of thermal/inertia-induced mechanical problem for a 3D PEMFC stack. The numerical results provide the rational guidance to preserve heat in PEMFC stack in order to start fast before electrochemical reactions occur and prevent the stack from interior and exterior mechanical damages. The optimization design for the material of PEMFC stack to reduce the remarkable mechanical effects due to inertia loading is presented as well.

1.
Mao
,
L.
,
Wang
,
C.
, and
Tabuchia
,
Y.
, 2007, “
A Multiphase Model for Cold Start of Polymer Electrolyte Fuel Cells
,”
J. Electrochem. Soc.
0013-4651,
154
, pp.
B341
B351
.
2.
Jiang
,
F.
,
Fang
,
W.
, and
Wang
,
C.
, 2007, “
Non-Isothermal Cold Start of Polymer Electrolyte Fuel Cells
,”
Electrochim. Acta
0013-4686,
53
, pp.
610
621
.
3.
Weber
,
A.
, and
Newman
,
J.
, 2004, “
A Theoretical Study of Membrane Constraint in Polymer-Electrolyte Fuel Cell
,”
AIChE J.
0001-1541,
50
, pp.
3215
3226
.
4.
Tang
,
Y.
,
Santare
,
M. H.
,
Karlsson
,
A. M.
,
Cleghorn
,
S.
, and
Johnson
,
W. B.
, 2006, “
Stresses in Proton Exchange Membranes Due to Hygro-Thermal Loading
,”
ASME J. Fuel Cell Sci. Technol.
1550-624X,
3
, pp.
119
124
.
5.
Martemianov
,
S.
,
Gueguen
,
M.
,
Grandidier
,
J.
, and
Bograchev
,
D.
, 2009, “
Mechanical Effects in PEM Fuel Cell: Application to Modeling of Assembly Procedure
,”
J. Appl. Fluid Mech.
,
2
, pp.
49
54
. 1735-3645
6.
Kröner
,
D.
, and
Rokyta
,
M.
, 1994, “
Convergence of Upwind Finite Volume Schemes for Scalar Conservation Laws in Two Dimensions
,”
SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal.
0036-1429,
31
, pp.
324
343
.
7.
Kroner
,
D.
,
Noelle
,
S.
, and
Rokyta
,
M.
, 1995, “
Convergence of Higher Order Upwind Finite Volume Schemes on Unstructured Grids for Scalar Conservation Laws in Several Space Dimensions
,”
Numer. Math.
0029-599X,
71
, pp.
527
560
.
8.
Kröner
,
D.
, and
Ohlberger
,
M.
, 2000, “
A Posteriori Error Estimates for Upwind Finite Volume Schemes for Nonlinear Conservation Laws in Multi Dimensions
,”
Math. Comput.
0025-5718,
69
, pp.
25
39
.
9.
Kang
,
T.
, and
Yu
,
D.
, 2001, “
Some a Posteriori Error Estimates of the Finite-Difference Streamline-Diffusion Method for Convection-Dominated Diffusion Equations
,”
Adv. Comput. Math.
1019-7168,
15
, pp.
193
218
.
10.
Johnson
,
C.
,
Schatz
,
A. H.
, and
Wahlbin
,
L. B.
, 1987, “
Crosswind Smear and Pointwise Errors in Streamline Diffusion Finite Element Methods
,”
Math. Comput.
0025-5718,
49
, pp.
25
38
.
11.
Niijima
,
K.
, 1989, “
Pointwise Error Estimates for a Streamline Diffusion Finite Element Scheme
,”
Numer. Math
,
56
, pp.
707
719
.
12.
Roos
,
H. G.
, and
Zarin
,
H.
, 2003, “
The Streamline-Diffusion Method for a Convection-Diffusion Problem With a Point Source
,”
J. Comput. Appl. Math.
0377-0427,
150
, pp.
109
128
.
13.
Stynes
,
M.
, and
Tobiska
,
L.
, 2003, “
The SDFEM for a Convection-Diffusion Problem With a Boundary Layer: Optimal Error Analysis and Enhancement of Accuracy
,”
SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal.
0036-1429,
41
, pp.
1620
1642
.
14.
Franca
,
L.
, and
Hughes
,
T.
, 1993, “
Convergence Analyses of Galerkin Least-Square Methods for Symmetric Advective-Diffusive Forms of the Stokes and Imcompressible Navier-Stokes Equations
,”
Comput. Methods Appl. Mech. Eng.
0045-7825,
105
, pp.
285
298
.
15.
Tezduyar
,
T. E.
, 1991, “
Stabilized Finite Element Formulations for Incompressible Flow Computations
,”
Adv. Appl. Mech.
0065-2156,
28
, pp.
1
44
.
16.
Thompson
,
L.
, and
Pinsky
,
P.
, 1995, “
A Galerkin Least-Squares Finite Element Method for the Two-Dimensional Helmholtz Equation
,”
Int. J. Numer. Methods Eng.
0029-5981,
38
, pp.
371
397
.
17.
Fan
,
Y.
,
Tanner
,
R.
, and
Phan-Thien
,
N.
, 1999, “
Galerkin/Least-Square Finite-Element Methods for Steady Viscoelastic Flows
,”
J. Non-Newt. Fluid Mech.
,
84
, pp.
233
256
.
18.
Feistauer
,
M.
, and
Felcman
,
J.
, 1997, “
On the Convergence of a Combined Finite Volume-Finite Element for Nonlinear Convection-Diffusion Probelms
,”
Numer. Methods Partial Differ. Equ.
0749-159X,
13
, pp.
163
190
.
19.
Feistauer
,
M.
,
Slavik
,
J.
, and
Stupka
,
P.
, 1999, “
On the Convergence of a Combined Finite Volume-Finite Element Methods for Nonlinear Convection-Diffusion Problems. Explicit Schemes
,”
Numer. Methods Partial Differ. Equ.
0749-159X,
15
, pp.
215
235
.
20.
Feistauer
,
M.
,
Felcman
,
J.
, and
Lukáčová-Medvid’ová
,
M.
, 1995, “
Combined Finite Element-Finite Volume Solution of Compressible Flow
,”
J. Comput. Appl. Math.
0377-0427,
63
, pp.
179
199
.
21.
Sun
,
P. T.
,
Xue
,
G.
,
Wang
,
C. Y.
, and
Xu
,
J. C.
, 2008, “
A Combined Finite Element-Upwind Finite Volume Newton’s Method for Liquid Feed Direct Methanol Fuel Cell Simulations
,”
Proceedings of the ASME Sixth International Fuel Cell Science, Engineering and Technology Conference
, ASME, Denver, pp.
851
864
.
22.
Sun
,
P. T.
,
Xue
,
G.
,
Wang
,
C. Y.
, and
Xu
,
J. C.
, 2009, “
Fast Numerical Simulation of Two-Phase Transport Model in the Cathode of a Polymer Electrolyte Fuel Cell
,”
Comm. Comp. Phys.
1815-2406,
6
, pp.
49
71
.
23.
Sun
,
P. T.
,
Xue
,
G.
,
Wang
,
C. Y.
, and
Xu
,
J. C.
, 2009, “
New Numerical Techniques for a Liquid Feed 3D Full Direct Methanol Fuel Cell Model
,”
SIAM Appl. Math.
,
70
, pp.
600
620
.
24.
Sun
,
P. T.
,
Xue
,
G.
,
Wang
,
C. Y.
, and
Xu
,
J. C.
, 2009, “
A Domain Decomposition Method for Two-Phase Transport Model in the Cathode of a Polymer Electrolyte Fuel Cell
,”
J. Comput. Phys.
0021-9991,
228
, pp.
6016
6036
.
25.
Sun
,
P. T.
,
Wang
,
C. Y.
, and
Xu
,
J. C.
, 2010, “
A Combined Finite Element-Upwind Finite Volume Method for Liquid-Feed Direct Methanol Fuel Cell Simulations
,”
ASME J. Fuel Cell Sci. Technol.
1550-624X,
7
, p.
041010
.
26.
Zienkiewicz
,
O. C.
,
Taylor
,
R. L.
, and
Zhu
,
J. Z.
, 2005,
The Finite Element Method: Its Basis and Fundamentals
, 6th ed.,
Butterworth-Heinemann
,
Burlinton, MA
.
27.
Kolin
,
A.
, 1953, “
Demonstration of Parabolic Velocity Distribution in Laminar Flow
,”
Am. J. Phys.
0002-9505,
21
, pp.
619
620
.
You do not currently have access to this content.