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Science, Chemistry Technology, Chemistry,
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. . , , , , . , . . , ( ) , , : , , , . , , .
. . (radiation): , . (convention): -, . . .
: (conduction): , .
Q: () (W), A: (m2), () U: (W/m2K)
U. .
T UQ
U , , . , . , , . , , , . , . . , . , . . .
, h, . , .
, , h1, h2, h3 1, 2 3. , .
11hQ 22hQ 33hQ :
11 h
1Q
22 h
1Q
33 h
1Q
:
321321 h1h1h1AQ
1+2+3= , :
321 h1h1h1AQ :
U1
AQ
:
321 h1
h1
h1
U1
.
UAQ
, , . . 1, 2, 3 :
332211321 Ah 1Ah 1Ah 1Q
. U, h1, h2 h3. .
U1
33122111 h1AAh1AAh1U1
1, 2 3 . Q , U . , , 1 :
AUQ 1111AU
Q
, 1 2. , ( 1) (2 ). , , (k), Fourier:
xT /x
TkAQ xTTkAQ 21 . , . : , , , .
, , ,
, , , . .
x
TTkAQ 21 x/k ATTQ 21 x/k k/x
1. (Science, 334, 962-965, 18 Nov. 2011).
, , , .
, dx, . :
()+() ()+()
x
TkAQ
x
TkAxQ dx
tTACp
AdxQ'
dxx
Tkx
Ax
TkAdxxQ tTACQ'
x
Tkx
p (),,
tTCQ'
x
Tk p22
,()
tTCQ'
z
TyT
x
Tk p22
2
2
2
2
, , . :
( Fourier)
tTCp
z
TyT
x
Tk 22
2
2
2
2
0z
TyT
x
Tk 22
2
2
2
2
( Poisson):
( Laplace):
0Q'z
TyT
x
Tk 22
2
2
2
2
, Laplace :
0x
T2
2
112
121 xx
xx
TTTT x=x1:1 x=x2:2 () (x):
, (x1 x2).
:
21
21
xx
TTkAQ
: 21
21
xx
TTkAQ
, . k1, k2, k3 x1, x2, x3 T1, T2, T3 4.
x
TTkAQ 21
:
QAk
xTT1
121 QAkxTT 2232 QAkxTT 3343
RRRR AQ
kx
kx
kx
AQQ
Akx
Akx
Akx
321
3
3
2
2
1
13
3
2
2
1
141 TT
/ A/kx TTQ ji 41 R1, R2 R3=
R = . .
x
TkA dxtTACp AdxQ' dxxTkxAxTkA tTACQ'
x
Tkx
p (),,
tTCQ'
x
Tk p22
,()
tTCQ'
z
TyT
x
Tk p22
2
2
2
2
()+() ()+()
+ + =
(r, , z):
tTCpQ'
z
TTr
1rr
T1r
Tk 22
2
2
22
2
tTCQ'T
sinr1
T
sinsinr1
rTrr
1p2
2
2222
2 k (r, , ):
. , , , aT1kk 0 0k .
, 0
rdr1dT
drTd2
2
1
1
2
121
r
r1n
r
r1n
TTTT
1
2
21
r
r1n
TTl2Q
r=r1:T=T1 r=r2:T=T2
( l , ).
( ) Laplace :
:
12
1121
r
1r
1r
1r
1
TTTT
21
21
r
1r
14Q
R
kx
xkAQ
R(=x/kA) (Ohm ) - () - :
N21
212
2
1
1
R...RR...
...
R
RQ
0rTrr
12
2
r1, r2 l. , , k. 1 2. , r r1 r2. dr r, . 2rl, :
dxdTkAQ
drdT
rlk2Q r1 r2
21
2
1
T
T
r
rdTlk2
r
drQ 12 21/rrln TTlk2Q
12
21m
rr
TTl2kQ r 12 12m /rrln rrr
rm . , ra :
12
21a
rr
TTlr2Q k
r :
2rk4Q drdT
r1 r2 :
dTk4r
drQ 21
2
1
T
T2
r
r 21 21 1/r1/r TTk4Q
: r1 r2 , 1 2 .
Fuel Cell Concept.
1,5 kW/L 2,1 kW/L
1 kW/kg 1,4 kW/kg 80 kW
2005 2008 April 2011 DRD/DRIA/TASE/SGSE PSA CONFIDENTIAL 29
PEM Fuel Cells Schematics Properties (for PEM)
High Ionic Conductivity
Electrical Insulator
Chemical and Oxidative Stability
Mechanical and Thermal Integrity
Low Gas Permeability
Low Production Cost Anode :
Cathode :
Summary :
H2 2H+ + 2e-
O2 + 2H+ + 2e- H2O
H2 + O2 H2O
-
-
+ +
, ,
2 2+ + 2e- : 2 + 4+ + 4e- : 2
22 + 2 :
22
Stack Assembly
Repeating U/C Plate Assy
Anode Hardware
Cathode I/F Plate Assy
MEA Fuel(Anode) Gasket
Anode I/F Plate Assy
Isolation Sheet Bus Plate
Air(Cathode) Gasket
MEA Fuel(Anode) Gasket
Air(Cathode) Gasket
Bus Plate
Isolation Sheet Cathode Hardware
, . Reynolds , . . , . , , .
. , Reynolds . . F1F1 F2F2 . F1F1 F2F2 . y x.
TaTbTc. Ta Tb . Tc . TdTeTf. , , . T2 . Tc Td . Tc Td Ta Tf
Q . 1 m . :
c111 TTA Qh x/k ATTQ 21 h1 k/x 1/h1A1 . h1 . h2
2d22 TTA Qh
: o 1/h1A1, o x/k Am o 1/h2A2.
/ A/kx TTQ ji 41
22m11 h1
kAx
h1
Q
1 :
22
1
m
1
1
1
AhA
kAxA
h1
AQ
22
1
m
1
1
1
AhA
kAxA
h1
1U U1 :
:
.
AUQ 11
1 2 m , U2 Um . . .
22
1
m
1
1
1
dhd
kdxd
h1
1U
U1 . x , 1 d1 2 d2. :
22
1
m
1
1
1
AhA
kAxA
h1
1U
(k) () , (h) - - . : , . , , , (, , ..). , .
22m11 h1
kAx
h1
Q
, , , ,
TTkA
kAQ bw
-, . (Tw) (Tb) , , . :
, , , , , . () , ( Newton):
(h=k/) (,,,,,), ,
ThAQ -Newton
N1i niipah pi ai n, . () h (, -, ). (.. Reynolds, Prandtl), . , ( ). , Nusselt (Nu), Prandtl (Pr) Reynolds (Re) :
PraReNu DRe ,khDNu kCPr p
, . , . . , . , , .
. , . . . , . , , . , -, , - . , , . : , Prandtl. .
Prandtl. . , , , . Prandtl k/cp
k
c
Prp
Prandtl > 1, , , . . Prandtl 70C 2.5, 600. Prandtl 1 .
12.1 .
, . , . , . . , . . , . , .
: u0 ,: T
xukcx)(x1 )T-0.332(TdydT 03 p3 3/40 ww
ww
x dydT
TTkh
11 0.
: x=0 x = x0, , x>x0 T=Tw, w>T. : , k, cp . :
(dT/dy)w . hx x :
(dT/dy)w
xukcx)(x1 0.332h 03 p3 3/40x
. , . . . , . , h, .
, :
kc,DGkc, VDkhD pp
kc,DGGch p1p
G . (DG/)(cp/k)
Nusselt, Reynolds Prandtl, . Stanton St.
NuStRePr .
,, n0,8Pr0,023Re/Nu kDhi
n 0,4 0,3 . (+)/2, . Reynolds 10000 Prandtl 0,7 160.
. :
klGC2,01ldRePr1,86Nu p1/30,14
s
G s l d
0,80.02ReNu Prandtl ,,
Prandtl.
n0,8Pr0,023ReNu .
:
0,60,24ReNu 0,30,6Pr0,26ReNu
, Pr 0,74, :
, . Re ( 0,2 200)
0,30,43Pr0,86ReNu f w m. (m=(T+)/2).
. . , , . , . .
, . . . . , . h . h .
, Nusselt :
4/1
f0
23
m jdgk0,72h
g d0 f j
Nusselt :
1/4
1
23
m xgk0,943h
x
f
fSUf 0,75,TT TSU
. , , . . . . . . , . , , h . h q (q=Q/A). , . . . .
. ,
,,(),,, ,
h, U U h. ,
, , . , , . . 0.8 400 microms. . . , . . .
1 ,1,1,1
- Kirchhoff.
. , , Stefan Boltzmann:
4b E
Stefan-Boltzmann (5.669*10-8W-2K-4). , (), , . Kirchhoff : E1/1 22 . e :
e=E/Eb
Kirchhoff :
b
bEE
bbEE
e b .
b=1, :
bEE
e
e . , .
. . . m . m. Stefan-Boltzmann:
4E Stefan-Boltzmann ,1-8 W/m2
K4
, : 124241112 FQ
11
1
1F
22
1
1
12
1 , 1 2 , , F12 , (, ) . , , F12 :
1 2 , 1 2 . , 12 , : 42411112 Q