. . , , , , . , . . , ( ) , , : , , , . , , .

. . (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