J. of Thermal Science Vol.5, No.3 [

= . . . . . .

N u c l e a t e P o o l B o i l i n g of P u r e Liquids a n d B i n a r y M i x t u r e s : P a r t II A n a l y t i c a l M o d e l for B o i l i n g H e a t Transfer of B i n a r y M i x t u r e s on S m o o t h T u b e s and C o m p a r i s o n of A n a l y t i c a l M o d e l s for b o t h P u r e Liquids and B i n a r y M i x t u r e s w i t h E x p e r i m e n t a l D a t a Guoqing Wang

Zhiwei Xie

Chemical Engineering Department, Guangdong University of Technology, Guangzhou 510090, China

Yingke Tan Chemical Engineering Research Institute, South China University of Technology, Guangzhou 510641, China

A combined physical model of bubble growth is proposed along with a corresponding bubble growth model for binary mixtures on smooth tubes. Using the general model of Wang et al. [11 and the bubble growth model for binary mixtures, an analytical model for nucleate pool boiling heat transfer of binary mixtures on smooth tubes is developed. In addition, nucleate pool boiling heat transfer of pure liquids and binary mixtures on a horizontal smooth tube was studied experimentally. The pure liquids and binary mixtures included water,

methanol, ethanol, and their binary mixtures. The analytical models for both pure liquids and binary mixtures are in good agreement with the experimental data.

Keywords: N u c l e a r p o o l b o i l i n g , p u r e l i q u i d s , b i n a r y m i x t u r e s .

q

INTRODUCTION

a1 - ATr

Since Bonilla and Perry (1941) [21 published the first article about boiling heat transfer of binary mixtures, a large body of research has been published concerning nucleate pool boiling heat transfer of binary mixtures on horizontal smooth tubes or plates. The results showed that boiling heat transfer coefficients of almost all binary mixtures are lower than their ideal boiling heat transfer coefficients. The ideal boiling heat transfer coefficient has two definitions. One is based on the average superheat of the binary mixture: AT I = xAAT A + zBATB

Received December, 1995.

(1)

(2)

The other is based on the average boiling heat transfer coefficient of the binary mixture: at

= ZAaA

+ zBc~B

(3)

Eqs.(2) and (3) are not equal, but there is little actual difference. The mechanism describing the drops of boiling heat transfer coefficients of binary mixtures can be explained in two aspects. One is that the mass transfer process causes a drop of the effective wall superheat; therefore, the boiling heat transfer coefficient calculated using the measured wall superheat is lower than the ideal boiling heat transfer coefficient calculated using the ideal wall superheat. This can be called the

202

Journal of Thermal Science, Vol. 5, No.3, 1996

M

Nomenclature mass diffusivity of more volatile component in less volatile component, m2/s combined number, ~Yi---~i ~' total heat flux, W / m 2 evaporation microlayer heat flux for binary mixtures, W / m 2 relaxation microlayer heat flux for binary mixtures, W / m 2 wall superheat of component A, K wall superheat of component B, K ideal wall superheat, K evaporation microlayer mass flux for binary mixtures, kg/(m2-s) relaxation microlayer mass flux for binary mixtures, kg/(m2-s) combined number, p v h ] g 3VZ3'-~aw

N

combined number,

x

instantaneous liquid mass fraction of more volatile component in binary mixtures. liquid mass fraction of component A in binary mixtures liquid mass fraction of component B in binary mixtures bulk liquid mass fraction of more volatile component in binary mixtures

D G q qe,m qr,m ATA ATB

ATx Jr J~

XA xs

Xb

5.367Prl

x~

x,~ X Yb

y~ Y a a1 aA

k

/ 6 p v h f g x/ra

mass transfer effect. T h e other is t h a t the physical properties of binary mixtures change nonlinearly with composition, so the boiling heat transfer coefficient measured experimentally is lower than the ideal boiling heat transfer coefficient calculated using a linear mixing law. This can be called the nonlinear effect. Predicting the influences of the mass transfer effect and the nonlinear effect on the boiling heat transfer coefficients of binary mixtures is a key problem in nucleate pool boiling heat transfer research of binary mixtures. Therefore, a n u m b e r of heat transfer correlations have been proposed to predict the boiling heat transfer coefficients for binary mixtures [3-s] . Some are empirical while others are semiempirical. Almost all these heat transfer correlations manage to predict the deviation between the boiling heat transfer coefficients and the ideal boiling heat transfer coefficients for their specified conditions; however, this m e t h o d is difficult to establish the correlations t h a t can be widely used to predict boiling heat transfer coefficients for binary mixtures. The present paper, through a theoretical analysis of the bubble growth process on a heated surface, directly derives an analytical model for nucleate pool boiling heat transfer of binary mixtures

(~B A0 Pb Pl

local liquid mass fraction of more volatile component at bubble b o u n d a r y in binary mixtures bulk liquid mole fraction of more volatile component in binary mixtures combined number, 3pt6tD bulk vapour mass fraction of more volatile component in binary mixtures local vapour mass fraction of more volatile component inside bubble in binary mixtures combined number, pzD 2pv~

boiling heat transfer coefficients, W / ( m 2. K) ideal boiling heat transfer coefficients, W / ( m 2. K) boiling heat transfer coefficients of component A, W / m ( m 2- K) boiling heat transfer coefficients of component B, W / ( m 2. K) increase of the local boiling t e m p e r a t u r e at the bubble boundary, K bulk liquid density, k g / m 3 local liquid density at bubble boundary, k g / m 3

on smooth tubes. ANALYTICAL TURES

MODEL

FOR BINARY

MIX-

The present p a p e r utilizes the concept t h a t the drops of boiling heat transfer coefficients of binary mixtures results from the mass transfer effect and the nonlinear effect.

M a s s Transfer E f f e c t W h e n vaporizing nuclei are activated, the bubble growth is in the initial stage (inertia controlled or isothermal growth). Because t h e r m a l diffusion has no influence on the initial stage of bubble growth, the mass transfer effect resulting from the thermal diffusion also has no influence on the active pore density. Therefore, the mass transfer effect only influences the bubble departure radius and the bubble growth time, thus affecting the bubble waiting time and the bubble emission frequency. Using the combined physical model for bubble growth in pure liquids on smooth tubes in the p a p e r of Wang et al. [1], a new combined physical model for

Guoqing Wang et al.

Nucleate Pool Boiling of Pure Liquids and Binary Mixtures: Part II - - Analytical Model 203

bubble growth in binary mixtures on smooth tubes is developed based on the following assumptions (Fig.l): (1) Continuing to use the concept of the relaxation microlayer, the present paper assumes that the height of the relaxation microlayer does not change during the bubble growth process and is equal to the thickness, ~ , of the thermal boundary layer near the heated surface. (2) The bubble growth process enters the asymptotic stage (thermal diffusion controlled) very shortly after the initial bubble formation. In the asymptotic stage, the bubble is a hemisphere with radius R, and R _< 5~. The local vapour mass fraction, y~, of the more volatile component in the binary mixture inside the bubble and the local liquid mass fraction, x~, of the more volatile component in the binary mixture at the bubble boundary are both uniform due to the large vapour mass diffusivity and are in equilibrium. The vapour temperature inside the bubble and temperature of the bubble boundary are both uniform due to the large vapour thermal diffusivity and both equal to the local boiling temperature, Ts + AO, corresponding to the local liquid mass fraction, x~, and system pressure. The liquid composition around the bubble is uniform and equal to the bulk liquid mass fraction, Xb, of the more volatile component in the binary mixture. (3) The latent heat required for bubble growth is supplied by conduction from both the evaporation microlayer under the hemispherical bubble and the relaxation microlayer around the bubble.

\\,\\\\\\\

reduction of the local liquid mass fraction of the more volatile component at the bubble boundary and an increase of the local boiling temperature at the bubble boundary. Consequently, the temperature difference driving the heat flow, the effective wall superheat, is reduced and the heat transfer coefficient is decreased. If the increase of the local boiling temperature at the bubble boundary is denoted by A0 and the measured wall superheat is denoted by AT, the effective wall superheat, AT~ff, is given by

AT~fs =

(4)

b. Heat and mass transfer from the relaxation microlayer Substitution of EQ.(4) for (T~ - Ts) into Eq.(27) in Ref.[1] gives the heat flux supplied by the relaxation microlayer in binary mixtures: k(AT qr, m - -

-

A0)

(5)

~/3~r a t

Using the heat and mass transfer analogy, the ideal mass flux through the bubble boundary, analogous to Eq.(24) in Wang et al. [1], is given by Jr -

D(pb

- p~) _

Dpz(xb

-- x i )

(6)

In the combined physical model for bubble growth in binary mixtures, the liquid composition around the bubble is assumed to be uniform and equal to the bulk liquid mass fraction, Xb. Therefore, Eq.(6) describes the mass flux supplied by the relaxation microlayer in binary mixtures. c. Heat and mass transfer from the evaporation microlayer Substitution of Eq.(4) for (T~ - Ts) into Eq.(33) in Ref.[1] gives the heat flux supplied by the evaporation microlayer in binary mixtures:

Fig.1 Combined physical model for bubble growth in binary mixtures

- A0) 21/37rR2

2~rR 2

k(AT qe,m =

Using these assumptions of the combined physical model for bubble growth in binary mixture, the bubble growth model for bindary mixtures on smooth tubes can be derived as follows: a. Effective wall superheat Because the vapour mass fraction of the more volatile component is higher t h a n its equilibrium liquid mass fraction, the more volatile component in the liquid must evaporate quicker to provide the additional more volatile vapour into the bubble to maintain equilibrium as the bubble grows. This results in a

A T -- A0

4.260Pr1/6(at)1/2

(7)

It is assumed that the mass flux supplied by the evaporation microlayer is transmitted through onedimensional, transient diffusion into a semi-infinite liquid. Using the heat and mass transfer analogy, the mass flux supplied by the evaporation microlayer is given by Jr -- Dpz(xb

-- x i )

(8)

d. The bubble growth model for binary mixtures on smooth tubes

204

Journal of Thermal Science, Vol. 5, No.3, 1996

A heat balance around the hemispherical bubble gives dR 2 r R 2 • -~- • p~hl9 = 2~rR6t • q~,~ + 7rR 2 • qe,m 21rR6t . k ( A T - AO) =

C_A8

k ( A T - AO) 21/3

+

Using the initial condition, R = 0 at t = 0, in Eq.(19) gives 1 [ X - X l n X ] + - ~ . [1M G y2

M

lnM]

(20)

Inserting Eq.(20) back into Eq.(19) gives the bubble growth model for binary mixtures on smooth tubes:

27rR 2 4.260 Pr1/6 ( at )1/2

(9)

A8 1 -G- " y 2 " [ Y R - X ln(X + Y R ) ]

Eq.(9) is of the form: dR R dt ~ ~_/.7 M+NR

AO = A T

where

kSt p~hlg 3 v ~

M-

k N = 5.367Prl/6pvhlg ~

1 + ~ 5 " [ N R - M ln(M + NR)]

(10)

M In M N2

(21)

Taking the derivative of Eq.(18) gives (11)

Ao [

x

M

]

A8

G " (X + YR) 2 + (M-~VR) 2 " \dt]

+ G-

(12)

A mass balance around the hemispherical bubble for the more volatile component gives dR 2~rR 2 " ~ • P,(Yi - xi) = 27rR6t . J~ + IrR 2 . J~ = 27rR6t. dpt(xb -- x,) + 7rn2 " Dpt(xb -- x,)

= 2 A T v ~ - A# . X In X G y2

(13)

R • (X+YR)

R + (M+NR)]"

AT 2x/~

d2R dt 2 -

(22)

Inserting Eq.(18) into Eq.(22) gives the second derivative: d2R dt2

AT 2x/~

G AO

(M + NR)(X + YR) R(M + NR + X + YR)

X

M

[AT

G

2

Eq.(13) is of the form: [ (M + NR)(X + YR)

dR a-

where G - (xb - xi) (y, - x,) 3pl6tD

=

y _

p~vi_3~rb ptD 2 Pv

(15)

AO RdR RdR dt -G--" X + Y ~ + M + N ~ -- A T - ~

r_ (__7 ~2

= 2ATv~ + C

5360 1

1 (17)

G

(X + YR)

A T p l 7/9 +

]

(M + NR)

1

•Pt [ AO G

(18)

Integration of Eq.(18) gives

1 + ~ 5 " [M + N R -

Inserting Eqs.(18) and (23) into Eq.(10) in the paper of Wang et al. [1] gives the bubble force balance equation for binary mixtures:

(16)

Dividing Eq.(14) by Eq.(10) gives

AO . 1 _ . [X + Y R G y2

(23)

(14)

X+YR

X

]3

1 1 + (X + YR) (M + NR)

AT 2 1 14 "(--R--) • ~ + ] - ~ r R a s i n ~ 4 3 { AT = U R "P'

Xln(X + YR)]

G 'ao

(M + NR)(X + YR) RiM + NR + X + YR)

Mln(M + NR)] (19)

X M + [ ( X + Y R ) 2 + ( M -~VR) 2]

Guoqing Wang et al.

/ 7 \2

Nucleate Pool Boiling of Pure Liquids and Binary Mixtures: Part II

/2~r

+(~-~) Ir(-~ + 15)R ~ +g

4

3 R • (pt - p.)a

(24)

The combined parameter -~ in Eqs.(21) and (24) can be evaluated graphically from the constant pressure vapour-liquid phase equilibrium diagram (Fig.2).

Analytical Model 205

tubes consists of Eqs.(1), (4), (5), (6), (21), (43), (46), and (53) in Ref.[1] and Eqs.(11), (12), (16), (17), (21), (24), and (25). Moreover, the precise values of the binary mixture physical properties should be used in the analytical model. The analytical model also contains two unknown constants C and n, which are only functions of the status of the heated surface. The constants C and n in the analytical model for binary mixtures are identical to the constants C and n in the analytical model for pure liquids for the same heated surface.

EXPERIMENTAL RESEARCH Apparatus and Working Fluids The experimental facility, Fig.3, includes a test section, a working fluid injection system, a heating system and a temperature measurement system. The test section includes a liquid boiling pool and a vapour condenser. The working fluid injection system includes a vacuum pump, three working fluid storage bottles, three graduated bottles, various control valves, and syringes. The heating system includes two series of steady-state voltage power sources, a 10kW variac, a wattmeter, two auxiliary heaters and two 2kW variacs. The temperature measurement system includes copper-constantan thermocouples, a microvoltage amplifier, a AD converter, an IBM-PS/2 microcomputer and an EPSON LQ-1600 K printer.

M

Xj

x~ ~c

Fig.2 Vapour-liquid phase equilibrium diagram From Eq.(15),

AO G

AO xb - -- xi Yi -- xi

-

~

-(yi

-

z,).

(dT) -~x z==~

Because the local vapour mass fraction, Yi, inside the bubble and the local liquid mass fraction, xi, at the bubble boundary cannot be measured, the bulk vapour mass fraction, Yb, and the bulk liquid mass fraction, xb, are substituted for Yl and xi, respectively. Therefore,

AO dT ---~- -.~ --(yb -- ~gb) . (-~-~X) z_~zb

ethanol

ethanol

itonzge

icgled bottles

bo~n

vn¢

AD ¢onvet~er

wattmeter

coolin water

(25) vacuum pump

The bubble departure radius, Rd, and the bubble growth time, ta, in binary mixtures can be obtained by numerically solving the coupled Eqs.(21) and (24).

Nonlinear Effect The second effect that causes the boiling heat transfer coefficients in binary mixtures to be less than those in pure liquids, the nonlinear effect, can be accounted for by using the precise values of the binary mixture physical properties to calculate the boiling heat transfer coefficients in binary mixtures. Therefore, the analytical model for nucleate pool boiling heat transfer of binary mixtures on smooth

Fig.3 Experimental facility Water, methanol, and ethanol were used as the pure working fluids in the experiment. Water-methanol, water-ethanol, and methanol-ethanol were used as the binary working fluids in the experiment. C o m p a r i s o n of A n a l y t i c a l M o d e l s w i t h Experimental Data a. For pure liquids In the bubble force balance equation, Eq.(7) in Ref.[1], ~b is the angle between the bubble and the heated surface. This angle changes with bubble

206

Journal of Thermal Science, Voi 5, No.3. 1996

growth, but is approximately equal to the liquid-solid contact angle, 0. Therefore, ~b is assumed to be equal to 0. Rearranging the bubble growth model for pure liquids, Eq.(40) in Ref.[l], gives R = 2 B v q + A . I u ( A + BR) - A

In A

(26)

Rearranging the bubble force balance equation for pure liquids, Eq.(42) in Ref.[1], gives

t=

F,+F

Cd

(27)

+Fb-F,

where lr

5360

A

2

÷-) (7 2 4

The above results show that the unknown constants, C and n, are basically constant for a given heated surface, rather than being related to the physical properties of the working fluids, thus confirming the theoret ical basis of the analytical model for pure liquids. The average values, C = 0.0718443 and n = 1.60748, can be taken as the constants that reflect the smoothness of the given heated surface. The analytical model for pure liquids can predict the nucleate pool boiling heat transfer coefficientsof pure liquids on the given heated surface. The experimental heat fluxes for the pure liquids (water, methanol, and ethanol) and the theoretical heat fluxes calculated using the analytical model for pure liquids at the different wall superheats are shown in Fig.4. The largest deviations, l~ q e x p bemax ' tween the theoretical and experimental heat fluxes were 17.7% for water, 5.7% for methanol, and 19.1% for ethanol.

o • [] • A •

15)R2 a

Fb = -~lrR " (pi

-

E -%.

Pv)g

1.0 Wat~ 1.0 water 1.0 M~hanol !.0 Methanol 1.0 Ethanol 1.0 Ethanol

~t

./i

,~

/~

_ ,~ll ,~/ ~,~w ,~}r

, ~ ~

,

6 $ 4

Fo = 141rRa sin 0 11 Eqs.(26) and (27) can be written as the GaussSeidel formulas: n ( l + 1) = 2 B v / ~

/

+ _A B

~ tube ( ! 01 bar) Watct - Methanol- Ethanol I Dashed- Experimental Solid - Theoretical I0

(28)

t(l + 1) ---Cd[R(I + 1), t ( I ) l / { F d R ( I + 1),t(1)]

L-L

The bubble departure radii, Rd, and the bubble growth times, tg, at the different experimental wall superheats in the pure liquids were obtained by numerically solving the coupled Eqs.(28) and (29) with the physical properties of the pure liquids. The unknown constants, C and n, were then obtained by inserting the bubble departure radii, Rd, the bubble growth times, tg, Eqs.(43), (46), and (53) in the paper of Wang et al.[ll, and the experimental heat fluxes of pure liquids into the general model, Eqs.(1), (4), (5), and (6) in the paper of Wang et al. [1], and using linear regression: n = 1.60638 n = 1.62096 n = 1.59506

~K)

Fig.4 N u c l e a t e b o i l i n g heat flux c u r v e s for w a t e r , methanol, and ethanol on the smooth tube

+Fe[R(I + 1)1 + Fb[R(I + 1)] - F,[R(I + 1)1} (29)

C = 0.00834357 C = 0.065395 C = 0.0667023

I

~

6$

A ln[A + BR(I)] - -B . In A

for water for methanol for ethanol

A

,,j/ ~7

b. For binary mixture Rearranging the bubble growth model for binary mixtures, Eq.(21), gives

R=

A0 G

1 Y

1 N

" -G-Y---~

ln(X + Y R )

M . ln(M + N R ) + 2 A T v ~

AO -G

XInX y2

MlnM] ~ J

(30)

Since Eq.(30) can be simplified to Eq.(26) by taking A0 = 0, the bubble growth model for pure liquids is a special case of the bubble growth model for binary

Guoqing Wang et al.

Nucleate Pool Boiling of Pure Liquids and Binary Mixtures: Part II - - Analytical Model 207

mixtures. Consequently, the analytical model for pure liquids is also a special case of the analytical model for binary mixtures. Therefore, the analytical model for binary mixtures can predict nucleate pool boiling heat transfer coefficients for both pure liquids and binary mixtures on the same heated surface. Rearranging the bubble force balance equation for binary mixtures, Eq.(24), gives t =

(31)

F¢+F~+F~-F.

where 5360

c~=~

1

G (X + YR)

ATpt

(M + NR)

1

"P~[AO

~

1

1

AT

the binary mixtures. The theoretical heat fluxes for the binary mixtures at the different wall s u p e r h e a t s and liquid compositions were then obtained by inserting the bubble departure radii, Rd, the bubble growth times, t~, Eqs.(43), (46), and (53) in Ref.[1], and t h e average constants, C = 0.0718443 and n = 1 . 6 0 7 4 8 , into the general model, E q s . ( 1 ) , ( 4 ) , ( 5 ) , a n d ( 6 ) in Ref.[1]. The experimental heat fluxes for the binary mixtures (water-methanol, water-ethanol, and methanol-ethanol) and the theoretical heat fluxes calculated using the analytical model for binary mixtures at the different wall superheats and liquid compositions are shown in Figs.5,6, and 7. The largest deviations, ~ ~ x p m a x , between theoretical and experimental heat fluxes were 20.5% for watermethanol, 23.7% for water-ethanol, and 19.1% for methanol-ethanol.

~

] "(-R-)

3

it

--G-" (X + Y R ) + (M + N R ) "4 3 { A T G (M + N R ) ( X + Y R ) Fi = -~rR • p, 2 ~ " A'-'O " R ( M + N R + X + Y R ) X M + [ ( X + Y R ) 2 + (M +---NR)2 ]

7 2

2a

0.05 Methanol

//J

~o ~-

15) R 2

:

itzz z j

/ z

.::/ /7 .::"J.:" i/

#

4

•

jj~" ~'/.,,~ ,,:= / = / " f

,oM ano, ,,/

2-

lff

~,/~ , ~ , ~ j--a~,~ ,~" ,, | ~

• o.3 Mothanol 0.9 M~anol

::

}

1~¢

• O.05Methanol A 0.3 Methanol

x°~ v

2 [ (M+NR)(X+YR)]3

0 1.0Water []

waW-Me, h~,,) D h d-r = a Solid-Theoretical

5

Fb = -37rR . (pl -- pv)9

I0 T~-T, (K)

14

F~ = ~ n R a sin 0 Fig.5 Nucleate boiling heat flux curves for

water-methanol on the smooth tube

Eqs.(30) and (31) can be written as the Gauss-Seidel formulas: R(I+I)=

(AO

1

1 ).{--~-.y21n[X+YR(,)]

~-

M . l n [ U + NR(I))] +

AO X ln X Y2

10z .

2AT~

M ln M "I N~

E

/

2

1.0 1.0

(32)

t(I + 1) = Ce[R(I + 1),t(I)]/{F1[R(I + 1),t(I)] +F~[R(I + 1)] + Fb[R(I + 1)] - F,[R(I + 1)]}

s 4

v

Water Water [] 0.05 Ethanol • 0.05 Ethanol A 0.3 Ethanol • 0.3 Ethanol t~ <~" 0.9 Ethanol ,~ ~/ -O- 0.9 Ethanol 1.0 Ethanol ,~( ~ 1,OE~ an9 ~' 0 •

AO X

1

-ff-V+

G

3 2

10 -

,'

,, ' ,

,,

_

(33)

The bubble departure radii, Rd, and the bubble growth times, ta, at the different experimental wall superheats and liquid compositions in the binary mixtures were obtained by numerically solving the coupled Eqs.(32) and (33) with the physical properties of

IO T~-Ts (K) Fig.6 Nucleate boiling heat flux curves for water-ethanol on the smooth tube

208

J o u r n a l o f T h e r m a l Science, Vol. 5, No.3, 1996

T h e experimental wall superheats at different heat fluxes are given as functions of the bulk liquid mole fraction, xm, of the more volatile c o m p o n e n t in the binary mixtures in Figs.8,9,10. T h e influence of the binary mixture liquid composition on the wall superheats can be seen from these figures.

O 1.0 Ethanol • 1.0 Ethanol D 0,3 Methanol • 0.3 Methanol A 0.5 Methanol • 0.5 Methanol Q" 0.7 Methanol -O 0.7 Methanol 0 1.0 Methanol !~ 1.0 Methanol

,o2! 43-

28

2-

24 Smooth tube (1.01 bar) Water -Methanol Dashed- Experimental Solid-Theoretical

102 ~ 6-

20

=

-

16

I0

12 Tw-Ts (K) r

F i g . ' / N u c l e a t e boiling h e a t flux curves for ethanol-methanol on the s m o o t h tube 28

16 v

12

~ 1

8 4

0 -4 )

217.03 kW/m 2 159 15 kW/rn 2 [~ 115 75 kW/m 2

"~

Smooth tube Ethanol-Methanol (1.01 bar)

-

i '

0,0

l

0.1

l

l

0,2

;

I

0.3

'

7958 kW/m2 z~ 50.64~W/m' iA ~ 28.94 kW/rn, 14.47kW/rn2 7 23 kW/m 2

I

0.4

l

I

0.5

'

'

0.6

I

0.7

'

I

0.8

'

l

0.9

l

1.0

xm ( Methanol ) I

F i g . 1 0 Boiling curves for e t h a n o l - m e t h a n o l on t h e s m o o t h t u b e

I

4

-4

0.1

0.0

0.2

0,3

CONCLUSIONS

I"7 115.75 kW/m 2

Smooth tube Water-Methanol (1.01 bar)

0-

•

Z~ A

79.58kW/m2

50.64 kW/rn 2 28.94 kW/m ~

"Q" 14.4rkW/m2 7.23 k\V/m 2

0.4

0.5

0.6

0.7

0.8

0,9

1,0

0.9

1.0

X,, ( Methanol ) F i g . 8 Boiling curves for w a t e r - m e t h a n o l on t h e s m o o t h t u b e 28 24 20 16

~

8 4 ~ "~

• '

I 0 -7

.

~ :

q

0.0

g ~

....

Smooth tube Water-Ethanol

0.1

i

Z~ 50.64kW/m2

.......

0.2

0.3

159.15 kW/m 2 115 75 kW/mg 7958 kW'/rn z

~ 28.94kw/m~ 0.4

0.5

0.6

0.7

0.8

X~(Eth~ol) F i g . 9 Boiling curves for w a t e r - e t h a n o l on t h e s m o o t h t u b e

1. An analytical model was derived to predict the nucleate pool boiling heat transfer coefficients for binary mixtures on smooth tubes. The analytical model for binary mixtures contains two unknown constants, C and n, which are identical to the unknown constants, C and n, in the analytical model for pure liquids in the p a p e r of Wang et al. {11. Therefore, for a given heated surface, after the constants, C and n, are determined through a simple boiling experiment using a pure liquid, the analytical model for binary mixtures can predict the nucleate pool boiling heat transfer coefficients for any pure liquid and for any binary mixture on the heated surface. 2. Nucleate pool boiling heat transfer coefficients were determined experimentally for three pure liquids and their binary mixtures on a horizontal smooth tube. T h e analytical models for b o t h pure liquids and binary mixtures are in good agreement with the experimental data.

REFERENCES [1] W a n g , G.Q., Xie, Z.W., a n d Tan, Y.K., " N u c l e a t e P o o l Boiling o f P u r e Liquids a n d B i n a r y M i x t u r e s : P a r t I -

Guoqing Wang et al.

Nucleate Pool Boiling of Pure Liquids and Binary Mixtures: Part II - - Analytical Model 209

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