Properties of new refrigerants and predictions for condensation heat transfer enhancement with low-finned tubes

Energy Vol. 21, No. 12, pp. 1189-1199, 1996

Pergamon

PIh S0360-5442(96)00069-2

Copyright © 1996 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0360-5442/96 $15.00+ 0.00

PROPERTIES OF NEW REFRIGERANTS AND PREDICTIONS FOR CONDENSATION HEAT TRANSFER ENHANCEMENT WITH LOW-FINNED

TUBES

A. STEGOU-SAGIA Department of Mechanical Engineering, Thermal Section, National Technical University of Athens, 42 Patission Street, 106 82 Athens, Greece

(Received 29 January 1996)

Abstract--The present article provides a review of thermophysical properties research of environmentally acceptable refrigerants. In recent years, it has become evident that common CFC type refrigerants can cause serious environmental damage when released into the atmosphere. The group of HFCs (HFC-32, HFC-125, HFC-134a, HFC-152a) with no chlorine atom in their chemical formulae and quite short atmospheric lifetime may be promising alternatives to CFCs. A compilation of properties is given which may be used to obtain arithmetic expressions for the vapour pressure, saturated liquid density, viscosity, latent heat of vaporization, saturated liquid thermal conductivity, and surface tension of these hydrofluorocarbons. For easily available comparisons, the results are presented in diagrams illustrating the dependence of thermophysical data on temperature at the saturated state. Heat-transfer predictions are specified for condensation of the HFCs on horizontal integral-fin tubes with rectangular fins. Parameters investigated include fin and tube geometry, etc. This study should be a useful input in developing new condensers with new refrigerants. Copyright © 1996 Elsevier Science Ltd.

INTRODUCTION

The fully halogenated chlorofluorocarbons (CFCs) have been widely used as refrigerants, blowing agents and cleaning solvents because of their excellent chemical properties. However, the destruction of stratospheric ozone by CFCs has become an important issue. In particular, owing to their high stability, when CFCs migrate to the atmosphere, they are broken down by ultraviolet radiation to release chlorine. The chlorine catalyses the destruction of stratospheric ozone, which shields the earth from harmful ultraviolet radiation. In addition to ozone depletion in the stratosphere, CFCs, have also been identified as major contributors to the greenhouse effect. Because of these increasing environmental concerns, the United Nations Montreal Protocol, which controls the use of these substances, was revised in 1990 to mandate the complete phasing out of the five most commonly used chlorofluorocarbons (R-11, R-12, R-113, R-114, R-115) by the year 2000. Proposed new refrigerants fell into two groups: HFCs with no chlorine atom and HCFCs with some chlorine atoms. The parties to the Montreal Protocol decided in November 1992 at Copenhagen to make HCFCs controlled substances, although their ozone depletion potential (ODP) is lower than that of CFCs. Reductions in use are unavoidable and research is needed on the remaining replacements, i.e. HFCs and their mixtures. Our objective is to provide thermophysical data with comparisons for the alternative refrigerants HFC-32, HFC-125, HFC-134a, HFC-152a. We consider the vapour pressure, saturated liquid density, viscosity, latent heat of vaporization, saturated liquid thermal conductivity, and surface tension as well as their variations with temperature for operation in refrigeration condensers. Extensive calculations have been carried out on condensation of HFCs on horizontal integral-fin tubes. Integral-fin tubes have been used in refrigeration for many years. Significant improvements over plain tubes have been found, due to the increased surface area and thinning of the condensate film by surface-tension-induced pressure gradients. Accurate predictions of condensation of new refrigerants are of vital importance to operation of existing condensers with these fluids and to the design of future units. A significant part of this work is to investigate the effect of fin spacing, fin thickness and finroot diameter on the vapour-side enhancement ratio, a measure to compare the heat-transfer performance of finned and smooth tubes. The simple semi-empirical model proposed by Rose ~ and extended in Refs. 2 - 4 is used for various condensing fluids in order to compare their behaviour. Consideration of 1189

1190

A. Stegou-Sagia Table 1. HFC-134a vapour pressure; D ( % ) = deviation from ASHRAE data: T-273.15 °C

ASHRAE data 6 Pa

ICI equation s Pa

D(%)

McLinden equation 7 Pa

D(%)

10 20 30 40 50

414490.0 571590.0 770080.0 1016500.0 1317700.0

413718.3 569334.0 765965.3 1010450.7 1310356.2

0.186 0.395 0.534 0.595 0.557

414845.8 572108.9 770704.2 1016992.8 1317828.2

-0.086 -0.091 -0.081 -0.048 -0.010

these theoretical results can lead to useful conclusions for equipment design and efficient operation, because condensers have high cost. THERMODYNAMIC AND TRANSPORT PROPERTIES OF HFCs

HFC-134a is expected to be an environmentally acceptable fluorocarbon in place of CFC-12. A significant number of experimental data and related correlations, concerning the vapour pressure, have been reported{ -7 Table 1 summarizes representative values. The surface tension tr is required to correlate and predict heat transfer when phase change occurs. Chae et ala and Higashi and Okada 9 carded out measurements and gave correlations for the HFC-134a surface tension. Appropriate curve fitting to ASHRAE data 6 by the present author leads to or= Cro(l -

T/Tc)',

(I)

where Tc = 374.18K, 6 n = 1.2448 for 283.15-323.15 K, and Cro= 0.059893 N / m with o- in N/re. C o m parisons of data are shown in Table 2. Figure i illustratesthe dependence of vapour pressure on temperature for HFC-32, HFC-125, H F C Table 2. H F C 134a surface tension; D ( % ) = deviation from A S H R A E

T-273.15 °C

A S H R A E data,6 N/m

Chae et al equation,s N/m

I0 20 30 40 50

0.01030 0.00892 0.00757 0.00627 0.00501

0.01024 0.00885 0.00750 0.00619 0.00494

data:

D(%)

Higashi equation,9 N/m

D(%)

Our equation, N/m

D(%)

-0.535 -0.807 -0.985 - 1.252 - 1.355

0.01005 0.00873 0.00745 0.00621 0.00500

-2.417 -2.078 -I .563 - 1.025 -0.167

0.01031 0.00892 0.00757 0.00627 0.00502

-0.083 0.018 0.004 0.050 -0.108

!

i

~

,

3 2,5

~

- "

. k

St

1

~

0

_~.."'~t.

" !

"''" I

~

...*.-~

.-'

. . . . . . . .

". -. -.~

. _

t 0

10

20

~2

30

40

Teml~,Oc Fig. 1. Variation of vapour pressure with temperature,

SO

R134a

lus2a

Properties of new refrigerants 1400

i

;

i

1200

,

~

1000

,

J

600

.......

400 200

..._ "

'

~

!

,

t

,t

,

1k

I

~

I

,

:

i

i

10

20

.30

Tempe

mlure,

~'-

b

....

~

i 0

~ ....

"

i

o

i

- - . . ~ . ~ 2 . . .

. . . . *

1191

40

R128

....

R134a

....

R152a

50

OC

Fig. 2. Variation of saturated liquid density with temperature.

134a, and HFC-152a. The HFC-134a curve has been plotted using the equation of McLinden et al, 7 while the other curves are derived from data in Ref. 6. Work by the present author, t° and information concerning the thermodynamic and transport properties of refrigerants 6 lead to the data in Figs. 2-6. Details on the thermal conductivity of HFC-125 saturated liquid may be found in Ref. 11. CONDENSATION OF HFCS ON INTEGRAL-FIN TUBES

Condensation on finned tubes is a complex process involving three-dimensional flow of the condensate film and many articles have been published on the heat transfer problem) -4A2-27 Recent theoretical models for condensation are given in Table 3. In this work, the performance of HFC-32, HFC-125, HFC-134a, and HFC-152a condensing vapours on fins of rectangular cross-section is investigated using the semi-empirical model of Refs. 1-3. Calculations are given for the vapour-side enhancement ratio with varying fin spacing, fin height, fin thickness, and tube diameter at fin root. The vapour-side enhancement ratio ear is the heat-transfer coefficient for a finned tube Ce~nr~atube divided by that for a smooth tube asmoothtube, both based on the smooth tube area at the fin-root diameter and for the same vapour-to-surface temperature difference AT, i.e.

Car=

~ m . ~ d tube/asmooth

tube

----"

[(q/AT)finned tube]/

200

i

......

i'

1~ j

i

" ......

. . . .

100

~

_ 'i~

. . . .

i "i~

.... - --

'

I

- ' - m "

,~. . . . . . .

|I

....

/I

~

, - ,.,.

, o

0

I0

20 Te rope rldu~,

I

:

30

40

~ .

1

SO

0,C

Fig. 3. Variation of latent heat of vaporization with temperature.

Rt34a

" " " RIS2a

1192

A. Stegou-Sagia 300,00 i

,[ 250,00

I

!

I

v

~P"

fat

,b 2 0 0 , 0 0

"

.

I

15o,oo

I

~

!

" ",-.

I

- - . . .__.." ' ,

i

~ 100,00 ~.

R32

"'-..

"~

--.

....

R152a

I

50,00

I

0,00

I 0

10

20

30

40

50

T e m p e r a t u r e , QC Fig. 4. Variation of saturated liquid viscosity with temperature.

120,00 100,00

i

80,00

~,

" ~

---......

"i . . . . . .

~..

60,00

I

~

J

. . . .

- - ..i.

m

,

q~

©

1132

....

40,00

E

20,00

R134a .

--

RIS2a

i

t..

! o,oo o

10

20

30

40

SO

T e m p e r a t u r e , OC Fig. 5. Variation of saturated liquid thermal conductivity with temperature.

12,00

"~ " .

~

'

/

10,00 R32 d "~

" 6,00

~".

,

4,00

L

~" .

2,00

.

.

"-

~

- - " - - P.J2S

" ' ' . . ]

.

.

.

RI52a

- '

i'

0,00 0

I0

20

L 30

40

Temperature, 0C Fig. 6. Variation of surface tension with temperature.

50

Wate,r methanol, n-pentane, CFC-11, CFC-12, HCFC-22, CFC-113

Steam, ethylene-glycol, CFC-113, methanol, CFC11, CFC-12

Steam, CFC-11, CFC-113

Rose2 (1994)

Briggs and Rose3 (1994)

Fluid tested

Adamek, Webb22 (1990)

Year reference

Copper, brass, or bronze integral-fin tubes with typical fin geometries.

Experimental data from 11 investigators.

Fins: a) continuous-profile shapes, ~4"~5.2~b) rectangular or trapezoidal shapes with 80 tube geometries used by 14 investigators,

Test tubes used: material/geometry

Heat-transfer theory, dimensional analysis. Fin-efficiency effects. Applicable to every fluid, tube material and geometry,

Heat transfer theory, dimensional analysis. There are no fin-efficiency effects, Applicable to every fluid, tube material and geometry,

Analytical model applicable to hand or computer calculations for all fluids, tube material and geometry. The effect of fin efficiency is included.

Technique used to determine the heattransfer coefficient

Table 3. Recently published theoretical models for condensation on horizontal integral-fin tubes.

Semi-empirical model in agreement with experimental data. The enhancement ratio is independent of fin thermal conductivity for conductivity exceeding 50 W/m.K.

Equation for the vapour-side enhancement ratio for condensation on low-finned tubes. The available experimental data are in good agreement with the equation.

The model divides the fin profile into several surface tension or gravity-drained regions. It was shown to predict results for 74 of the tubes within -15%.

Remarks--results

~"

=

~~. -~

'~ ~.

1194

A, Stegou-Sagia

[(q/AT)smoothtube] ~finn~i t,bJq,moothtube.

(2)

Details on heat flux qtinnedtube are described in Refs. 1-3 and on q,moothtube in Ref. 12. The model considered is a combination of the Nusselt approach 12 for gravity-drained condensation on vertical plates and horizontal tubes with dimensional analysis to account for the effects of surface tension on condensate flow. It is known that externally finned tubes in horizontal tube-surface condensers have shown significant increases in the rate of heat transfer, although surface tension causes condensate retention or flooding between fins, thereby reducing the effective surface area for condensation. Recent studies 22,2+ have shown that despite flooding, integral-fin tubes produce significant improvements in performance over plain tubes. Comparisons have been made of condensate retention angles ~: for HFCs. Figure 7 shows the geometry of a finned tube and the flooding angle. For rectangular fins, 16 ~f =

cos-l[4o'lpgsdo -

1 ].

(3)

RESULTS We are concerned with computational methods for predicting vapour pressure, saturated liquid density, latent heat of vaporization, saturated liquid viscosity, thermal conductivity, and surface tension of four HFC refrigerants. Results are given in Figs. 1-6. We see that, HFC-152a and HFC-134a have (a)

L t

J. s

1t/2

(b)

I +

Tubewall Condensate ~~

i

L n

4~=LOK

Fig. 7. (a) Geometryof the finned tube; (b) Condensateretentionangle ~bf.

Properties of new refrigerants 14,00 ~ '''•

12,00

!

!

I

I

. j

I °t'-"-__l'.

m

1195

i

10,00 I l l ' * -

".

8,00 ~ - ~ ' = ~ - ~ ,

~

h=l ram,d-19.1 - - " - - h=e2nl~ds,9.1

4,00

....

b=2mm,d-25,4

2,00 0,00

0,50

0,00

1,00

1,50

2,00

Fin spacing, mum

Fig. 8. Enhancementratio as a function of fin spacing for R32 fluid with a fin thickness of 0.5 mm.

similar vapour pressures for 10-50°C and that the density of HFC-152a is the same as that of HFC32 between 40 and 50°C. The density curves for HFC-125 and HFC-134a coincide for 10-30°C (Fig. 2). The refrigerants HFC-32 and HFC-152a have similar latent heats of vaporization between 10 and 30°C (Fig. 3), while the HFC-32 viscosity curve is almost the same as that of HFC-125 for the same temperature range (Fig. 4). The heat-transfer performance of HFC-32, HFC-125, HFC-134a, HFC-152a vapours condensing on low-finned tubes were next investigated. The influence of fin spacing, height, thickness, and tube diameter at the fin root on the enhancement ratio ~ar was calculated by using the model of Refs. 1-4. The smooth-tube heat-transfer coefficient is multiplied by ~ar. We have calculated the variations of car on fin spacing for a copper tube with a vapour saturation temperature of 30°C and a vapour-side temperature difference A T = 2 0 K (Figs. 8-11). Results are given for tube diameters at the fin root of 19.1 and 25.4 mm. The fin shape is rectangular with a thickness of 0.5 mm (Fig. 7a). The fin height varies between 1 and 2 mm and the spacing ranges up to 2 mm. We see that the enhancement ratio increases with increases of tube diameter and fin height. HFC-32 and HFC-132a have similar car values (Figs. 8, 10), while HFC-125 has higher values than all other fluids (Fig. 9). Figure 12 has been plotted using the correlation (3) and relevant thermophysical property equations derived by the author; it shows the variation of condensate retention angle with fin spacing and type of refrigerant. We obtain increased values for HFC-125. The HFC-134a and HFC-32 curves coincide. 16,00 14 ' O0

e

•",

ee .jl

~ •

o 12,00

/

~i

. ~ ~~.,

I

10,00

iI

" • •

~ ' • ~-~

t

~"~ .•" . ,

6,00

~

". . ~..... "~.~-- ..._..

4,00

h-Iram,d-I9.1 ~-2~ ~-19.1 , "~:

"-'-';

-- - - ' ~lnmd-2S~S .... h-2mll~ d,,25A

1 i

2,00 0,00

l 0,00

0,50

1,00

1,50

2,00

Fin spacing, m m Fig. 9. Enhancement ratio as a function of fin spacing for R125 fluid with a fin thickness of 0.5 mm.

1196

A. Stegou-Sagia 14,00 ~

i

12,00 o 10,00 "~

'

8,00

i

"

""

.

.

.

i i

"-

%

.

.

d-19.1mm, h-lmm

:

6,00

~

" ""

" ~ d-19.1mm, h-2mm

. . . . . . . .

d-25.4m~ h-I mm

....

0,00 o,oo

0,50

1,oo

1,so

2,00

Fin spacing, mm Fig. 10. Enhancement ratio as a function of fin spacing for R134a fluid with a fin thickness of 0.5 mm.

12,00

i ,

~ 1"---.'

10,00 8,00

,,/

6,00

'.'I

i

"-.

i

,~,

.,.,~ .

r ~

" ".~ . . ~

- -

,

~' " .

~ .

~" i- ~

"~.

"" " ' 4,002,00 l ~

-" " -,

"

h=lmm, d-19.1 --

h'2~

d'19.1

_

- " " ""

~

....

h,.-lmm~d-25A

....

h..2nun, d-LS.4

0,00 0,00

0,50

1,00

1,50

2,00

Fin s pacing, mm Fig. 11. Enhancement ratio as a function of fin spacing for R152a fluid with a fin thickness of 0.5 mm.

lSO,OO | 160,00

o"".

t

140,00 L

f •

I:,,<-

=. 1 2 0 , 0 0

100,00 J I

1

i

i

[--~__!

. . . .

. . . .

.-

~ =l

. - _ _ - - "-- - -

- . , . ' ~ ,~ -..- "- "- - i

;

/

so,oo

I

'~

---

60,00

11/

i

- - - - " R152a

40,00

#i

1

20,00

J

i

o,oo

x,~,

I

0,00

0~q0

1,00

1,Y~O

2,00

Fin spacing, nun Fig. 12. Condensate retention angle for HFCs condensation on integral-fin tubes; d= 25.4 mm, t = 0.5 mm, h=2mm.

Properties of new refrigerants

12,00

[~.. ..

B"

1o,oo

•

i

"~ i

8,00 ~ I . - ~-. 6,00

~

1197

. ~

~

b=lmm,d=19.1

~ ' " ~' ~ . . . " ' ' ~ " ' " ~.~: "'~--. ""

4,00 t ~ 2,00 0,00 0,00

'"v

....

!

0,50

-- " -- h~2mm,(l-19.1 .... h-1 ram,d-2.S.4

1,00 1,50 Fin spacing, mm

h-2mm,d-25A

2,00

Fig. 13. Dependence of enhancement ratio on fin thickness for R152a fluid with a fin spacing of 0.25 mm.

Figures 13 and 14 illustrate the dependence of enhancement ratio Ear on fin thickness. There is an optimum fin thickness, i.e. a maximum value for the ratio e a r of about 0.04 mm for a fin height of 2 mm and a tube diameter of 19.1 mm. In Fig. 15, CFC-12 and HFC-134a are compared. It is seen that replacement of HFC-134a leads to lower ear values. CONCLUSIONS Arithmetic expressions and comparisons for the vapour pressure, saturated liquid density, latent heat of vaporization, saturated liquid thermal conductivity, viscosity and surface tension of refrigerants HFC32, HFC-125, HFC-134a, HFC-152a are presented by this article. Predictions are reported for film condensation of these fluids on horizontal integral-fin tubes; the vapour-side enhancement ratio is calculated with parameters the fin and tube geometry. There is a strong dependence on fin height, while the influence of tube diameter is lower. The optimum fin thickness for a maximum ear value is smaller than presently used in practice. We have very similar results for HFC134a and HFC-32 but higher enhancement ratios are observed with HFC-125. All data are of vital importance to the operation of existing condensers and to the design of future ones.

30,00 l 25,00

i .-.'" " ~ - . --.

20,00 I -idv I't~''--"~

""

"

"

"

R32

,,oo / •~

10,00

R152a

5,00 0,00 0,00

0,10

0,20 F in l h J c k B e s $ ,

0,30

0,40

mm

Fig. 14. Dependence of enhancement ratio on fin thickness for HFCs; d = 19.1 mm, s = 0.25 ram, h = 2 mm.

1198

A. Stegou-Sagia 25,00

zo,oo

i

-

~

i

I

!

I I0,00 I

Rl;34a

5,00 0,00 0,00

0,10

0,20

0,30

0,40

Fin lhickness, mm Fig. 15. Ri2 and its replacement during condensation on integral-fin tube; variation with fin thickness, d= 19.1 mm, s = 0.25 mm, h= 2 ram.

REFERENCES 1. J.W. Rose, "Condensation on Low-Finned Tubes--an Equation for Vapour-Side Enhancement," Proc. Engineering Foundation Conf. on Condensation and Condenser Design, pp. 317-333, ASME, St. Augustine, FL (1994). 2. J.W. Rose, Int. J. Heat Mass Transfer 37, 865 (1994). 3. A. Briggs and J. W. Rose, Int. J. Heat Mass Transfer 37 (Suppl. 1), 457 (1994). 4. A. Stegou-Sagia, A. Briggs, and J. W. Rose, "A Theoretical Investigation of Condensation of HCFC-123 on Horizontal Integral-Fin Tubes", CFCs The Day After, International Conference, pp. 617-626 (Joint Meeeting of IIR Commissions B1, B2, El, E2, University of Padua), Padua, Italy (1994). 5. ICI, "KLEA 134a, Preliminary Data Sheet", 5th edn., Runcorn, Cheshire, England (1990). 6. ASHRAE Fundamentals Handbook, ASHRAE, New York (1993). + 7. M.O. McLinden, J. S. Gallagher, L. A. Weber, G. Morrison, D. Ward, A. R. H. Goodwin, M. R. Moldover, J. W. Schmidt, H. B. Chae, T. J. Bruno, J. F. Ely, and M. L. Huber, ASHRAE Trans. 95, 263 (1989). 8. H.B. Chae, J. W. Schmidt, and M. R. Moldover, J. Chem. Eng. Data 35, 6 (1990). 9. Y. Higashi and M. Okada, "Measurements of the Surface Tension for CFC Alternatives", Paper No. 83, Proc. XVlllth International Congress of Refrigeration, Montreal (1991). 10. R.H. Perry and D. W. Green, Perry's Chemical Engineer's Handbook, 6th edn, McGraw-Hill International Editions, Chemical Engineering Series, Singapore (1984). 11. M. Papadaki and W. A. Wakeham, Inter. J. of Thermophysics 14, 1215 (1993). 12. W. Nusselt, Z. Ver. Dt. Ing, 60, 541 (1916). 13. R. M. Armstrong, Trans. ASME 67, 675 (1945). 14. R. Gregorig, Z. Angew. Math. Phys. 5, 36 (1954). 15. T. Adamek, Waerme-und Stoffuebertr. 15, 255 (1981). 16. H. Honda, S. Nozu, and K. Mitsumori, "Augmentation of Condensation on Horizontal Finned Tubes by Attaching a Porous Drainage Plate", Proc. ASME-JSME Thermal Engineering Joint Conference, Vol. 3, pp. 289-296, Honolulu, HI (1983). 17. R. L. Webb, T. M. Rudy, and M. A. Kedzierski, Trans. ASME J. Heat Transfer 107, 369 (1985). 18. A. Cavallini, S. Frizzerin, and L. Rossetto, "Condensation of R-I 1 Vapour Flowing Downward Outside a Horizontal Tube Bundle", Proc. of 8th Int. Heat Transfer Conference, Vol. 4, pp. 1707-1712, San Francisco, CA (1986). 19. H. Honda and S. Nozu, Trans. ASME J. Heat Transfer 109, 218 (1987). 20. J.W. Rose, Int. Comm. Heat Mass Transfer 15, 449 (1988). 21. R.L. Webb, Int. Comm. Heat Mass Transfer 15, 475 (1988). 22. T. Adamek and R. L. Webb, Int. J. Heat Mass Transfer 33, 1721 (1990). 23. K. Stephan, Heat Transfer in Condensation and Boiling, Springer-Verlag, Berlin (1992). 24. A. Briggs, X. -L. Wen, and J. W. Rose, Trans. ASME J. Heat Transfer 114, 719 (1992). 25. A. Cavallini, L. Doretti, G. A. Longo and L. Rosetto, "Experimental Investigations on Condensate Flow Patterns on Enhanced Surfaces", CFCs The Day After, International Conference, pp. 627 (Joint Meeting of IIR Commissions B1, B2, El, E2, University of Padua), Padua, Italy (1994). 26. A. Briggs and J. W. Rose, "Condensation of Refrigerants on Horizontal Integral Fin Tubes: Performance Predictions", Proc. ASME-JSME Thermal Engineering Joint Conference, Vol. 2, pp. 431-437, Maui, HI (1995). 27. J.W. Rose, "Models for Condensation Heat Transfer on Horizontal Low-Finned Tubes", Proc. 4th UK Heat Transfer Conference, pp. 417-429, IMechE, Manchester (1995).

Properties of new refrigerants

1199

NOMENCLATURE do = Diameter at the fin tip d = Diameter at the fin root g = Specific gravity h = Fin height q = Heat flux s = Fin spacing t = Fin thickness T = Temperature Tc = Critical temperature c~ = Vapour-side heat-transfer coefficient car = Enhancement ratio (heat-transfer coefficient for a finned tube divided by that for a smooth tube, both

AT = p= o" = ~bI =

based on the smooth tube area at the fin-root diameter and for the same AT) Vapour-to-surface temperature difference Density of condensate Surface tension Condensate retention or flooding angle measured from the top of the tube to the position at which the interfin space becomes full of condensate