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Enhancement of heat transfer from air-fin coolers with water spray
Chemical Engineering and Processing, 32 ( 1993) 13 1- 138
Enhancement Honorata Institute
of heat transfer from air-fin coolers with water spray
Walczyk
of Chemical Engineering,
Polish Academy
of Sciences, ul. Baltycka
5, 44-100 Gliwice (Poland)
(Received September 23, 1992)
Abstract An experimental study of heat transfer from an air-fin roof-type condenser additionally sprayed with water (up to 10 wt.%) has been presented. Based on experimental data a correlation for the effective air-side heat transfer coefficient has been elaborated. The calculation method proposed has been verified using the experimental results obtained in a horizontal air-fin cooler partially sprayed with water. In the case when the external thermal resistance was comparable with the internal reistance, a good agreement between the experimental and calculated data was obtained.
Synopsis Problem intensyfikacji wymiany ciepla w aparatach chlodzonych powietrzem posiada istotne znaczenie ze wzglqdu na znaczne koszty inwestycyjne tego typu aparat6w. Stosowanie dodatkowego zraszania wodq lub zastosowanie tzw. przeplywu mglowego pozwala na zmniejszenie powierzchni wymiany ciepla aparatbw, jak tei umoiliwia plynnq regulacje wymiany ciepla, przy zachowaniu iqdanej temperatury schladzanego czynnika technologicznego, niezaleinie od zmian temperatury otaczajqcego powietrza. Celem pracy jest okreglenie moiliwogci intensyfikacji wymiany ciepla poprzez, przeciwprqdowe do powietrza, zraszanie wodq wymiennik6w chlodzonych powietrzem, wykonanych z rur o duiym stopniu oiebrowania (cp = 22.5), jak tei opracowanie metodyki oblicze6 tego typu aparat6w. Badania podstawowe przeprowadzono na kondensatorzt: dachowym pary wodnej (rys. l), wykonanym z bimetalowych rur oiebrowanych (rys. 2), w nastqpujqcych zakresach zmian parametrbw: 1.2
0255-2701/93/$6.00
rys. 3 i 4. Wsp6lczynnik W roSnie ze zwickszaniem iloBci wody zraszajqcej i maleje ze wzrostem prqdkoici przeplywu powietrza. Na rys. 5 przedstawiono wartoSci eksperymentalnych wsp6iczynnikbw wzmocnienia wymiany ciepla w zaleinoSci od masowego stosunku wody zraszajqcej do powietrza chlodzqcego (G,,,/G,). Jak widaC wsp6lczynnik wzmocnienia wymiany ciepla (W) maleje ze wzrostem iloSci rzqd6w rur w wiqzce kondensatora. W oparciu o doSwiadczalnie zmierzone wsp&zynniki wzmocnienia wymiany ciepla W okreSlono wartoeci zastcpczego wsp6lczynnika wnikania ciepla w fazie gazowej $ uwzgledniajqc w obliczeniach pozostale opory cieplne, kt6re obliczano ze znanych korelacji literaturowych. Uwzglqdniajqc zaloienia 1O,2” i 3” oraz wprowadzajqc zastqpcze wspblczynniki wnikania ciepia q, i a& zdefiniowane zaleinoSciami (5) i (6), r6wnanie (1) przeksztalcono w zaleinoSC (7) z ktbrej, po prostych przeksztalceniach, uzyskano wz6r (8) na stosunek wsp6lczynnik6w wnikania ciepla na zewnqtrz rur oiebrowanych z i bez zraszania wodq. Dla wszystkich 79 punkt6w doSwiadczalnych obliczono wartoSci stosunk6w u~/c(~ ze wzoru (8) przy wykorzystaniu zaleinogci (l), (S), (6) i (9- 14). Znajqc dla poszczeg6lnych eksperymentbw wartoSci as /cl, oraz obliczajqc X,, jako Sredniq arytmetycznq z wartoSci na wlocie i wylocie, okreSlono w oparciu o wz6r (15) wartoici parametru E. WartoSci te skorelowano (r6wnanie (19)) jako funkcjq innych parametrbw majqcych wplyw na przebieg procesu ( RenpwrN) uzyskujqc wz6r (20) na obliczanie wsp&zynnika wnikania ciepla na zewnqtrz rur oiebrowanych chlodzonych powietrzem i dodatkowo zraszanych wodq. Jak widaC z wykresu (rys. 6)
0 1993 -
Elsevier Sequoia. All rights reserved
132
zaleinobc (20) koreluje dane eksperymentalne dla kondensatora dachowego dodatkowo zraszanego woda z dokladnoscia f 20% w zakresie liczb Reynoldsa 2.3 < Respw < 7.0 i przy predkosciach przeplywu powietrza w granicach 1.2 < wg < 2.6 m s-‘. Zaproponowana w pracy metodyke obliczania wymiennikbw ciepla oparta o otrzymana korelacje (20) na zastepczy wspolczynnik wnikania ciepla uz zweryfikowano dodatkowymi badaniami eksperymentalnymi przeprowadzonymi dla poziomej chlodnicy wody. Obliczone na podstawie rownania (22) wartosci W, porownano na rys. 9 z wartoiciami eksperymentalnymi We,, wzynaczonymi z wartosci bilansowych (rownanie (21)). Dobra zgodnosc wynikow prowadzi do wniosku, ie proponowana metodyka obliczen moie bye stosowana rowniei wtedy gdy opor cieplny wewnatrz rur jest porownywalny z oporami cieplnymi od strony powietrza.
koduction
The intensification of heat transfer in air-fin coolers is an important objective due to great investment cost for this type of apparatus. It can be achieved by ,water spraying on a facial surface of a bundle of tubes or by using an air-water mist flow. We can thus diminish the heat transfer surface and regulate smoothly the heat flux independently of the weather conditions. Heat transfer in air-fin coolers (with 0.305 x 0.305 m facial areas) with an air-water mist flow has been studied in refs. 1- 3. The effects ,of water and ethylene glycol spray on the heat transfer, and friction loss performance of three automotive radiator cores, tubular types with plain, louvered and perforated fins have been investigated experimentally by Yang and Clark [l]. A good improvement in heat transfer performance has been observed by spraying 3.62-7.7 kg h-’ of liquid. It has been found that friction losses are not affected by the sprays, while the heat transfer performance was increased substantially. Improvement in the overall heat transfer coefficient of up to 40% for the air Reynolds number of 1000 was observed. In the turbulent regime, the increases in the heat transfer coefficients are about 12 and 6% for plain and perforated-finned units and the louvered-finned core, respectively. The sprays of water and ethylene glycol yield essentially the same results in spite of the fact that ethylene glycol evaporates at a temperature (197 “C) nearly double that for water (100 “C). One may thus conclude that the augmentation of air-side convective heat transfer by liquid spray is due mainly to the formation of liquid film on the heat transfer surface, while the contribution of evaporation is rather negligible, at least in this application.
The performance of a fin and tube heat exchanger wetted by water sprays of different mass fluxes and drop diameters, while air is blown across it with velocities between 0.8 and 2.3 m s-l, has been examined by Tree [2]. The three drop diameters examined were 64, 444 and 3300 pm. The water mass flow rates used were 10.8, 21.6 and 32.4 kg h-‘. The heat exchanger tested was a 0.3048 x 0.3048 m, four-row staggered arrangement, 0.0091/0.0092 m inside diameter copper tube with 0.00015 m thickness of aluminium fins with 476 fins per metre. The authors [2] have found that it is the mass flow rate of sprayed water which has the greatest effect on the heat transfer enhancement; the drop diameter has only a small effect in the ranges studied. The major source of enhancement of heat transfer in the presence of water drops is the direct evaporation of the drops on the exchanger. If all of the spray water enters into direct contact with the heat exchanger and evaporates, the enhancement (for spray water flow rates less then 54 kg h-‘) realized should be equal to the amount of water evaporated times the heat of vaporization of water (to within 10% accuracy). For the exchanger examined whose f d cial area was 0.305 m’, the possible enhancement for droplets of 64-3300 pm in diameter and for mass flow rate of water of 32 kg hhi was 40”/. Measurements of heat transfer from a single row of finned tubes to air-water mist in cross flow, at velocities from 4.57 to 9.14 m s-’ and water mist contents up to 5% have been presented by Simpson et al. [3]. The three monometallic finned tubes forming the single ,row tube bundle were heated internally by condensation of steam at a pressure of 1.36 bar fed to the slightly superheated top manifold of test bundle (0.6 K f 0.2). This gave an essentially constant temperature inside the tubes. The finned tubes were machined from solid leaded brass bar, 63.5 mm in diameter, 480 mm long, bored out to an internal diameter of 16 mm. Fins of thickness 1.6 mm were machined to give a fin height of 22.2 mm and fin spacing of 3.2 mm and 6.35 mm. The fins were later machined to give fin heights of 15.9 mm and 9.5 mm and a further fin spacing of 14.3mm. The tinned tubes were located in a single row of three vertical tubes with pitch equal to 89 mm. The authors [3] report that the heat transfer coefficient decreases with increase in the fin height and decrease in spacing, although, particularly for wider fin spacing and higher mist content, this trend was reversed for the longest fins. The enhancement factors, expressed as the ratio of a two-phase overall coefficient to a single-phase overall coefficient, were much greater for short widely spaced fins than for long fins of close spacing. From experimental data and theoretical calculations they find that at low mist contents and approach velocities the finned surface plays a more significant part in the heat transfer
133
process but with increased mist content and approach velocity the contribution of the base-tube surface becomes more important. Oshima et al. [4] have done an experiment on heat transfer from the surface of a six-row vertical air-fin cooler with hot water flowing inside, onto which water was sprayed concurrently to air flow from three nozzles situated in front of the exchanger. The finned tubes (rp = 9.45) were made of copper and the fins were spiral. The heat exchanger used was 700 mm high, 600 mm wide and 350 mm long, and contained 51 finned tubes arranged hexagonally with a pitch equal to 50 mm. The experimental range was: air mass velocity, 2000-12 000 kgm-* h-‘, amount of water spray, 72heat transfer co190 kg h-‘. The air-side apparent efficient was 93-418 W m-* degg’ and depended on the flow rate of the water spray. The authors report that the heat transfer rate is much larger in a heat exchanger with water spray than in that without spray and that the minimum amount of sprayed water is 0.03 kg/(kg dry air) at the air mass velocity of 12 000 kg rnp2 hh’. The objective of the present study is to determine the possibility of the enhancement of heat transfer from air-fin coolers with water sprayed countercurrently to air. A calculation method is elaborated based on experiments performed in a roof-type air-fin condenser. The method proposed is further verified using experiments carried out in a horizontal water cooler.
Experimental
apparatus
and results
The air-fin roof-type condenser was made up of bimetallic highly finned tubes (cp = 22.5). The flow system is shown in Fig. 1. The bimetallic finned tubes used were made of carbon steel and aluminium and the fins were spiral. The details of the tube are shown in Fig. 2. The experiments were carried out in apparatus with
aluminium A--
Fig. 2. Details
of a bimetallic
four-, three-, two- and one-row test bundles. Each of them was 1OOOmm high, 1050 mm wide and was inclined at an angle of 60”. The air-fin roof-type condenser (1) contained 70, 53, 35 and 17 one-metre long tubes arranged hexagonally in, four-, three-, two- and one-row test bundles respectively, with pitch equal to 59 mm. The finned tubes were heated internally by condensing low pressure steam fed to the top manifold (4) of the test bundle. This gave an essentially constant temperature inside the tubes. The condensate from the bottom manifold (5) flowed into a well-lagged tank. Air from a fan (2) flowed perpendicularly to the tube bundle. The changes in air mass flow rate were produced by using suitable perforated plates, built into the fan connector. The air velocity was measured by a Pitot tube, only in the experiments without water spray, at 16 selected points immediately behind the last row of tubes. At the same points the air temperature was measured. Water was sprayed by 4 nozzles (3) on the facial area of the condenser. The experimental range was: air velocity, 1.22.6 m ss’; sprayed water, 180-300 kg hh’; temperature of inlet air and of sprayed water, 15-25 “C and w 15 “C, respectively, and l-4 rows of the test bundle. The heat transfer rate was determined from the amount of the condensate obtained from the tested bundle of tubes. The enhancement factor W is defined as a ratio of heat transfer rates in the apparatus with (Q’) and without (Q) water spraying and is calculated as:
w=!&‘=GLrL Q
Fig. 1. Scheme of the air-fin roof-type condenser. 2, fan; 3, nozzles; 4, steam collector; 5, condensate
1, test bundle; collector.
finned tube.
GcrA
(1)
Some of the results for the enhancement factor W as a function of water flow rate and mist content are presented in Figs. 3-5. It can be seen in Fig. 3 and Fig. 4 that W increases with the amount of spray water and decreases with rising air velocity. In Fig. 5, where W is plotted against the mist content (G,,,/G,), the
134
2.31
I
I
22. 0 29
W
1.9 .
1.8 .
1.7 2JI//0 1.5 Ik
0
/, 200
Wgh/sl 1.5
0
2.1
.
2.5
250
Fig. 3. The enhancement function of water spray
_ 0
300
factor from a one-row mass flow rate.
tube bundle
as a
W
1.3 1.7
0
1.5:;/:;I_ / 180
( G;,-,w,Gg15x 100 6 Fig. 5. The dependence of the enhancement denser on a mist content.
wQhlvk1
2.0. o
3
260
300
GSPW [kg/h] Fig. 4. The enhancement factor from a three-row function of the water spray mass flow rate.
effect of the number significant.
bundle
as a
of rows (N) in the bundle on W is
Model and design method
If water is sprayed on the hot surface of the heat exchanger simultaneous heat and mass transfer occurs. In the case studied, the intensification of heat transfer is affected mainly by the mass transfer process. The mass transfer, in this case, takes place by evaporation of water droplets into the air stream or by evaporation from a thin water film formed by droplets impinging on the heating surface. Under the experimental conditions, the liquid film can be formed only on a small part of an outer surface of the heat exchanger due to its highly finned surface (cp = 22.5) and a small amount of the sprayed water. Taking into account the low temperature of the cooling air, one can assume that under the experimental conditions the air-water mixture was close
factor
for a con-
to saturation. For turbulent flow of a saturated air-water mixture, it is possible to &d a relationship between the heat and mass driving forces and apply the heat and mass transfer analogy [8] to determine the effective air-side heat transfer coefficient (c$), including heat transfer connected with mass transfer. The effective air-side heat transfer coefficient was determined on the basis of the experimental values of W. For the correlation of the experimental data the following assumptions are made. (1) The average temperature driving force for experiments with and without water spray has been assumed to be identical at the same air flow rate (At’ = At). (2) Thermal resistance of the film formed on the outer surface of the tubes is negligible. (3) Fin efficiency for the experiments with and without water spray is identical (q: = q,). Taking into account assumption (l), the enhancement factor W can be expressed as:
f+&LE Q k The overall heat transfer coefficient (k) without water spray for the exchanger made up of finned tubes can be calculated as:
Applying assumptions (2) and (3) the overall heat transfer coefficient (k’) with water spray can be defined by the similar relationship:
135
Introducing the global heat transfer c&,defined as:
coefficients
s(~ and
equation similar to that proposed by Hobler [7] for the effective heat transfer coefficient of a saturated airwater mixture: cc* <=
(6) into eqns. (3) and (4) the enhancement rewritten as:
factor
From eqn. (7) we can obtain an expression for the ratio of the air-side heat transfer coefficients with and without water spray as: WMW,)
%
where &,, is defined as:
and is equal to 130 for an air-water mixture at a low temperature. The value of X,, was calculated as an arithmetical mean of the inlet (X,,) and outlet (X,,) conditions for each experimental run. The outlet mass ratio (X,,) for this correlation was calculated as:
(8)
All the values appearing on the right side of eqn. (8) are known. The enhancement factor W was calculated from the experimental data (eqn. (1)). The air-side heat transfer coefficient as was calculated using the empirical correlation for a four-row roof-type condenser given in ref. 5: Nu,=~=O.l331 Rez,6x7 (9) B The fin efficiency q7 was taken from ref. 6 where it is given as a function of two parameters (4, p):
Inserting &,, = 130 and X,,, into eqn. ( 15) the E-values have been calculated for all 79 experimental points. Then the values of E were correlated as a function of two variables, Respw and N, which were considered as significant for the process. The mass flow rate (I,,,) in ReJpw was calculated as: l-
G =spw
Spw
(18)
2L e
where L, = Ii L, = 21i
for N = 1 for N = 2, 3, 4
The correlation
(11) where A,=6
D,-db
2
(12)
Taking into account the mass flow rate of condensate from the experiments performed with and without water spray the internal heat transfer coefficients (cri, x,) were calculated from Nusselt correlation [ 71: Nu, =y
= 1.5 Re;‘13
u: = v,(sin /3-“’
(15)
W can be
(7)
a;
1 +ci,Xnm
(13)
(14)
The values of the ratio of air-side heat transfer coefficients with and without water spray (eqn. (8)) were calculated using eqns. ( l), (S), (6) and (9) -( 14). The values of a,*/~, thus obtained were correlated using an
thus obtained
is:
s = 0 176 Re0.562N-0.3R VW
(19)
Introducing eqn. (19) into eqn. (15) the effective airside heat transfer coefficient with water spray can be calculated from: 2
= 1 + 0.176 Re~5,62N-0~38[,X,,
(20)
As can be seen from Fig. 6, eqn. (20) correlates experimental data for the air-fin roof-type condenser with an accuracy of f 20% for 2.3 < Respw < 7.0, 1
of the design method proposed
The experimental data concerning the enhancement factor W obtained in a horizonatal water cooler partially sprayed with water were used for the verification of the calculation method proposed.
1.5. 1.4 w
1.3
1.2. 13 . I.01
0 0 Re
a05 0562 -0,s SPW N
010
The horizontal cooler (1) was made up of 22 one-metre long finned tubes (see Fig. 2), arranged hexagonally with pitch equal to 59 mm in a four-row bundle of tubes. Its facial area is 0.354 x 1.0 m. The flow system is shown in Fig. 7. The tubes were heated internally with hot water with a constant inlet temperature and the mass flow rate equal to 3.9 m3 h-‘. The air from a fan enters the cooler through a measuring orifice placed in a circular pipe. Above the horizontal cooler, there are two nozzles (2) from which water is sprayed onto the facial area of the exchanger. The sprayed area was l/3 or 213 of the facial area when one or two nozzles were working, respectively. The experimental range was: air velocity, 1.322.75 m s-‘, amount of water spray, 20-150 kg h-‘, inlet air and water spray temperature, 21-30 “C and N 15 “C, respectively. The values of the enhancement factor W for the horizontal cooler, calculated as G,c,At'
wexp = G,c,At
(21)
were compared with similar experimental by Tree [2] in Fig. 8.
Fig. 7. Scheme of the air-fin horizontal 2, nozzles; 3, hot water 6, circular pipe.
.
2
3
4 5 6 7 (‘&pw/Sgb 100
1
.
8
9
10
Fig. 8. The comparison between the enhancement factor W obtained for a four-row bundle in a horizontal water cooler ( 0) and the data ( +) given by Tree [2].
‘A,
Fig. 6. The values of G(~*/c(~ obtained from the experimental data for the roof-type condenser as a function of Reynolds number (Respu) and the number of rows (N) in the bundle,
cooler; heater;
.+
1
tank;
data reported
water cooler. 1, test 4, water pump; 5, water
The verification of the design method described previously was performed by comparing the two enhancement factors, Wexp and W, (Fig. 9). The values of W, were calculated from eqn. (22): w =k’FE+kF(l t kF
-E)
(22)
where E represents a fraction of the facial area of the exchanger sprayed with water (E = l/2 or E = 2/3). The overall heat transfer coefficients for the dry (k) and wet (k’) parts of the horizontal cooler were calculated from eqns. (3) and (4), respectively. The air-side heat transfer coefficient (LX,) was calculated in this case from an empirical correlation reported in ref. 9: ud Nu = A..!? = 0.4799 Re0.‘588 &lax 1,
This equation was obtained for a four-row horizontal exchanger made up of the same type of finned tubes. The effective heat transfer coefficient LX: was calculated from eqn. (20) and the McAdams correlation was applied to calculate the heat transfer coefficient GL~ for the inside water flow in turbulent regime. A good agreement between the experimental and calculated values of Wexpand W, for a horizontal water cooler can be regarded as a successful verification of the calculation method proposed (Fig. 9).
Fig. 9. The comparison between the calculated (W,) and experimental (W,,,) values of the enhancement factor for a horizontal water cooler 0 - l/3 of the facial area sprayed by water, 0 - 2/3 ._;, of the facial area sprayed by water.
137
Conclusions
RA
The results of the experimental study performed in an air-fin roof-type condenser additionally sprayed with water, with a countercurrent air flow, show that the heat enhancement factor W can be increased by up to 125%. The quantitative results for the finned tubes (q = 22.5) were similar to those obtained by Simpson [3] for the mist flow experiments carried out with tubes of similar geometry (cp = 25.7). It leads to the conclusion that the type of water sprayer has only limited effect on the heat transfer, thus confirming the results obtained by Tree [2] for water droplet diameters of 64-3300 pm. The calculation method proposed, which introduces the effective heat transfer coefficient for the gas phase cl: given by eqn. (20) seems to be a handy tool for solving this type of problem. This has been confirmed by other experiments performed in a horizontal air-fin cooler with water spraying. In this case, the external thermal resistance was comparable with the internal resistance. A good agreement between the experimental values of W,,, (eqn. (21)) and the values W, calculated from eqn. (22) in which the overall heat transfer coefficients (k and k’) were determined theoretically (eqns. (3) (4) (20), (23)), is shown in Fig. 9. The method of calculation proposed can be applied to determining the values of W for air-fin coolers with countercurrent water spraying (up to 10 wt.% of water in cooling air).
rA S
Nomenclature CW
DO
4 E 6 F, Gg GC G, G ww s i 1A
k L 1 M m* N
Q
specific heat, J kg-’ K-i outer diameter of finned tube, m base fin tube diameter, m fraction of exchanger surface sprayed with water inner surface of finned tube, m2 total outer surface of finned tube, m2 air mass flow rate, kg h-’ condensate mass flow rate, kg h-’ water mass flow rate, kg h-’ sprayed water mass flow rate, kg h-’ acceleration of gravity, m s-’ number of tubes in row enthalpy of diffusing component, J kg-’ overall heat transfer coefficient, W mm2 K-’ equivalent length, m tube length, m molecular weight, kg kmol-’ =M,/M, = 18/29 = 0.622 number of rows in bundle heat transfer rate, W
T t L: W Wg W nmx XA
constant of diffusing component, J kg-’ K-’ heat of vaporization, J kg-’ wall thickness, m temperature, K inlet temperature of air, “C temperature difference, “C = Q’/Q, enhancement factor of heat transfer air velocity, m s-’ air velocity calculated for minimal crosssection, m s-i mass ratio of component A, (kg H,O)/( kg dry air) gas
Greek letters u heat transfer
G a0 a0 B lcp 4
: L r % 1 a,
coefficient, W m-* K-i effective heat transfer coefficient, W m-* K-’ heat transfer coefficient defined by eqn. (4), W m-* K-’ heat transfer coefficient defined by eqn. (.5), W mm2 K-’ angle of tube inclination, o mass flow rate per unit width, kg m-’ s-’ = F,/F,, ratio of overall outer finned tube surface to inner surface of tube ratio of heat and mass transfer coefficients, J kg-’ K-’ density, kg me3 fin thickness, m dimensionless value given by eqn. (16) coefficient of dynamic viscosity, kg m-i s-i tin efficiency thermal conductivity, W m-’ K-’ = [a ‘/(BY 31“3, equivalent thickness, m
Dimensionless
numbers
4r =-z
Re, Re e max
, condensate Reynolds number % 4r =x , sprayed water Reynolds number G&v = @&&by,
, gas Reynolds
number
%
Subscripts C
g i spw A”
condensate gas phase refers to inside of tube sprayed water mean value water
Superscripts
refers to spraying
conditions
with
additional
water
138
References 1 Yang Wen-Jei and D. W. Clark, Spray cooling of air-cooled compact heat exchangers, Int. J. Heat Mass Transfer, 18( 1975), 31 I-317. 2 D. R. Tree, V. W. Goldschmidt, R. W. Garrett and E. Hach, Effect of water sprays on heat transfer of a fin and tube exchangers, 6th ht. Heat Transfer Conf., Toronto, Ont. ( 1978). 3 H. C. Simpson, G. C. Beggs and G. N. Sen, Heat transfer from extended surface tubes to an air-water mist flow, Symp. on Multi-Phase Flow Systems, Univ. Strathciyde, ( 1974) l-22. Design 4 T. Oshima, S. Iuchi, A. Yoshida and K. Takamatsu, calculation method of air-cooled beat exchangers with water spray, Heat Transfer-Japanese Research, I (1972).
5 R. Krupiczka, H. Walczyk and J. Przybyla, Experimental study of heat transfer and air flow pressure drop for bimetallic finned tube manufactured in Poland, Ini. Apal. Chem., 6 (1978) (in Polish). 6 D. Q. Kern and A. D. Kraus, Extended Surface Heat Transfer, McGraw-Hill, New York, 1972. 7 T. Hobler, Heat Transfer and Heat Exchangers, WNT, Warsaw, 1972 (in Polish). 8 W. H. Walker, W. K. Lewis, W. H. McAdams and E. R. Gilliland, Principles of Chemical Engineering, McGraw-Hill, New York, (1937). 9 Investigation of regulation and intensification of heat transfer in air-fin heat exchangers by water spray, Report for the Institute of Chemical Engineering of the Polish Academy of Sciences, Gliwz’ce, Part X (1985) (in Polish).
Enhancement Honorata Institute
of heat transfer from air-fin coolers with water spray
Walczyk
of Chemical Engineering,
Polish Academy
of Sciences, ul. Baltycka
5, 44-100 Gliwice (Poland)
(Received September 23, 1992)
Abstract An experimental study of heat transfer from an air-fin roof-type condenser additionally sprayed with water (up to 10 wt.%) has been presented. Based on experimental data a correlation for the effective air-side heat transfer coefficient has been elaborated. The calculation method proposed has been verified using the experimental results obtained in a horizontal air-fin cooler partially sprayed with water. In the case when the external thermal resistance was comparable with the internal reistance, a good agreement between the experimental and calculated data was obtained.
Synopsis Problem intensyfikacji wymiany ciepla w aparatach chlodzonych powietrzem posiada istotne znaczenie ze wzglqdu na znaczne koszty inwestycyjne tego typu aparat6w. Stosowanie dodatkowego zraszania wodq lub zastosowanie tzw. przeplywu mglowego pozwala na zmniejszenie powierzchni wymiany ciepla aparatbw, jak tei umoiliwia plynnq regulacje wymiany ciepla, przy zachowaniu iqdanej temperatury schladzanego czynnika technologicznego, niezaleinie od zmian temperatury otaczajqcego powietrza. Celem pracy jest okreglenie moiliwogci intensyfikacji wymiany ciepla poprzez, przeciwprqdowe do powietrza, zraszanie wodq wymiennik6w chlodzonych powietrzem, wykonanych z rur o duiym stopniu oiebrowania (cp = 22.5), jak tei opracowanie metodyki oblicze6 tego typu aparat6w. Badania podstawowe przeprowadzono na kondensatorzt: dachowym pary wodnej (rys. l), wykonanym z bimetalowych rur oiebrowanych (rys. 2), w nastqpujqcych zakresach zmian parametrbw: 1.2
0255-2701/93/$6.00
rys. 3 i 4. Wsp6lczynnik W roSnie ze zwickszaniem iloBci wody zraszajqcej i maleje ze wzrostem prqdkoici przeplywu powietrza. Na rys. 5 przedstawiono wartoSci eksperymentalnych wsp6iczynnikbw wzmocnienia wymiany ciepla w zaleinoSci od masowego stosunku wody zraszajqcej do powietrza chlodzqcego (G,,,/G,). Jak widaC wsp6lczynnik wzmocnienia wymiany ciepla (W) maleje ze wzrostem iloSci rzqd6w rur w wiqzce kondensatora. W oparciu o doSwiadczalnie zmierzone wsp&zynniki wzmocnienia wymiany ciepla W okreSlono wartoeci zastcpczego wsp6lczynnika wnikania ciepla w fazie gazowej $ uwzgledniajqc w obliczeniach pozostale opory cieplne, kt6re obliczano ze znanych korelacji literaturowych. Uwzglqdniajqc zaloienia 1O,2” i 3” oraz wprowadzajqc zastqpcze wspblczynniki wnikania ciepia q, i a& zdefiniowane zaleinoSciami (5) i (6), r6wnanie (1) przeksztalcono w zaleinoSC (7) z ktbrej, po prostych przeksztalceniach, uzyskano wz6r (8) na stosunek wsp6lczynnik6w wnikania ciepla na zewnqtrz rur oiebrowanych z i bez zraszania wodq. Dla wszystkich 79 punkt6w doSwiadczalnych obliczono wartoSci stosunk6w u~/c(~ ze wzoru (8) przy wykorzystaniu zaleinogci (l), (S), (6) i (9- 14). Znajqc dla poszczeg6lnych eksperymentbw wartoSci as /cl, oraz obliczajqc X,, jako Sredniq arytmetycznq z wartoSci na wlocie i wylocie, okreSlono w oparciu o wz6r (15) wartoici parametru E. WartoSci te skorelowano (r6wnanie (19)) jako funkcjq innych parametrbw majqcych wplyw na przebieg procesu ( RenpwrN) uzyskujqc wz6r (20) na obliczanie wsp&zynnika wnikania ciepla na zewnqtrz rur oiebrowanych chlodzonych powietrzem i dodatkowo zraszanych wodq. Jak widaC z wykresu (rys. 6)
0 1993 -
Elsevier Sequoia. All rights reserved
132
zaleinobc (20) koreluje dane eksperymentalne dla kondensatora dachowego dodatkowo zraszanego woda z dokladnoscia f 20% w zakresie liczb Reynoldsa 2.3 < Respw < 7.0 i przy predkosciach przeplywu powietrza w granicach 1.2 < wg < 2.6 m s-‘. Zaproponowana w pracy metodyke obliczania wymiennikbw ciepla oparta o otrzymana korelacje (20) na zastepczy wspolczynnik wnikania ciepla uz zweryfikowano dodatkowymi badaniami eksperymentalnymi przeprowadzonymi dla poziomej chlodnicy wody. Obliczone na podstawie rownania (22) wartosci W, porownano na rys. 9 z wartoiciami eksperymentalnymi We,, wzynaczonymi z wartosci bilansowych (rownanie (21)). Dobra zgodnosc wynikow prowadzi do wniosku, ie proponowana metodyka obliczen moie bye stosowana rowniei wtedy gdy opor cieplny wewnatrz rur jest porownywalny z oporami cieplnymi od strony powietrza.
koduction
The intensification of heat transfer in air-fin coolers is an important objective due to great investment cost for this type of apparatus. It can be achieved by ,water spraying on a facial surface of a bundle of tubes or by using an air-water mist flow. We can thus diminish the heat transfer surface and regulate smoothly the heat flux independently of the weather conditions. Heat transfer in air-fin coolers (with 0.305 x 0.305 m facial areas) with an air-water mist flow has been studied in refs. 1- 3. The effects ,of water and ethylene glycol spray on the heat transfer, and friction loss performance of three automotive radiator cores, tubular types with plain, louvered and perforated fins have been investigated experimentally by Yang and Clark [l]. A good improvement in heat transfer performance has been observed by spraying 3.62-7.7 kg h-’ of liquid. It has been found that friction losses are not affected by the sprays, while the heat transfer performance was increased substantially. Improvement in the overall heat transfer coefficient of up to 40% for the air Reynolds number of 1000 was observed. In the turbulent regime, the increases in the heat transfer coefficients are about 12 and 6% for plain and perforated-finned units and the louvered-finned core, respectively. The sprays of water and ethylene glycol yield essentially the same results in spite of the fact that ethylene glycol evaporates at a temperature (197 “C) nearly double that for water (100 “C). One may thus conclude that the augmentation of air-side convective heat transfer by liquid spray is due mainly to the formation of liquid film on the heat transfer surface, while the contribution of evaporation is rather negligible, at least in this application.
The performance of a fin and tube heat exchanger wetted by water sprays of different mass fluxes and drop diameters, while air is blown across it with velocities between 0.8 and 2.3 m s-l, has been examined by Tree [2]. The three drop diameters examined were 64, 444 and 3300 pm. The water mass flow rates used were 10.8, 21.6 and 32.4 kg h-‘. The heat exchanger tested was a 0.3048 x 0.3048 m, four-row staggered arrangement, 0.0091/0.0092 m inside diameter copper tube with 0.00015 m thickness of aluminium fins with 476 fins per metre. The authors [2] have found that it is the mass flow rate of sprayed water which has the greatest effect on the heat transfer enhancement; the drop diameter has only a small effect in the ranges studied. The major source of enhancement of heat transfer in the presence of water drops is the direct evaporation of the drops on the exchanger. If all of the spray water enters into direct contact with the heat exchanger and evaporates, the enhancement (for spray water flow rates less then 54 kg h-‘) realized should be equal to the amount of water evaporated times the heat of vaporization of water (to within 10% accuracy). For the exchanger examined whose f d cial area was 0.305 m’, the possible enhancement for droplets of 64-3300 pm in diameter and for mass flow rate of water of 32 kg hhi was 40”/. Measurements of heat transfer from a single row of finned tubes to air-water mist in cross flow, at velocities from 4.57 to 9.14 m s-’ and water mist contents up to 5% have been presented by Simpson et al. [3]. The three monometallic finned tubes forming the single ,row tube bundle were heated internally by condensation of steam at a pressure of 1.36 bar fed to the slightly superheated top manifold of test bundle (0.6 K f 0.2). This gave an essentially constant temperature inside the tubes. The finned tubes were machined from solid leaded brass bar, 63.5 mm in diameter, 480 mm long, bored out to an internal diameter of 16 mm. Fins of thickness 1.6 mm were machined to give a fin height of 22.2 mm and fin spacing of 3.2 mm and 6.35 mm. The fins were later machined to give fin heights of 15.9 mm and 9.5 mm and a further fin spacing of 14.3mm. The tinned tubes were located in a single row of three vertical tubes with pitch equal to 89 mm. The authors [3] report that the heat transfer coefficient decreases with increase in the fin height and decrease in spacing, although, particularly for wider fin spacing and higher mist content, this trend was reversed for the longest fins. The enhancement factors, expressed as the ratio of a two-phase overall coefficient to a single-phase overall coefficient, were much greater for short widely spaced fins than for long fins of close spacing. From experimental data and theoretical calculations they find that at low mist contents and approach velocities the finned surface plays a more significant part in the heat transfer
133
process but with increased mist content and approach velocity the contribution of the base-tube surface becomes more important. Oshima et al. [4] have done an experiment on heat transfer from the surface of a six-row vertical air-fin cooler with hot water flowing inside, onto which water was sprayed concurrently to air flow from three nozzles situated in front of the exchanger. The finned tubes (rp = 9.45) were made of copper and the fins were spiral. The heat exchanger used was 700 mm high, 600 mm wide and 350 mm long, and contained 51 finned tubes arranged hexagonally with a pitch equal to 50 mm. The experimental range was: air mass velocity, 2000-12 000 kgm-* h-‘, amount of water spray, 72heat transfer co190 kg h-‘. The air-side apparent efficient was 93-418 W m-* degg’ and depended on the flow rate of the water spray. The authors report that the heat transfer rate is much larger in a heat exchanger with water spray than in that without spray and that the minimum amount of sprayed water is 0.03 kg/(kg dry air) at the air mass velocity of 12 000 kg rnp2 hh’. The objective of the present study is to determine the possibility of the enhancement of heat transfer from air-fin coolers with water sprayed countercurrently to air. A calculation method is elaborated based on experiments performed in a roof-type air-fin condenser. The method proposed is further verified using experiments carried out in a horizontal water cooler.
Experimental
apparatus
and results
The air-fin roof-type condenser was made up of bimetallic highly finned tubes (cp = 22.5). The flow system is shown in Fig. 1. The bimetallic finned tubes used were made of carbon steel and aluminium and the fins were spiral. The details of the tube are shown in Fig. 2. The experiments were carried out in apparatus with
aluminium A--
Fig. 2. Details
of a bimetallic
four-, three-, two- and one-row test bundles. Each of them was 1OOOmm high, 1050 mm wide and was inclined at an angle of 60”. The air-fin roof-type condenser (1) contained 70, 53, 35 and 17 one-metre long tubes arranged hexagonally in, four-, three-, two- and one-row test bundles respectively, with pitch equal to 59 mm. The finned tubes were heated internally by condensing low pressure steam fed to the top manifold (4) of the test bundle. This gave an essentially constant temperature inside the tubes. The condensate from the bottom manifold (5) flowed into a well-lagged tank. Air from a fan (2) flowed perpendicularly to the tube bundle. The changes in air mass flow rate were produced by using suitable perforated plates, built into the fan connector. The air velocity was measured by a Pitot tube, only in the experiments without water spray, at 16 selected points immediately behind the last row of tubes. At the same points the air temperature was measured. Water was sprayed by 4 nozzles (3) on the facial area of the condenser. The experimental range was: air velocity, 1.22.6 m ss’; sprayed water, 180-300 kg hh’; temperature of inlet air and of sprayed water, 15-25 “C and w 15 “C, respectively, and l-4 rows of the test bundle. The heat transfer rate was determined from the amount of the condensate obtained from the tested bundle of tubes. The enhancement factor W is defined as a ratio of heat transfer rates in the apparatus with (Q’) and without (Q) water spraying and is calculated as:
w=!&‘=GLrL Q
Fig. 1. Scheme of the air-fin roof-type condenser. 2, fan; 3, nozzles; 4, steam collector; 5, condensate
1, test bundle; collector.
finned tube.
GcrA
(1)
Some of the results for the enhancement factor W as a function of water flow rate and mist content are presented in Figs. 3-5. It can be seen in Fig. 3 and Fig. 4 that W increases with the amount of spray water and decreases with rising air velocity. In Fig. 5, where W is plotted against the mist content (G,,,/G,), the
134
2.31
I
I
22. 0 29
W
1.9 .
1.8 .
1.7 2JI//0 1.5 Ik
0
/, 200
Wgh/sl 1.5
0
2.1
.
2.5
250
Fig. 3. The enhancement function of water spray
_ 0
300
factor from a one-row mass flow rate.
tube bundle
as a
W
1.3 1.7
0
1.5:;/:;I_ / 180
( G;,-,w,Gg15x 100 6 Fig. 5. The dependence of the enhancement denser on a mist content.
wQhlvk1
2.0. o
3
260
300
GSPW [kg/h] Fig. 4. The enhancement factor from a three-row function of the water spray mass flow rate.
effect of the number significant.
bundle
as a
of rows (N) in the bundle on W is
Model and design method
If water is sprayed on the hot surface of the heat exchanger simultaneous heat and mass transfer occurs. In the case studied, the intensification of heat transfer is affected mainly by the mass transfer process. The mass transfer, in this case, takes place by evaporation of water droplets into the air stream or by evaporation from a thin water film formed by droplets impinging on the heating surface. Under the experimental conditions, the liquid film can be formed only on a small part of an outer surface of the heat exchanger due to its highly finned surface (cp = 22.5) and a small amount of the sprayed water. Taking into account the low temperature of the cooling air, one can assume that under the experimental conditions the air-water mixture was close
factor
for a con-
to saturation. For turbulent flow of a saturated air-water mixture, it is possible to &d a relationship between the heat and mass driving forces and apply the heat and mass transfer analogy [8] to determine the effective air-side heat transfer coefficient (c$), including heat transfer connected with mass transfer. The effective air-side heat transfer coefficient was determined on the basis of the experimental values of W. For the correlation of the experimental data the following assumptions are made. (1) The average temperature driving force for experiments with and without water spray has been assumed to be identical at the same air flow rate (At’ = At). (2) Thermal resistance of the film formed on the outer surface of the tubes is negligible. (3) Fin efficiency for the experiments with and without water spray is identical (q: = q,). Taking into account assumption (l), the enhancement factor W can be expressed as:
f+&LE Q k The overall heat transfer coefficient (k) without water spray for the exchanger made up of finned tubes can be calculated as:
Applying assumptions (2) and (3) the overall heat transfer coefficient (k’) with water spray can be defined by the similar relationship:
135
Introducing the global heat transfer c&,defined as:
coefficients
s(~ and
equation similar to that proposed by Hobler [7] for the effective heat transfer coefficient of a saturated airwater mixture: cc* <=
(6) into eqns. (3) and (4) the enhancement rewritten as:
factor
From eqn. (7) we can obtain an expression for the ratio of the air-side heat transfer coefficients with and without water spray as: WMW,)
%
where &,, is defined as:
and is equal to 130 for an air-water mixture at a low temperature. The value of X,, was calculated as an arithmetical mean of the inlet (X,,) and outlet (X,,) conditions for each experimental run. The outlet mass ratio (X,,) for this correlation was calculated as:
(8)
All the values appearing on the right side of eqn. (8) are known. The enhancement factor W was calculated from the experimental data (eqn. (1)). The air-side heat transfer coefficient as was calculated using the empirical correlation for a four-row roof-type condenser given in ref. 5: Nu,=~=O.l331 Rez,6x7 (9) B The fin efficiency q7 was taken from ref. 6 where it is given as a function of two parameters (4, p):
Inserting &,, = 130 and X,,, into eqn. ( 15) the E-values have been calculated for all 79 experimental points. Then the values of E were correlated as a function of two variables, Respw and N, which were considered as significant for the process. The mass flow rate (I,,,) in ReJpw was calculated as: l-
G =spw
Spw
(18)
2L e
where L, = Ii L, = 21i
for N = 1 for N = 2, 3, 4
The correlation
(11) where A,=6
D,-db
2
(12)
Taking into account the mass flow rate of condensate from the experiments performed with and without water spray the internal heat transfer coefficients (cri, x,) were calculated from Nusselt correlation [ 71: Nu, =y
= 1.5 Re;‘13
u: = v,(sin /3-“’
(15)
W can be
(7)
a;
1 +ci,Xnm
(13)
(14)
The values of the ratio of air-side heat transfer coefficients with and without water spray (eqn. (8)) were calculated using eqns. ( l), (S), (6) and (9) -( 14). The values of a,*/~, thus obtained were correlated using an
thus obtained
is:
s = 0 176 Re0.562N-0.3R VW
(19)
Introducing eqn. (19) into eqn. (15) the effective airside heat transfer coefficient with water spray can be calculated from: 2
= 1 + 0.176 Re~5,62N-0~38[,X,,
(20)
As can be seen from Fig. 6, eqn. (20) correlates experimental data for the air-fin roof-type condenser with an accuracy of f 20% for 2.3 < Respw < 7.0, 1
of the design method proposed
The experimental data concerning the enhancement factor W obtained in a horizonatal water cooler partially sprayed with water were used for the verification of the calculation method proposed.
1.5. 1.4 w
1.3
1.2. 13 . I.01
0 0 Re
a05 0562 -0,s SPW N
010
The horizontal cooler (1) was made up of 22 one-metre long finned tubes (see Fig. 2), arranged hexagonally with pitch equal to 59 mm in a four-row bundle of tubes. Its facial area is 0.354 x 1.0 m. The flow system is shown in Fig. 7. The tubes were heated internally with hot water with a constant inlet temperature and the mass flow rate equal to 3.9 m3 h-‘. The air from a fan enters the cooler through a measuring orifice placed in a circular pipe. Above the horizontal cooler, there are two nozzles (2) from which water is sprayed onto the facial area of the exchanger. The sprayed area was l/3 or 213 of the facial area when one or two nozzles were working, respectively. The experimental range was: air velocity, 1.322.75 m s-‘, amount of water spray, 20-150 kg h-‘, inlet air and water spray temperature, 21-30 “C and N 15 “C, respectively. The values of the enhancement factor W for the horizontal cooler, calculated as G,c,At'
wexp = G,c,At
(21)
were compared with similar experimental by Tree [2] in Fig. 8.
Fig. 7. Scheme of the air-fin horizontal 2, nozzles; 3, hot water 6, circular pipe.
.
2
3
4 5 6 7 (‘&pw/Sgb 100
1
.
8
9
10
Fig. 8. The comparison between the enhancement factor W obtained for a four-row bundle in a horizontal water cooler ( 0) and the data ( +) given by Tree [2].
‘A,
Fig. 6. The values of G(~*/c(~ obtained from the experimental data for the roof-type condenser as a function of Reynolds number (Respu) and the number of rows (N) in the bundle,
cooler; heater;
.+
1
tank;
data reported
water cooler. 1, test 4, water pump; 5, water
The verification of the design method described previously was performed by comparing the two enhancement factors, Wexp and W, (Fig. 9). The values of W, were calculated from eqn. (22): w =k’FE+kF(l t kF
-E)
(22)
where E represents a fraction of the facial area of the exchanger sprayed with water (E = l/2 or E = 2/3). The overall heat transfer coefficients for the dry (k) and wet (k’) parts of the horizontal cooler were calculated from eqns. (3) and (4), respectively. The air-side heat transfer coefficient (LX,) was calculated in this case from an empirical correlation reported in ref. 9: ud Nu = A..!? = 0.4799 Re0.‘588 &lax 1,
This equation was obtained for a four-row horizontal exchanger made up of the same type of finned tubes. The effective heat transfer coefficient LX: was calculated from eqn. (20) and the McAdams correlation was applied to calculate the heat transfer coefficient GL~ for the inside water flow in turbulent regime. A good agreement between the experimental and calculated values of Wexpand W, for a horizontal water cooler can be regarded as a successful verification of the calculation method proposed (Fig. 9).
Fig. 9. The comparison between the calculated (W,) and experimental (W,,,) values of the enhancement factor for a horizontal water cooler 0 - l/3 of the facial area sprayed by water, 0 - 2/3 ._;, of the facial area sprayed by water.
137
Conclusions
RA
The results of the experimental study performed in an air-fin roof-type condenser additionally sprayed with water, with a countercurrent air flow, show that the heat enhancement factor W can be increased by up to 125%. The quantitative results for the finned tubes (q = 22.5) were similar to those obtained by Simpson [3] for the mist flow experiments carried out with tubes of similar geometry (cp = 25.7). It leads to the conclusion that the type of water sprayer has only limited effect on the heat transfer, thus confirming the results obtained by Tree [2] for water droplet diameters of 64-3300 pm. The calculation method proposed, which introduces the effective heat transfer coefficient for the gas phase cl: given by eqn. (20) seems to be a handy tool for solving this type of problem. This has been confirmed by other experiments performed in a horizontal air-fin cooler with water spraying. In this case, the external thermal resistance was comparable with the internal resistance. A good agreement between the experimental values of W,,, (eqn. (21)) and the values W, calculated from eqn. (22) in which the overall heat transfer coefficients (k and k’) were determined theoretically (eqns. (3) (4) (20), (23)), is shown in Fig. 9. The method of calculation proposed can be applied to determining the values of W for air-fin coolers with countercurrent water spraying (up to 10 wt.% of water in cooling air).
rA S
Nomenclature CW
DO
4 E 6 F, Gg GC G, G ww s i 1A
k L 1 M m* N
Q
specific heat, J kg-’ K-i outer diameter of finned tube, m base fin tube diameter, m fraction of exchanger surface sprayed with water inner surface of finned tube, m2 total outer surface of finned tube, m2 air mass flow rate, kg h-’ condensate mass flow rate, kg h-’ water mass flow rate, kg h-’ sprayed water mass flow rate, kg h-’ acceleration of gravity, m s-’ number of tubes in row enthalpy of diffusing component, J kg-’ overall heat transfer coefficient, W mm2 K-’ equivalent length, m tube length, m molecular weight, kg kmol-’ =M,/M, = 18/29 = 0.622 number of rows in bundle heat transfer rate, W
T t L: W Wg W nmx XA
constant of diffusing component, J kg-’ K-’ heat of vaporization, J kg-’ wall thickness, m temperature, K inlet temperature of air, “C temperature difference, “C = Q’/Q, enhancement factor of heat transfer air velocity, m s-’ air velocity calculated for minimal crosssection, m s-i mass ratio of component A, (kg H,O)/( kg dry air) gas
Greek letters u heat transfer
G a0 a0 B lcp 4
: L r % 1 a,
coefficient, W m-* K-i effective heat transfer coefficient, W m-* K-’ heat transfer coefficient defined by eqn. (4), W m-* K-’ heat transfer coefficient defined by eqn. (.5), W mm2 K-’ angle of tube inclination, o mass flow rate per unit width, kg m-’ s-’ = F,/F,, ratio of overall outer finned tube surface to inner surface of tube ratio of heat and mass transfer coefficients, J kg-’ K-’ density, kg me3 fin thickness, m dimensionless value given by eqn. (16) coefficient of dynamic viscosity, kg m-i s-i tin efficiency thermal conductivity, W m-’ K-’ = [a ‘/(BY 31“3, equivalent thickness, m
Dimensionless
numbers
4r =-z
Re, Re e max
, condensate Reynolds number % 4r =x , sprayed water Reynolds number G&v = @&&by,
, gas Reynolds
number
%
Subscripts C
g i spw A”
condensate gas phase refers to inside of tube sprayed water mean value water
Superscripts
refers to spraying
conditions
with
additional
water
138
References 1 Yang Wen-Jei and D. W. Clark, Spray cooling of air-cooled compact heat exchangers, Int. J. Heat Mass Transfer, 18( 1975), 31 I-317. 2 D. R. Tree, V. W. Goldschmidt, R. W. Garrett and E. Hach, Effect of water sprays on heat transfer of a fin and tube exchangers, 6th ht. Heat Transfer Conf., Toronto, Ont. ( 1978). 3 H. C. Simpson, G. C. Beggs and G. N. Sen, Heat transfer from extended surface tubes to an air-water mist flow, Symp. on Multi-Phase Flow Systems, Univ. Strathciyde, ( 1974) l-22. Design 4 T. Oshima, S. Iuchi, A. Yoshida and K. Takamatsu, calculation method of air-cooled beat exchangers with water spray, Heat Transfer-Japanese Research, I (1972).
5 R. Krupiczka, H. Walczyk and J. Przybyla, Experimental study of heat transfer and air flow pressure drop for bimetallic finned tube manufactured in Poland, Ini. Apal. Chem., 6 (1978) (in Polish). 6 D. Q. Kern and A. D. Kraus, Extended Surface Heat Transfer, McGraw-Hill, New York, 1972. 7 T. Hobler, Heat Transfer and Heat Exchangers, WNT, Warsaw, 1972 (in Polish). 8 W. H. Walker, W. K. Lewis, W. H. McAdams and E. R. Gilliland, Principles of Chemical Engineering, McGraw-Hill, New York, (1937). 9 Investigation of regulation and intensification of heat transfer in air-fin heat exchangers by water spray, Report for the Institute of Chemical Engineering of the Polish Academy of Sciences, Gliwz’ce, Part X (1985) (in Polish).