Determination of apparent heat transfer coefficient by condensation in an industrial finned-tube heat exchanger: prediction

Applied Thermal Engineering 25 (2005) 1863–1870 www.elsevier.com/locate/apthermeng

Determination of apparent heat transfer coefficient by condensation in an industrial finned-tube heat exchanger: prediction C. Bougriou a, R. Bessaı¨h a

b,*

LESEI, De´partement de Me´canique, Universite´ de Batna, rue A. Boukhlouf, 05000 Batna, Algeria b Laboratoire d’Energe´tique Applique´e et de Pollution, De´partement de Ge´nie Me´canique, Universite´ Mentouri-Constantine, Route d’Ain El. Bey, 25000 Constantine, Algeria Received 18 April 2004; accepted 6 November 2004 Available online 16 December 2004

Abstract The determination of apparent heat transfer coefficient by condensation in a fined-tube heat exchanger is presented numerically in this paper. The film method is used in order to predict the partial or total condensation of the water vapour, contained in the humid air over the smooth or finned tubes-heat recuperators. This method is incorporated in a computer code developed here. The determination of the fin portion, which functions in wet regime, is carried out by the calculation of temperature field over a circular fin. The computer code predicts the heat flux exchanged in a range of 20–5%, in wet and dry regime, respectively. The apparent heat transfer coefficient by condensation can exceed 10 times the value of the heat transfer coefficient. Ó 2004 Elsevier Ltd. All rights reserved. Keywords: Heat exchangers; Finned tube; Condensation; Film method

*

Corresponding author. Tel.: + 213 31 94 90 02; fax: +213 31 94 29 57. E-mail address: [email protected] (R. Bessaı¨h).

1359-4311/$ - see front matter Ó 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.applthermaleng.2004.11.004

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Nomenclature A Cp de di h h* KC Km L0 l P DPml S Sa Se Si U Greek u gg k l p h t

Ackermann coefficient Specific heat, J kg
1 K
1 Outer diameter of tube, m Inner diameter of tube, m Heat transfer coefficient, W m
2 K
1 Effective heat transfer coefficient of the humid air, W m
2 K
1 Combined heat transfer coefficient, W m
2 K
1 Mass transfer coefficient, kg m
2 s
1 Latent heat, J kg
1 Length of tube, m Pressure, Pa Log-mean pressure difference, Pa Exchange surface per meter of equivalent smooth tube, m Exchange surface of fined tubes per meter, m Total outer exchange surface, m2 Total inner exchange surface, m2 Velocity of the fluid, m s
1 Letters Heat flux density, W m
2 Total fined surface efficiency Thermal conductivity, W m
1 K
1 Dynamic viscosity, Pa s 3.14l59 rad Temperature, °C Kinematic viscosity, m2 s
1

Dimensionless numbers Pr Prandtl number: Pr = lCP/k Re Reynolds number: Re = Ud/t Indices C e I i lam

Condensate Water, outside Interface Interior Laminar

C. Bougriou, R. Bessaı¨h / Applied Thermal Engineering 25 (2005) 1863–1870

m p S t tot v

1865

Average Primary Secondary, sensitive, dry Tube Total Vapour

1. Introduction Fin-and-tube heat exchangers are employed in a wide variety of engineering applications like air-conditioning apparatus, process gas heaters and coolers. The problem considered in this study concerns the finned-tube-heat exchangers calculation in the case of condensation of a vapour, in the presence of incondensable gases. This case is encountered during the heat evacuated by the dryers or boilers chimneys and/or by vapour condensation contained in the ambient air on the heat exchangers used for air-conditioning, . . . etc. A large number of studies have been done by many researchers. The local heat transfer coefficients on the outer surface of tubes, in shell-and-tube heat exchangers, with staggered tube arrangement are visualised and determined from mass transfer measurements by Li and Kottke [1]. These coefficients are transformed to heat transfer coefficients by employing the analogy between heat and mass transfer. An experimental study of local heat transfer coefficients in a staggered tube array with plate fins was investigated by Murray et al. [2]. The results indicate that most positions on the tubes and on the fins record an increase in heat transfer with decreasing fin spacing, although there is an optimal spacing below which local heat transfer coefficients decrease. Ay et al. [3] used the technique of energy balance based on infrared thermography to estimate the local heat transfer coefficients of plate fin in a 2-D inverse heat conduction problem. The results demonstrate that the averaged heat transfer coefficient of staggered configuration is 14–32% higher than that of in-lined configuration. Experimental results for the convective coefficient distribution in both the inside and conical end zones of the extended surface in a finned pipe are presented for three different flow velocities in the paper of Mariscal et al. [4]. The results show that the convective coefficient distributions in the conical region and in the inside region of the fin are quite different; and the heat transfer coefficient distribution on the pipe surface is very similar to the one obtained for a flat cylinder. Lalot et al. [5] present the effect of flow nonuniformity on the performance of heat exchangers, based on the study of flow maldistribution in an experimental electrical heater. Optical methods for measuring local heat transfer coefficients using thermochromic liquid crystals were discussed by Critoph et al. [6]. Two techniques using radiative steady state and transient heating have been used to measure local heat transfer on the fin of a plate fin-tube heat exchanger. Our objective is to solve the present problem by using the film method, which holds in account the influence of mass transfer on the thermal calculation and the estimate of the fin portion, which works in wet regime.

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2. Mathematical model The heat and mass transfer model was the subject of many studies (see for example, [7–14]). The film method [12] (or Colburn–Hougen method) is based on the mass, momentum and energy equations. In this method, the analogy between the heat and mass transfer is used. The heat transfer coefficient outside the tube he is calculated according to the tubes bundle arrangement [15] as:

0:17 kp 0:633 1=3 S a he ¼ 0:29 Rep Prp ð1Þ de S valid for 1000 < Rep < 40000 Sa 4 < < 34 S and the effective heat transfer coefficient of the humid air he : us ¼ he ðhm;p
hI Þ

ð2Þ

The total heat flux density utot is the sum of the significant heat flux density and the latent heat flux density: utot ¼ he ðhm;p
hI Þ þ

Km 0 L ðP v;m
P v;I Þ ¼ he;tot ðhm;p
hI Þ DP mla

ð3Þ

where he;tot is the apparent heat transfer coefficient with condensation, which is higher than the heat transfer coefficient of the gas phase in wet regime, he;tot  he (in dry regime, he;tot ¼ he ¼ he ). he;tot ¼ he þ

K m 0 P v;m
P v;I L DP mla hm;p
hI

ð4Þ

The global heat transfer coefficient Kg is calculated from the following equation: 1 1 1 ¼ þ K g K c gg he;tot where the combined heat transfer coefficient Kc is " #
1 1 Se Se de 1 Kc ¼ Ln þ þ hi S i 2pkt l d i gg hc

ð5Þ

ð6Þ

3. Various flow patterns The flow configuration studied here concerns a humid air flow (primary fluid) horizontal and perpendicular to tubes, in aligned and staggered arrangement. In our computer code, we have studied three types of secondary water fluid flows inside the tubes.

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4. Results and discussion

Temperature [˚C]

When the heat exchanger works in wet regime, the condensation of the water vapour is done mainly towards the exit of the heat exchanger; the water and the tubes wall temperature are lower at the exit of the counter cross-flow heat exchanger. Separately, the water and wall temperature, the same remark remains valid for a parallel cross-flow heat exchanger. In dry regime, the heat transfer coefficients drop of the inlet to the exit of the heat exchanger. This is due to the bringing together of two fluids temperature, according to the direction of airflow along the heat exchanger (Figs. 1 and 2). This phenomenon is reversed in wet regime, that is due to the condensation of the humid air, that is, the latent heat of the water (Figs. 2 and 3). The apparent heat transfer coefficient with condensation he;tot is very large, it can exceed 10 times the value of he. This is due to the strong apparent specific heat of the saturated humid air. For example, we give Figs. 2 and 3, where the apparent heat transfer coefficient is the double of the heat transfer coefficient of the humid air. The effective heat transfer coefficient of the gas phase he to the heat transfer coefficient ratio outside the tubes he is about 10% (it is equal to the AckermannÕs coefficient, A [8]). The he can reach 170 W m
2 K
1 and 100 W m
2 K
1, in wet and dry regime, respectively. The total heat transfer coefficient K can reach l00 W m
2 K
1. The heat transfer rate exchanged decreases from the inlet to the exit of the heat exchanger. This is due to the great temperature variations between the primary and secondary fluid at the inlet of the heat exchanger (Figs. 1 and 3). The fin portion, which works in wet regime, grows towards the exit of the heat exchanger. In our tests, the code estimates that the maximum fin portion working in wet regime is about 12%.

200 190 180 170 160 150 140 130 120 110 100 90 80 70 60 50 40 30 20

Moist air

water

0

2

4

6

8

Rang

Fig. 1. Air and water temperature profiles in the heat exchanger.

10

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Heat transfer coefficients [W/m².K]

110 *

h e,tot Kg

100 90 80 70 60 50 40

Dry model

30

Wet model

20 10 0 1

3

5 Row

7

9

Heat flux [kW]

Fig. 2. Evolutions of heat transfer coefficients versus the number of row.

3.4 3.2 3 2.8 2.6 2.4 2.2 2 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 1

3

5 Row

7

9

Fig. 3. Heat transfer rate exchanged.

For example, we can give the fin portion profile in wet regime with function of the number of rows (Fig. 4). We can notice that for the same conditions at the inlet of the heat exchanger and the same flowrate of the secondary fluid circulating inside each tube, the cross-flow configuration is most effective. Whereas, the counter cross-flow configuration is most powerful. The later can exchange 50%

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9 8

Wet fin portion [%]

7 6 5 4

Dry model

3

Wet model

2 1 0 1

3

5 Row

7

9

Fig. 4. Wet fin portion profile versus the number of row.

of more than one simple cross heat exchanger. The difference between the heat flux exchanged in a counter cross-flow and with parallel cross-flow heat exchanger is lower than 10%. Generally, in a cross heat exchanger, the heat transfer is done in dry regime. This is due to the bad heat transfer, that is, the water does not manage to cool the tubes below the dew temperature. The fall in temperature of the hot fluid is higher in the case of the counter cross-flow heat exchanger compared to the other configurations considered in this study.

5. Conclusions We have developed a modelling permitting to simulate the heat transfers by condensation of the humid air on fined tubes bundles, by using the film method. For finned tubes, the knowledge of the fin surface, which works in wet regime, is very important for the heat transfer rate calculation evacuated by the heat exchanger. The determination of the wet fin portion, was carried out by the calculation of the temperature field distribution on a plane circular fin. The condensation of the water vapour contained in the humid air is done preferentially with the last rows of the heat exchanger. In wet regime, the effective heat transfer coefficient of the gas phase and the apparent heat transfer coefficient with condensation grow proportionally with the condensation flowrate. These coefficients are higher at the exit of the heat exchanger. The heat transfer coefficient increases outside the tubes by the negligible diffusion effect, since it is lower than 10%. The apparent heat transfer coefficient with condensation can exceed 10 times the value of the heat transfer coefficient of the gas phase. The heat transfer rate exchanged decrease from the inlet of the exchanger. This is due to the great temperature variations between the secondary and primary fluid at the inlet of the heat exchanger.

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Acknowledgement This study was carried out and financed by le Groupement pour la Recherche sur les Echangeurs de Thermiques (Greth-CEA/Grenoble-France), to which we address our thanks.

References [1] H. Li, V. Kottke, Visualization and determination of local heat transfer coefficients in shell-and-tube heat exchangers for staggered tube arrangement by mass transfer measurements, Exp. Ther. Fluid Sci. 17 (3) (1998) 210– 216. [2] D.B. Murray, B. McMahon, D. Hanley, Local heat transfer coefficients in a finned tubular heat exchanger using liquid crystal thermography, Int. J. Heat Exchangers 1 (2000) 31–48. [3] H. Ay, J.Y. Jang, J. Yeh, Local heat transfer measurements of plate finned-tube heat exchangers by infrared thermography, Int. J. Heat Mass Transfer 45 (20) (2002) 4069–4078. [4] I. Carvajal-Mariscal, F. Sanchez-Silva, M. Toledo-Velazquez, V.A. Pronin, Experimental study on the local convective coefficient distribution on a pipe surface with inclined fins, Exp. Ther. Fluid Sci. 25 (5) (2001) 293–299. [5] S. Lalot, P. Florent, S.K. Lang, A.E. Bergles, Flow maldistribution in heat exchangers, App. Therm. Eng. 19 (1999) 847–863. [6] R.E. Critoph, M.K. Holland, M. Fisher, Comparison of steady state and transient methods for measurement of local heat transfer in plate fin-tube heat exchangers using liquid crystal thermography with radiant heating, Int. J. Heat Mass Transfer 42 (1) (1998) 1–12. [7] A.P. Colburn, O.A. Hougen, Design of cooler condensers for mixtures or vapors with noncondensing gases, Ind. Eng. Chem. 26 (11) (1934) 1178–1182. [8] A.P. Colburn, T.B. Drew, The condensation of mixed vapours, Trans. AIChE 33 (1937) 197–215. [9] R. Krishna, G.L. Standart, A multicomponent film model incorporating a general matrix method of solution to the Maxwell–Stefan equations, AIChE J. 22 (2) (1976) 383–399. [10] A.C. Banwart, Etude the´orique et expe´rimentale de la condensation dÕune vapeur en pre´sence dÕincondensables: proposition dÕun mode`le de film gazeux en convection force´e turbulente. Ph.D Thesis, INP Grenoble, 1988. [11] F. Marlin, Condensation en pre´sence dÕincondensables a` lÕexte´rieur dÕun faisceau de tubes, Application a` lÕe´tude dÕun e´changeur tubulaire. Grenoble, C.E.N. de Grenoble, S.T.T.L.P.M.L., Rapport de stage dÕinge´nieur no. 88/07/ A, 1988. [12] J.G. Collier, Convective boiling and condensation, Second ed., McGraw-Hill International Book Company Limited, Maidenhead, UK, 1981. [13] D. Butterworth, Condensation of vapour mixturesH.E.D.H. Handbook, Dusseldorf Hemisphere Publishing Corporation, 1983. [14] G. Ackermann, Simultaneous heat and mass transfer with large temperature and partial pressure differences, Ver. Deutsch. Ing. Forsch. 8 (382) (1937) 1–16. [15] PFR Engineering Systems, Heat transfer and pressure drop characteristics of dry towers extended surfaces. Part II: DATA analysis and correlation. Calif. Marina del Rey : PFR, Rapport dÕe´tude no. BNWL-BFR-7-102, 1976.