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Experimental investigation during condensation of R-600a vapor over single horizontal integral-fin tubes
International Journal of Heat and Mass Transfer 88 (2015) 247–255
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International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Experimental investigation during condensation of R-600a vapor over single horizontal integral-fin tubes Sanjeev K. Sajjan ⇑, Ravi Kumar, Akhilesh Gupta Department of Mechanical and Industrial Engineering, Indian Institute of Technology Roorkee, 247667 Uttarakhand, India
a r t i c l e
i n f o
Article history: Received 7 February 2015 Received in revised form 18 April 2015 Accepted 24 April 2015 Available online 14 May 2015 Keywords: Vapor condensation Iso-butane Integral fin tube External heat transfer coefficient
a b s t r a c t In this study, condensation heat transfer coefficients (HTCs) of refrigerant R-600a (iso-butane) over a horizontal smooth tube of outer diameter 19 mm and five integral fin tubes of different fin-densities (945, 1024, 1102, 1181, and 1260 fpm) were determined at vapor temperature of 39 ± 0.5 °C with different wall sub-cooling temperatures in a range of 3–12 °C. Like other refrigerants, condensation heat transfer coefficients of R-600a showed the same trend with wall sub-cooling where condensation HTCs decrease with the rise in wall sub cooling temperatures. The heat flux was 11–20 kW/m2 for the plain tube and 28–82 kW/m2 for integral fin tubes. Based upon the data taken in this study, different graphs were plotted varying different parameters to show their dependency on other parameters. The experimental data were also validated by comparing them against different models. Ó 2015 Elsevier Ltd. All rights reserved.
1. Introduction Many experimental and theoretical investigations have analyzed the effects of fin geometry, tube material and condensing fluid properties for the condensation heat transfer on integral finned tubes. Also significant improvements over plain tubes have been made in order to increase surface area and reduce the thickness of the condensate film by surface-tension-induced pressure gradients. The integral finned tube enhances heat transfer by increasing surface area as well as surface tension controlled condensation drainage on the sides of the fins. Integral fin tubes enhance the heat transfer by reducing the film thickness much more than the simple increase in surface area. The concept of integral fin-tubes for the enhancement of heat transfer rate was developed in the late 1940’s. The first idea, to introduce integral fin-tubes, was to increase the heat transfer area, but later on, many models like gravity drainage mechanism, surface tension drainage mechanism, and condensate retention model due to surface tension came into existence. The first effort to predict the heat transfer rate for outside condensation of a horizontal integral fin-tube was carried out by Beatty and Katz [1]. Their model was based upon Nusselt [2] equations for film condensation over a vertical wall and a horizontal tube. They assumed that the condensate is not retained in between the fins and the surface force can be neglected ⇑ Corresponding author. E-mail addresses: [email protected] (S.K. Sajjan), ravikfme@iitr. ernet.in (R. Kumar), [email protected] (A. Gupta). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2015.04.079 0017-9310/Ó 2015 Elsevier Ltd. All rights reserved.
with only the gravitational force considered for draining out the condensate. The effect of surface tension over condensation heat transfer coefficient for vertical fluted tubes was first analyzed by Gregorig [3]. He showed that surface tension forces played an important role in enhancing the heat transfer coefficient by thinning the condensate film at the tips of the flutes. Thereafter Karkhu and Borovkov [4] first implemented the concept of surface tension for the condensation of the pure vapors over the horizontal integral fin-tubes. Their model assumes that the flooded zone is constant and independent of fin geometry and fluid properties. Rifert et al. [5] modified Karkhu and Brokovkov [4] model to account the effect of tube geometry and fluid properties on the condensate retention. Canvas [6] conducted experiments using CFC11 as the working fluid for different fin densities of low integral fin tubes and determined the optimum fin density for the condensation of CFC11 over fin tubes. Rudy and Webb [7] distributed the whole fin surface and interfin spacing into two regions: unflooded and flooded. They assumed that heat transfer occurred only by the unflooded region and neglected the heat transfer by the flooded region. Owen et al. [8] included the unflooded and the flooded region both into their analysis and improved Beatty and Katz model which explicitly accounted for the unflooded region as well as the flooded region. Webb, Rudy and Kedzierski [9] proposed surface tension drainage mechanism on the fin surface and gravity drainage mechanism in the interfin spacing. Wanniarachchi et al. [10] measured HTCs of outside condensation of steam over 24 finned tubes of different geometry and obtained best fin spacing between 1.5–2.0 mm.
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Nomenclature A Cp fpm h hfg ho m Pf Q q R t T DTf
surface area (m2) specific heat (kJ kg1 K) fins per meter fin-height (m) latent heat of vaporization (kJ/kg) condensing-side heat transfer coefficient (kW/m2–°C) mass flow rate (kg s1) pitch of the fin (m) heat transfer rate (kW) heat flux (kW/m2) distance from tube center line (m) thickness of fin (m) temperature (K or °C) difference of temperature between refrigerant vapor and tube wall (K or °C) (wall sub-cooling temperature)
r
surface tension (N/m)
Subscripts b bottom of fin c condensate cw cooling water exp experimental values f saturated liquid phase g saturated vapor phase i inlet o outet or outside or top of fin r root of fin s saturated vapor t tip of fin w wall of tube or surface of tube
Greek letters q density (kg/m3) l viscosity (l Pa s)
An important factor which has been ignored in the above theoretical models was the nonuniformity of wall temperature. Previous all models assumed uniform circumferential temperature distribution of the tube surface, but in fact, there developed a considerable temperature gradient along the circumference of the tube due to a variable thickness of the condensate-film over the tube. This would cause the deviation in heat transfer coefficients from that predicted by the uniform wall temperature model. Honda and Nozu [11] included the effect of variable wall temperature in their analysis and presented a method for predicting the average heat transfer coefficient for film condensation on horizontal low integral-fin tubes which was applicable to a wide range of conditions. Their model predicted most of the available experimental data, including 11 fluids and 22 tubes within ± 20 percent. Marto et al. [12] conducted experiments using R-113 as a working fluid for 1 smooth tube ad 24 specially machined rectangular-fin tubes with various fin spacings, thicknesses, and heights and found that fin spacing between 0.2–0.5 mm showed better heat transfer rate, also heat transfer performance increased with thinner and taller fins. Masuda and Rose [13] found a 1.0 mm as optimum fin spacing for ethylene glycol and for this tube, enhancement ratio was 4.7. Adamek and Webb [14] presented an analytical model for prediction of film condensation on horizontal integral fin tubes. Their model predicted condensation on all surfaces in the flooded and unflooded regions and included the effect of fin efficiency. Briggs and Rose [15] derived a semi-empirical model for condensation on horizontal, integral fin-tubes to account for fin efficiency effects. Park and Jung [16] found that for condensation of HCFC123, HTCs increased up to the fin density of 1102 fpm but decreased sharply beyond that density. Al-Badri et al. [17] developed element by element prediction model of condensation heat transfer on a horizontal integral finned tube. This model showed good agreement with the experimental data with a mean deviation of 4.7 percent. The data include condensation heat transfer characteristics of R-600a over smooth and five different finned tubes with different fin densities varying different parameters. All finned tubes are of standard dimensions and can be used commercially due to easy and low cost fabrication. These tubes cover a significant range of fin density varying from 945 fpm to 1260 fpm and the optimized value of fin density giving highest heat transfer rate lies in this range. No researcher has performed experiments for this range of
fin density for the refrigerant R-600a. R-600a can be better alternative for CFCs and HCFCs because R-600a is eco-friendly (since its ODP is zero and GWP is low) having good thermodynamic properties. However the data cover a significant range of fin geometries, these can also be applied for other geometries within the permissible range of acceptance. Also the data may be useful to industrial application. 2. Experimental set-up and procedure The experimental set-up fabricated for this study is illustrated in Fig. 1, a schematic diagram of the set-up, which comprised of major components like condenser, evaporator and data collection unit. The test condenser (5) is a stainless steel-304 cylinder of thickness 3 mm, inside diameter 100 mm and length 414 mm. The dead end pipe (6) of 350 mm length and 6.5 mm diameter has equally spaced 125 holes, each of 1 mm diameter, in a straight line. The test-section (3) of length 400 mm is fixed inside the test-condenser with the help of chuck nut assembly. The details of the geometry of test-sections are shown in Fig. 2 and listed in Table 1. The viewing window (17) is provided in the middle of the test-condenser fitted with the Teflon glass to observe condensation. The evaporator (10) is a stainless steel-304 cylinder of thickness 3 mm, inside diameter 140 mm and length 670 mm. Three immersion heaters (12) each of 3 kW heating capacity are fixed in the bottom of the evaporator to transfer heat directly to the liquid refrigerant. The cylinder is closed by a flange (13), sealed with a 12 mm diameter hardened rubber O-ring and 8 holes of 10 mm hole diameter. The auxiliary condenser (2) is a stainless steel-304 cylinder of thickness 3 mm, inside diameter 120 mm and length 140 mm fixed approximately 45 cm above the test-condenser. On the top of the auxiliary condenser a purge valve (1) is fixed to remove air from the system. To ensure leak proof experimental set-up, a pneumatic gauge pressure of 2.0 MPa was maintained inside the set-up for 24 hours, followed by a vacuum of 60 cm of Hg for same duration. No pressure drop inside the set-up ensured that the set-up was leak proof. Assuring the leak proof of the set-up, the refrigerant was charged in the set-up under vacuum. While charging the refrigerant, the required purging was done via purging pipe (1) to escape air and other non condensable gases from the set-up. After charging, the cooling water was circulated inside the test-condenser and the
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Fig. 1. Schematic diagram of the experimental set-up. 1 – purging pipe 2 – auxiliary condenser 3 – test-section 4,9 – pressure gauge & pressure transducer 5 – test-condenser 6 – perforated pipe 7 – thermocouple exit port 8,11 – centrifugal pump 10 – evaporator 12 – heaters 13 – flange 14,15 – turbine flow meters 16 – U-bend tube.
Fig. 2. Details of geometry of test-section.
Table 1 Details of test-section. Fin density (fpm)
Ro (mm)
Rr (mm)
Pf (mm)
h (mm)
tt (mm)
tb (mm)
925 1024 1102 1181 1260
9.56 9.47 9.54 9.49 9.56
8.68 8.75 8.80 8.85 8.89
1.06 0.98 0.91 0.85 0.79
0.88 0.72 0.74 0.64 0.67
0.24 0.22 0.20 0.19 0.18
0.82 0.76 0.71 0.66 0.61
auxiliary condenser by centrifugal pumps (8) and (11) respectively. A U-bend tube (16) was fixed at the end of exit of water supply passing through test-condenser to ensure water in water-line of the test-condenser when the set-up is not operative. The refrigerant in the evaporator was heated with the electric immersion heaters (12). The vapor of refrigerant thus generated rushed to the test-condenser (5) and passing through the perforated pipe (6), it was subsequently condensed by coming in contact with the cold surface of test-section (3). The condensate was drained to the evaporator and thus the refrigerant flow cycle was completed. The rate of vapor generation was controlled by a variac. The cooling water flow rate through the test condenser was changed in such manner so that the wall sub cooling temperature (difference between refrigerant vapor temperature and tube wall temperature, DTf) would approximately vary from 3 °C to 12 °C in the interval of 0.5 °C. The pressure of condensing vapor was maintained constant throughout the investigation by regulating the energy supply to immersion heaters in the evaporator and cooling water flow rate in the auxiliary condenser and at that pressure, the temperature
of the condensing vapor remained close to the vapor saturation temperature of R-600a, hence saturated vapor of R-600a entered the tested condenser. For each test run, data were collected only when the set-up attained a steady state condition. The steady state condition occurred when the rate of vapor generation became equal to the condensation rate, consequently the pressure inside the set-up became stable and so, the temperature of condensing vapor. For each test run, the temperature of condensing vapor, the surface temperature of the test-section, the temperature of cooling water at the inlet and outlet of the test-section and the cooling water flow rates were recorded. Purging was done after every 4–5 hours of operation to escape air and non-condensable gases from the set-up. The primary function of the auxiliary condenser is to keep the test-condenser free from air and non condensable gases. Temperature measurement includes the measurement of the condensing vapor temperature, surface temperatures of the test section and the temperature rise of the cooling water. Measurement of the surface temperature of the test-section is the most sensitive job due to fluctuations in the tube wall temperature. The tube wall temperature fluctuates because of the periodic wrapping of the tube’s surface of the condensate layer, followed by the condensate drainage from the bottom of the test section in the form of drops under gravity. Hence, the thickness of the condensate layer varies with time, resulting in a variable condensate film thermal resistance. Thus, the outcome is variable tube wall temperature. J-type thermocouples of 20 gauge thickness and an 8 channel data acquisition module (ADAM-4019) are used for temperature measurement. To measure average outside tube wall temperature was the most difficult measurement. During film condensation on a horizontal condenser tube, the wall temperature varies both axially and circumferentially. The wall temperature will depend upon the local vapor-to-coolant temperature difference and local condensate film thickness. Since the coolant bulk temperature varies along the length of the tube, the wall temperature will naturally change from the coolant inlet to outlet. Although this change is not linear with axial position, the measurement of wall temperature is made at the midpoint of the test-tube to represent an appropriate average. The wall temperature also varies circumferentially. The installation of numerous thermocouple leads more time consumption, more cost and more measurement errors. Therefore, four thermocouples are fixed at top,
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bottom and two sides of the test-section. At each predetermined position, a hole of 0.5 mm depth is drilled in which the bead of thermocouple is inserted. After placing the thermocouples, the hole is filled with solder wire. The measurement error associated with this technique is distortion of the temperature profile due to a perturbation in heat flux lines around the dissimilar materials created by the thermocouple wires, their insulation, soldering non-uniformities, etc. In spite of the measurement error associated with this technique, we can use this technique with some care, since this technique is simple, cheap and still being used by researchers. The pressure of condensing vapor was measured with the help of a dial type pressure gauge and pressure transducers (4,9). The cooling water flow rate was measured with the help of turbine type flow meters (14,15). 3. Data reduction and error analysis The condensing-side heat transfer coefficient, ho, was determined by taking the ratio of heat flux, q, and the wall sub-cooling temperature, DTf:
ho ¼ q=DT f
ð1Þ
The heat flux, q, was calculated by taking the ratio of heat transfer rate, Q, and the outer surface area of the plain tube, AO:
q ¼ Q=AO
ð2Þ
The heat transfer rate, Q, was determined by calculating the heat carried away by the cooling water from the test-condenser, which is measured by a simple energy balance equation as follows:
Q ¼ mcw Cpcw ðT cwo T cwi Þ
ð3Þ
where mcw , Cpcw, Tcwo, Tcwi are the mass flow rate, specific heat, and temperatures of the cooling water at the outlet and inlet of the tube, respectively. There are also different measurement techniques of film heat transfer coefficient for film condensation on the tubes. Another common technique for determining the heat transfer rate is to
measure the mass flow rate mc and the temperature Tc of the condensate collected from the test-tube, thenafter calculation has been done by the well known equation (4).
q ¼ mc ½hfg þ Cpc ðT s T c Þ
ð4Þ
The third method for determining the heat transfer rate is to measure the power input into the evaporator very accurately and eliminate heat losses by installing the entire apparatus within a constant-temperature enclosure as proposed by White [18]. The expense and operational problems experienced with this technique make its use very unlikely. There are also some indirect methods for determining heat transfer coefficients like Wilson Plot technique which was proposed by Wilson [19] in 1915 and Modified Wilson Plot technique which was proposed by Briggs and Young [20]. An uncertainty analysis of the results was carried out by the method suggested by Kline and McClintock [21]. The uncertainty intervals of measuring instruments used are listed in Table 2. Temperature measuring devices and their required instrumentation are precisely calibrated. Also, the use of thermopile increases the accuracy in temperature measurement. The test tube wall temperature, the temperature of condensing vapor, the wall sub-cooling temperature and the cooling water temperature rise were measured with an accuracy of 0.05, 0.1, 0.11, and 0.1 °C respectively. The cooling water flow rate was measured with an accuracy of 20 kg/h. The uncertainty in the outer surface area was 0.255%. While doing error analysis, it was evident that the
Table 2 Uncertainties in the measured parameters. Measurements
Instruments
Uncertainty
Temperature Pressure
Thermocouple (J-type) Pressure gauge Pressure transducer Water turbine flow meter Steel rule Vernier calipers
0.1 °C 6.87 kPa 0.25% FS (2 MPa) 0.5 kg/h 1.0 mm 0.01 mm
Coolant flow rate Test-tube length Test-tube diameter
maximum uncertainty in the measurement was contributed by two parameters: the cooling water flow rate and the cooling water temperature rise. At high cooling water flow rates, % uncertainty in cooling water flow rate was very less; therefore the error in heat transfer coefficient was controlled only by the error in the measurement of the cooling water temperature rise. Similarly, at low cooling water flow rates, the error in the measurement of flow rate controlled the error in heat transfer coefficient. The maximum uncertainty in the determination of heat transfer coefficient, ho, was estimated to be less than 15% for smooth tube and less than 11% for circular integral fin tubes. 4. Results and discussion In this study, outside condensation HTCs of R-600a were measured at the vapor temperature of 39 °C with wall sub-cooling temperatures of 5–12 °C under heat flux of 11–20 kW/m2 for plain tube and with wall sub-cooling temperature of 3–10 °C under heat flux of 28–82 kW/m2 for five integral fin tubes of different fin-densities (945, 1024, 1102, 1181 and 1260 fpm). Based upon the Data taken in this study, different graphs were plotted varying different parameters to show their dependency on other parameters. Fig. 3 shows the measured heat flux as a function of wall sub-cooling. From the figure, it is clear that heat flux increases as wall sub-cooling temperature increases, which can also be verified by Eq. (1). It is inferred from Fig. 4 that the heat transfer coefficient (HTC) reduces with rise in temperature difference across the condensate (wall sub-cooling), DTf. With increase in DTf, the heat flux increases, resulting in an increased rate of vapor condensation on the tube surface which brings a thicker condensate layer on the tube surface. The condensate layer offers higher thermal resistance decreasing the heat transfer coefficient. In Fig. 5, a graph has been plotted between condensation heat transfer coefficient and heat flux. This graph depicts that HTCs decreases as heat flux increases. As we know from Eq. (1) that q = ho DTf
q aho
if ho and DT f are independent to each other:
but from Nusselt’s equation, Eq. (5),
" ho ¼ C 0
qf ðqf qg Þgk3f hfg lf D0 DT f
#1=4 ð5Þ
It is clear that ho = f (DTf)
ho aD T 1=4 f
ð6Þ
from Eq. (1), q a DT1/4 DTf f
q aD T f3=4
ð7Þ
From Eqs. (6) and (7), it is clear that if DTf increases, heat transfer coefficient decreases but heat flux increases. Reason can also be explained in other words that with increase in DTf, the heat flux increases, resulting in an increased rate of vapor condensation on the tube surface which brings a thicker
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Fig. 3. Variation in heat flux with wall sub-cooling temperature for different tubes.
Fig. 4. Variation in heat transfer coefficient with wall sub-cooling temperature for different tubes.
condensate layer on the tube surface. The condensate layer offers higher thermal resistance decreasing the heat transfer coefficient. This is also verified by other researchers like Kumar et al. [22]. It is clear from Figs. 3–5 that the trend for dependency of one parameter on the other does not alter with variation in fin-density which is also in good agreement with Sajjan et al. [23] where trend does not change with change in vapor pressure.
Also from Figs. 3–5; it is clear that 1102 fpm integral fin tube shows the highest heat transfer characteristics among all tubes whereas 1260 fpm integral fin tube shows the lowest. The possible reason behind this may be explained by the basics of the condensation over integral fin tubes. Higher fin-density of the integral fin tubes enhances heat transfer characteristics by increasing surface area and by promoting surface tension drainage of the condensate
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Fig. 5. Variation in heat transfer coefficient with heat flux for different tubes.
Table 3 Value of a and b in Eq. (8). Tube
a
b
% deviation of the predicted heat flux from the experimental heat flux
Plain 945 fpm 1024 fpm 1102 fpm 1181 fpm 1260 fpm
3.29 14.1 12.84 14.56 12.96 12.97
0.735 0.718 0.797 0.753 0.759 0.698
0.77 to +0.33 2.7 to +6.3 1.9 to +2.4 3.0 to +1.8 3.1 to +2.1 6.8 to +8.3
to reduce the thickness of condensate-film on the sides of the fins. However, on the other hand, higher fin-density of the integral fin tubes decreases heat transfer characteristics with increasing condensate retention on the lower part of the tube by capillary forces, thus reducing the effective area for heat transfer. Hence there should be a balance between these two opposing factors to get an optimum value of fin-density of the integral fin tubes which is determined experimentally, since no single theoretical model well predicts for all cases and conditions. According to Nusselt’s theory [2] for film condensation, heat transfer coefficient, ho, is proportional to DTf0.25 at fixed
Fig. 6. Comparison between experimental heat flux and predicted heat flux.
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saturation temperature and vapor pressure, thus, the equation for the heat flux, q, can be written in the following form:
q ¼ aðDT f Þb
ð8Þ
where a and b are constants. According to Nusselt’s theory, the value of b should be equal to 0.75 but in actual practice, it lies between 0.7 to 0.8 because assumptions made by Nusselt for film condensation are not taking place in actual cases. In our cases, the values of a and b for different tubes are listed in Table 3. Fig. 6 shows the comparison between experimental heat flux and predicted heat flux. The predicted heat flux, qpre, in Fig. 6 is calculated by Eq. (8) putting the values of ‘‘a’’ and ‘‘b’’ from Table 3 according to the fin-density of tube and the value of DTf corresponding to the experimental heat flux. This figure illustrates that
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the values given by Eq. (5) are in the range of 7% to +8% of the experimental values which is considered as a good fit of experimental data. The variation in enhancement factor with wall sub cooling temperature for different integral fin tubes is drawn in Fig. 7. The enhancement factor (EF) is defined as the ratio of the heat transfer coefficient of finned tube to that for a plain tube at the same value of wall sub cooling temperature. Since it is difficult to generate same wall sub cooling temperature for plain and finned tube during experimentation, hence heat transfer coefficient for plain tube is calculated by Nusselt’s equation, Eq. (5) for same wall sub cooling temperature which is generated in finned tube during experimentation. Fig. 8 draws a bar chart for the performance comparison of different integral fin tubes. It is clear from Figs. 7 and 8 that enhancement factors are in the same order in which their heat transfer characteristics are shown in Figs. 3–5. Fig. 9 shows a
Fig. 7. Variation in enhancement factor with wall sub cooling temperature for different fin tubes.
Fig. 8. Performance comparison of different integral fin-tubes.
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Fig. 9. Comparison between experimental results of different fin-tubes and different theoretical models.
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comparison between experimental results of different fin-tubes and different theoretical models. Fig. 9 also shows % deviations of theoretical models from the experimental values for different fin-densities. Although, % deviations are different for different fin-densities, Fig. 9(a)–(e) illustrate the same trend that Rudy– Webb and Webb–Rudy–Kedzierski models overpredict the experimental results whereas Beatty–Katz and Owen et al. models underpredict the experimental values. However, there are two major reasons behind this. The first reason is that the density of R-600a is low, whereas surface tension is high; hence surface tension effects are more dominating than gravitational effects. There are two effects of surface tension: first is the surface tension drainage effect which thins the condensate-film, therefore this is an enhancing factor for heat transfer; the second is surface tension condensate retention effect which reduces the effective surface area, hence this is a depreciating factor for heat transfer. In Beatty– Katz model, only gravitational effects (condensate drainage by gravity) are considered. However, Owen et al. extended Beatty and Kazt model to include the condensate retention-effect which is a depreciating factor for heat transfer. Hence, heat transfer rates given by Owen et al. model are lower than those given by Beatty and Katz model. In Rudy–Webb and Webb–Rudy– Kedzierski models, in addition to gravity-drainage mechanism, surface tension-drainage mechanism (an enhancing factor for heat transfer) and surface tension condensate-retention (a depreciating factor for heat transfer) are also considered. The surface tension-drainage mechanism is more dominating over the surface tension condensate-retention, hence the net result is an enhancement in heat transfer rate. In Rudy–Webb model, heat transfer by the flooded region is neglected whereas in Webb–Rudy–Kedzi erski model, heat transfer by the flooded region is also considered. Hence, heat transfer rates given by Webb–Rudy–Kedzierski model is higher than those given by Rudy–Webb model. The second reason is that Beatty–Katz and Owen et al. models are based upon the Nusselt equation, Eq. (5) for film condensation over horizontal tube in which film flow is assumed to be in laminar flow regime, but in real, even at low Reynold numbers, formation of waves occurs creating turbulence. These waves lead to an improvement in the heat transfer rate. Therefore, Beatty–Katz and Owen et al. models underpredict the experimental values. 5. Conclusions On the basis of the experimental results, following conclusions have been drawn: 1. Heat flux is directly proportional to ‘‘b’’th power of wall subcooling temperature, DTf where b lies between 0.797 to 0.698 depending upon fin density. 2. HTC is inversely proportional to (DTf)n where n lies between 0.302 to 0.203 depending upon fin density. 3. HTC decreases as heat flux increases with a increment in DTf. 4. 1102 fpm integral fin tube shows the highest heat transfer characteristics among all tubes with EF = 5.1 whereas 1260 fpm integral fin tube shows the lowest with EF = 4.1. 5. Rudy–Webb and Webb–Rudy–Keidersky models overpredict the experimental results whereas Beatty–Katz and Owen et al. models underpredict the experimental values.
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Conflict of interest None declared. Acknowledgement Authors are thankful to Department of Science and Technology, New Delhi, India for funding our work (Grant No. DST-559-MID). References [1] K.O. Beatty, D.L. Katz, Condensation of vapors on outside of finned tubes, Chem. Eng. Progr. 44 (1) (1948) 55–70. [2] W. Nusselt, Die Oberflaohen-Kondensation des Wasser-dampfes, VDI Zeitung 60 (1916) 541–546. 569–575. [3] R. Gregorig, Film condensation on finely rippled surfaces with consideration of surface tension, Z. Angew. Math. Phys. 5 (1954) 36–49. [4] V.A. Karkhu, V.P. Borovkov, Film condensation of vapor at finely-finned horizontal tubes, Heat Transfer–Soviet Res. 3 (2) (1971) 183–191. [5] V.G. Rifert, P.A. Barabash, Y.F. Vizel, Y.Y. Trokoz, Effect of surface tension on the hydrodynamics and heat transfer in condensation of vapor on finned or corrugated surfaces, Heat Transfer–Soviet Res. 17 (1) (1985) 18–27. [6] T.C. Carnavos, An experimental study: condensing R-11 on augmented tubes, ASME Pap. 80 (54) (1980) 54–60. [7] T.M. Rudy, R.L. Webb, An analytical model to predict condensate retention on horizontal, integral-fin tubes, in: Y. Mori, W.-J. Yang (Eds.), Proc. of ASME-JSME Thermal Engineering Conference, vol. 1, 1983, pp. 373–378. [8] R.G. Owen, R.G. Sardesai, R.A. Smith, W.C. Lee, Gravity controlled condensation on low integral-fin tubes, Proc. Symp. Condens.: Theory Practice, I. Chem. E Symp. Ser. 75 (1983) 415–428. [9] R.L. Webb, T.M. Rudy, M.A. Kedzierski, Prediction of the condensation coefficient on horizontal integral-fin tubes, ASME J. Heat Transfer 107 (1985) 369–376. [10] A.S. Wanniarachchi, P.J. Marto, J.W. Rose, Film condensation of steam on horizontal finned tubes: effect of fin spacing, J. Heat Transfer 108 (1986) 960– 966. [11] H. Honda, S. Nozu, A prediction method for heat transfer during film condensation on horizontal low integral-fin tubes, ASME J. HEAT TRANSFER 109 (1987) 218–225. [12] P.J. Marto, D. Zebrowski, A.S. Wanniarachchi, J.W. Rose (Film condensation of R-113 on horizontal finned tubes), in: H.R. Jacobs (Ed.), Fundamentals of Phase Change: Boiling and Condensation, Proc. 1988 National Heat Transfer Conf., 2, ASME, 1988, pp. 583–592. [13] H. Masuda, J.W. Rose (An experimental study of condensation of refrigerant 113 on low integral-fin tubes), in: Heat Transfer Science and Technology, Hemisphere Publishing Corp., Washington, DC, 1987, pp. 480–487 (Proc. Int. Symp. on Heat Transfer, Beijing, China, vol. 2, Paper No. 32). [14] T. Adamek, R.L. Webb, A prediction of film condensation on horizontal low integral fin tubes, Int. J. Heat Mass Transfer 33 (1990) 1721–1735. [15] A. Briggs, J.W. Rose, Effect of fin efficiency on a model for condensation heat transfer on a horizontal, integral-fin tube, Int. J. Heat Mass Transfer 37 (1994) 457–463. [16] K.J. Park, D. Jung, Optimum fin density of low fin tubes for the condensers of building chillers with HCFC123, Energy Convers. Manage. 49 (2008) 2090– 2094. [17] A.R. Al-Badri, T. Gebauer, A. Leipertz, A.P. Froba, Element by element prediction model of condensation heat transfer on a horizontal integral finned tube, Int. J. Heat Mass Transfer 62 (2013) 463–472. [18] R.E. White, Condensation of refrigerant vapours apparatus and film coefficient for freon-12, Trans. ASME 70 (1948) 689–693. [19] E.E. Wilson, A basis for rotational design of heat transfer apparatus, Trans. ASME 37 (1915) 47–82. [20] D.E. Briggs, E.H. Young, Modified Wilson Plot techniques for obtaining heat transfer correlations for shell and tube heat exchangers, Chem. Eng. Progr. Symp. Ser. 65 (92) (1969) 35–45. [21] S.J. Kline, F.A. McClintock, Describing uncertainties in singlesample experiments, Mech. Eng. 75 (1953) 3–9. [22] R. Kumar, A. Gupta, S. Vishvakarma, Condensation of R-134a vapour over single horizontal integral-fin tubes: effect of fin height, Int. J. Refrig. 28 (2005) 428–435. [23] S.K. Sajjan, R. Kumar, A. Gupta, Experimental investigation of vapor condensation of iso-butane over single horizontal plain tube under different vapor pressures, Appl. Therm. Eng. 76 (2014) 435–440.
Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Experimental investigation during condensation of R-600a vapor over single horizontal integral-fin tubes Sanjeev K. Sajjan ⇑, Ravi Kumar, Akhilesh Gupta Department of Mechanical and Industrial Engineering, Indian Institute of Technology Roorkee, 247667 Uttarakhand, India
a r t i c l e
i n f o
Article history: Received 7 February 2015 Received in revised form 18 April 2015 Accepted 24 April 2015 Available online 14 May 2015 Keywords: Vapor condensation Iso-butane Integral fin tube External heat transfer coefficient
a b s t r a c t In this study, condensation heat transfer coefficients (HTCs) of refrigerant R-600a (iso-butane) over a horizontal smooth tube of outer diameter 19 mm and five integral fin tubes of different fin-densities (945, 1024, 1102, 1181, and 1260 fpm) were determined at vapor temperature of 39 ± 0.5 °C with different wall sub-cooling temperatures in a range of 3–12 °C. Like other refrigerants, condensation heat transfer coefficients of R-600a showed the same trend with wall sub-cooling where condensation HTCs decrease with the rise in wall sub cooling temperatures. The heat flux was 11–20 kW/m2 for the plain tube and 28–82 kW/m2 for integral fin tubes. Based upon the data taken in this study, different graphs were plotted varying different parameters to show their dependency on other parameters. The experimental data were also validated by comparing them against different models. Ó 2015 Elsevier Ltd. All rights reserved.
1. Introduction Many experimental and theoretical investigations have analyzed the effects of fin geometry, tube material and condensing fluid properties for the condensation heat transfer on integral finned tubes. Also significant improvements over plain tubes have been made in order to increase surface area and reduce the thickness of the condensate film by surface-tension-induced pressure gradients. The integral finned tube enhances heat transfer by increasing surface area as well as surface tension controlled condensation drainage on the sides of the fins. Integral fin tubes enhance the heat transfer by reducing the film thickness much more than the simple increase in surface area. The concept of integral fin-tubes for the enhancement of heat transfer rate was developed in the late 1940’s. The first idea, to introduce integral fin-tubes, was to increase the heat transfer area, but later on, many models like gravity drainage mechanism, surface tension drainage mechanism, and condensate retention model due to surface tension came into existence. The first effort to predict the heat transfer rate for outside condensation of a horizontal integral fin-tube was carried out by Beatty and Katz [1]. Their model was based upon Nusselt [2] equations for film condensation over a vertical wall and a horizontal tube. They assumed that the condensate is not retained in between the fins and the surface force can be neglected ⇑ Corresponding author. E-mail addresses: [email protected] (S.K. Sajjan), ravikfme@iitr. ernet.in (R. Kumar), [email protected] (A. Gupta). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2015.04.079 0017-9310/Ó 2015 Elsevier Ltd. All rights reserved.
with only the gravitational force considered for draining out the condensate. The effect of surface tension over condensation heat transfer coefficient for vertical fluted tubes was first analyzed by Gregorig [3]. He showed that surface tension forces played an important role in enhancing the heat transfer coefficient by thinning the condensate film at the tips of the flutes. Thereafter Karkhu and Borovkov [4] first implemented the concept of surface tension for the condensation of the pure vapors over the horizontal integral fin-tubes. Their model assumes that the flooded zone is constant and independent of fin geometry and fluid properties. Rifert et al. [5] modified Karkhu and Brokovkov [4] model to account the effect of tube geometry and fluid properties on the condensate retention. Canvas [6] conducted experiments using CFC11 as the working fluid for different fin densities of low integral fin tubes and determined the optimum fin density for the condensation of CFC11 over fin tubes. Rudy and Webb [7] distributed the whole fin surface and interfin spacing into two regions: unflooded and flooded. They assumed that heat transfer occurred only by the unflooded region and neglected the heat transfer by the flooded region. Owen et al. [8] included the unflooded and the flooded region both into their analysis and improved Beatty and Katz model which explicitly accounted for the unflooded region as well as the flooded region. Webb, Rudy and Kedzierski [9] proposed surface tension drainage mechanism on the fin surface and gravity drainage mechanism in the interfin spacing. Wanniarachchi et al. [10] measured HTCs of outside condensation of steam over 24 finned tubes of different geometry and obtained best fin spacing between 1.5–2.0 mm.
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Nomenclature A Cp fpm h hfg ho m Pf Q q R t T DTf
surface area (m2) specific heat (kJ kg1 K) fins per meter fin-height (m) latent heat of vaporization (kJ/kg) condensing-side heat transfer coefficient (kW/m2–°C) mass flow rate (kg s1) pitch of the fin (m) heat transfer rate (kW) heat flux (kW/m2) distance from tube center line (m) thickness of fin (m) temperature (K or °C) difference of temperature between refrigerant vapor and tube wall (K or °C) (wall sub-cooling temperature)
r
surface tension (N/m)
Subscripts b bottom of fin c condensate cw cooling water exp experimental values f saturated liquid phase g saturated vapor phase i inlet o outet or outside or top of fin r root of fin s saturated vapor t tip of fin w wall of tube or surface of tube
Greek letters q density (kg/m3) l viscosity (l Pa s)
An important factor which has been ignored in the above theoretical models was the nonuniformity of wall temperature. Previous all models assumed uniform circumferential temperature distribution of the tube surface, but in fact, there developed a considerable temperature gradient along the circumference of the tube due to a variable thickness of the condensate-film over the tube. This would cause the deviation in heat transfer coefficients from that predicted by the uniform wall temperature model. Honda and Nozu [11] included the effect of variable wall temperature in their analysis and presented a method for predicting the average heat transfer coefficient for film condensation on horizontal low integral-fin tubes which was applicable to a wide range of conditions. Their model predicted most of the available experimental data, including 11 fluids and 22 tubes within ± 20 percent. Marto et al. [12] conducted experiments using R-113 as a working fluid for 1 smooth tube ad 24 specially machined rectangular-fin tubes with various fin spacings, thicknesses, and heights and found that fin spacing between 0.2–0.5 mm showed better heat transfer rate, also heat transfer performance increased with thinner and taller fins. Masuda and Rose [13] found a 1.0 mm as optimum fin spacing for ethylene glycol and for this tube, enhancement ratio was 4.7. Adamek and Webb [14] presented an analytical model for prediction of film condensation on horizontal integral fin tubes. Their model predicted condensation on all surfaces in the flooded and unflooded regions and included the effect of fin efficiency. Briggs and Rose [15] derived a semi-empirical model for condensation on horizontal, integral fin-tubes to account for fin efficiency effects. Park and Jung [16] found that for condensation of HCFC123, HTCs increased up to the fin density of 1102 fpm but decreased sharply beyond that density. Al-Badri et al. [17] developed element by element prediction model of condensation heat transfer on a horizontal integral finned tube. This model showed good agreement with the experimental data with a mean deviation of 4.7 percent. The data include condensation heat transfer characteristics of R-600a over smooth and five different finned tubes with different fin densities varying different parameters. All finned tubes are of standard dimensions and can be used commercially due to easy and low cost fabrication. These tubes cover a significant range of fin density varying from 945 fpm to 1260 fpm and the optimized value of fin density giving highest heat transfer rate lies in this range. No researcher has performed experiments for this range of
fin density for the refrigerant R-600a. R-600a can be better alternative for CFCs and HCFCs because R-600a is eco-friendly (since its ODP is zero and GWP is low) having good thermodynamic properties. However the data cover a significant range of fin geometries, these can also be applied for other geometries within the permissible range of acceptance. Also the data may be useful to industrial application. 2. Experimental set-up and procedure The experimental set-up fabricated for this study is illustrated in Fig. 1, a schematic diagram of the set-up, which comprised of major components like condenser, evaporator and data collection unit. The test condenser (5) is a stainless steel-304 cylinder of thickness 3 mm, inside diameter 100 mm and length 414 mm. The dead end pipe (6) of 350 mm length and 6.5 mm diameter has equally spaced 125 holes, each of 1 mm diameter, in a straight line. The test-section (3) of length 400 mm is fixed inside the test-condenser with the help of chuck nut assembly. The details of the geometry of test-sections are shown in Fig. 2 and listed in Table 1. The viewing window (17) is provided in the middle of the test-condenser fitted with the Teflon glass to observe condensation. The evaporator (10) is a stainless steel-304 cylinder of thickness 3 mm, inside diameter 140 mm and length 670 mm. Three immersion heaters (12) each of 3 kW heating capacity are fixed in the bottom of the evaporator to transfer heat directly to the liquid refrigerant. The cylinder is closed by a flange (13), sealed with a 12 mm diameter hardened rubber O-ring and 8 holes of 10 mm hole diameter. The auxiliary condenser (2) is a stainless steel-304 cylinder of thickness 3 mm, inside diameter 120 mm and length 140 mm fixed approximately 45 cm above the test-condenser. On the top of the auxiliary condenser a purge valve (1) is fixed to remove air from the system. To ensure leak proof experimental set-up, a pneumatic gauge pressure of 2.0 MPa was maintained inside the set-up for 24 hours, followed by a vacuum of 60 cm of Hg for same duration. No pressure drop inside the set-up ensured that the set-up was leak proof. Assuring the leak proof of the set-up, the refrigerant was charged in the set-up under vacuum. While charging the refrigerant, the required purging was done via purging pipe (1) to escape air and other non condensable gases from the set-up. After charging, the cooling water was circulated inside the test-condenser and the
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Fig. 1. Schematic diagram of the experimental set-up. 1 – purging pipe 2 – auxiliary condenser 3 – test-section 4,9 – pressure gauge & pressure transducer 5 – test-condenser 6 – perforated pipe 7 – thermocouple exit port 8,11 – centrifugal pump 10 – evaporator 12 – heaters 13 – flange 14,15 – turbine flow meters 16 – U-bend tube.
Fig. 2. Details of geometry of test-section.
Table 1 Details of test-section. Fin density (fpm)
Ro (mm)
Rr (mm)
Pf (mm)
h (mm)
tt (mm)
tb (mm)
925 1024 1102 1181 1260
9.56 9.47 9.54 9.49 9.56
8.68 8.75 8.80 8.85 8.89
1.06 0.98 0.91 0.85 0.79
0.88 0.72 0.74 0.64 0.67
0.24 0.22 0.20 0.19 0.18
0.82 0.76 0.71 0.66 0.61
auxiliary condenser by centrifugal pumps (8) and (11) respectively. A U-bend tube (16) was fixed at the end of exit of water supply passing through test-condenser to ensure water in water-line of the test-condenser when the set-up is not operative. The refrigerant in the evaporator was heated with the electric immersion heaters (12). The vapor of refrigerant thus generated rushed to the test-condenser (5) and passing through the perforated pipe (6), it was subsequently condensed by coming in contact with the cold surface of test-section (3). The condensate was drained to the evaporator and thus the refrigerant flow cycle was completed. The rate of vapor generation was controlled by a variac. The cooling water flow rate through the test condenser was changed in such manner so that the wall sub cooling temperature (difference between refrigerant vapor temperature and tube wall temperature, DTf) would approximately vary from 3 °C to 12 °C in the interval of 0.5 °C. The pressure of condensing vapor was maintained constant throughout the investigation by regulating the energy supply to immersion heaters in the evaporator and cooling water flow rate in the auxiliary condenser and at that pressure, the temperature
of the condensing vapor remained close to the vapor saturation temperature of R-600a, hence saturated vapor of R-600a entered the tested condenser. For each test run, data were collected only when the set-up attained a steady state condition. The steady state condition occurred when the rate of vapor generation became equal to the condensation rate, consequently the pressure inside the set-up became stable and so, the temperature of condensing vapor. For each test run, the temperature of condensing vapor, the surface temperature of the test-section, the temperature of cooling water at the inlet and outlet of the test-section and the cooling water flow rates were recorded. Purging was done after every 4–5 hours of operation to escape air and non-condensable gases from the set-up. The primary function of the auxiliary condenser is to keep the test-condenser free from air and non condensable gases. Temperature measurement includes the measurement of the condensing vapor temperature, surface temperatures of the test section and the temperature rise of the cooling water. Measurement of the surface temperature of the test-section is the most sensitive job due to fluctuations in the tube wall temperature. The tube wall temperature fluctuates because of the periodic wrapping of the tube’s surface of the condensate layer, followed by the condensate drainage from the bottom of the test section in the form of drops under gravity. Hence, the thickness of the condensate layer varies with time, resulting in a variable condensate film thermal resistance. Thus, the outcome is variable tube wall temperature. J-type thermocouples of 20 gauge thickness and an 8 channel data acquisition module (ADAM-4019) are used for temperature measurement. To measure average outside tube wall temperature was the most difficult measurement. During film condensation on a horizontal condenser tube, the wall temperature varies both axially and circumferentially. The wall temperature will depend upon the local vapor-to-coolant temperature difference and local condensate film thickness. Since the coolant bulk temperature varies along the length of the tube, the wall temperature will naturally change from the coolant inlet to outlet. Although this change is not linear with axial position, the measurement of wall temperature is made at the midpoint of the test-tube to represent an appropriate average. The wall temperature also varies circumferentially. The installation of numerous thermocouple leads more time consumption, more cost and more measurement errors. Therefore, four thermocouples are fixed at top,
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bottom and two sides of the test-section. At each predetermined position, a hole of 0.5 mm depth is drilled in which the bead of thermocouple is inserted. After placing the thermocouples, the hole is filled with solder wire. The measurement error associated with this technique is distortion of the temperature profile due to a perturbation in heat flux lines around the dissimilar materials created by the thermocouple wires, their insulation, soldering non-uniformities, etc. In spite of the measurement error associated with this technique, we can use this technique with some care, since this technique is simple, cheap and still being used by researchers. The pressure of condensing vapor was measured with the help of a dial type pressure gauge and pressure transducers (4,9). The cooling water flow rate was measured with the help of turbine type flow meters (14,15). 3. Data reduction and error analysis The condensing-side heat transfer coefficient, ho, was determined by taking the ratio of heat flux, q, and the wall sub-cooling temperature, DTf:
ho ¼ q=DT f
ð1Þ
The heat flux, q, was calculated by taking the ratio of heat transfer rate, Q, and the outer surface area of the plain tube, AO:
q ¼ Q=AO
ð2Þ
The heat transfer rate, Q, was determined by calculating the heat carried away by the cooling water from the test-condenser, which is measured by a simple energy balance equation as follows:
Q ¼ mcw Cpcw ðT cwo T cwi Þ
ð3Þ
where mcw , Cpcw, Tcwo, Tcwi are the mass flow rate, specific heat, and temperatures of the cooling water at the outlet and inlet of the tube, respectively. There are also different measurement techniques of film heat transfer coefficient for film condensation on the tubes. Another common technique for determining the heat transfer rate is to
measure the mass flow rate mc and the temperature Tc of the condensate collected from the test-tube, thenafter calculation has been done by the well known equation (4).
q ¼ mc ½hfg þ Cpc ðT s T c Þ
ð4Þ
The third method for determining the heat transfer rate is to measure the power input into the evaporator very accurately and eliminate heat losses by installing the entire apparatus within a constant-temperature enclosure as proposed by White [18]. The expense and operational problems experienced with this technique make its use very unlikely. There are also some indirect methods for determining heat transfer coefficients like Wilson Plot technique which was proposed by Wilson [19] in 1915 and Modified Wilson Plot technique which was proposed by Briggs and Young [20]. An uncertainty analysis of the results was carried out by the method suggested by Kline and McClintock [21]. The uncertainty intervals of measuring instruments used are listed in Table 2. Temperature measuring devices and their required instrumentation are precisely calibrated. Also, the use of thermopile increases the accuracy in temperature measurement. The test tube wall temperature, the temperature of condensing vapor, the wall sub-cooling temperature and the cooling water temperature rise were measured with an accuracy of 0.05, 0.1, 0.11, and 0.1 °C respectively. The cooling water flow rate was measured with an accuracy of 20 kg/h. The uncertainty in the outer surface area was 0.255%. While doing error analysis, it was evident that the
Table 2 Uncertainties in the measured parameters. Measurements
Instruments
Uncertainty
Temperature Pressure
Thermocouple (J-type) Pressure gauge Pressure transducer Water turbine flow meter Steel rule Vernier calipers
0.1 °C 6.87 kPa 0.25% FS (2 MPa) 0.5 kg/h 1.0 mm 0.01 mm
Coolant flow rate Test-tube length Test-tube diameter
maximum uncertainty in the measurement was contributed by two parameters: the cooling water flow rate and the cooling water temperature rise. At high cooling water flow rates, % uncertainty in cooling water flow rate was very less; therefore the error in heat transfer coefficient was controlled only by the error in the measurement of the cooling water temperature rise. Similarly, at low cooling water flow rates, the error in the measurement of flow rate controlled the error in heat transfer coefficient. The maximum uncertainty in the determination of heat transfer coefficient, ho, was estimated to be less than 15% for smooth tube and less than 11% for circular integral fin tubes. 4. Results and discussion In this study, outside condensation HTCs of R-600a were measured at the vapor temperature of 39 °C with wall sub-cooling temperatures of 5–12 °C under heat flux of 11–20 kW/m2 for plain tube and with wall sub-cooling temperature of 3–10 °C under heat flux of 28–82 kW/m2 for five integral fin tubes of different fin-densities (945, 1024, 1102, 1181 and 1260 fpm). Based upon the Data taken in this study, different graphs were plotted varying different parameters to show their dependency on other parameters. Fig. 3 shows the measured heat flux as a function of wall sub-cooling. From the figure, it is clear that heat flux increases as wall sub-cooling temperature increases, which can also be verified by Eq. (1). It is inferred from Fig. 4 that the heat transfer coefficient (HTC) reduces with rise in temperature difference across the condensate (wall sub-cooling), DTf. With increase in DTf, the heat flux increases, resulting in an increased rate of vapor condensation on the tube surface which brings a thicker condensate layer on the tube surface. The condensate layer offers higher thermal resistance decreasing the heat transfer coefficient. In Fig. 5, a graph has been plotted between condensation heat transfer coefficient and heat flux. This graph depicts that HTCs decreases as heat flux increases. As we know from Eq. (1) that q = ho DTf
q aho
if ho and DT f are independent to each other:
but from Nusselt’s equation, Eq. (5),
" ho ¼ C 0
qf ðqf qg Þgk3f hfg lf D0 DT f
#1=4 ð5Þ
It is clear that ho = f (DTf)
ho aD T 1=4 f
ð6Þ
from Eq. (1), q a DT1/4 DTf f
q aD T f3=4
ð7Þ
From Eqs. (6) and (7), it is clear that if DTf increases, heat transfer coefficient decreases but heat flux increases. Reason can also be explained in other words that with increase in DTf, the heat flux increases, resulting in an increased rate of vapor condensation on the tube surface which brings a thicker
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Fig. 3. Variation in heat flux with wall sub-cooling temperature for different tubes.
Fig. 4. Variation in heat transfer coefficient with wall sub-cooling temperature for different tubes.
condensate layer on the tube surface. The condensate layer offers higher thermal resistance decreasing the heat transfer coefficient. This is also verified by other researchers like Kumar et al. [22]. It is clear from Figs. 3–5 that the trend for dependency of one parameter on the other does not alter with variation in fin-density which is also in good agreement with Sajjan et al. [23] where trend does not change with change in vapor pressure.
Also from Figs. 3–5; it is clear that 1102 fpm integral fin tube shows the highest heat transfer characteristics among all tubes whereas 1260 fpm integral fin tube shows the lowest. The possible reason behind this may be explained by the basics of the condensation over integral fin tubes. Higher fin-density of the integral fin tubes enhances heat transfer characteristics by increasing surface area and by promoting surface tension drainage of the condensate
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Fig. 5. Variation in heat transfer coefficient with heat flux for different tubes.
Table 3 Value of a and b in Eq. (8). Tube
a
b
% deviation of the predicted heat flux from the experimental heat flux
Plain 945 fpm 1024 fpm 1102 fpm 1181 fpm 1260 fpm
3.29 14.1 12.84 14.56 12.96 12.97
0.735 0.718 0.797 0.753 0.759 0.698
0.77 to +0.33 2.7 to +6.3 1.9 to +2.4 3.0 to +1.8 3.1 to +2.1 6.8 to +8.3
to reduce the thickness of condensate-film on the sides of the fins. However, on the other hand, higher fin-density of the integral fin tubes decreases heat transfer characteristics with increasing condensate retention on the lower part of the tube by capillary forces, thus reducing the effective area for heat transfer. Hence there should be a balance between these two opposing factors to get an optimum value of fin-density of the integral fin tubes which is determined experimentally, since no single theoretical model well predicts for all cases and conditions. According to Nusselt’s theory [2] for film condensation, heat transfer coefficient, ho, is proportional to DTf0.25 at fixed
Fig. 6. Comparison between experimental heat flux and predicted heat flux.
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saturation temperature and vapor pressure, thus, the equation for the heat flux, q, can be written in the following form:
q ¼ aðDT f Þb
ð8Þ
where a and b are constants. According to Nusselt’s theory, the value of b should be equal to 0.75 but in actual practice, it lies between 0.7 to 0.8 because assumptions made by Nusselt for film condensation are not taking place in actual cases. In our cases, the values of a and b for different tubes are listed in Table 3. Fig. 6 shows the comparison between experimental heat flux and predicted heat flux. The predicted heat flux, qpre, in Fig. 6 is calculated by Eq. (8) putting the values of ‘‘a’’ and ‘‘b’’ from Table 3 according to the fin-density of tube and the value of DTf corresponding to the experimental heat flux. This figure illustrates that
253
the values given by Eq. (5) are in the range of 7% to +8% of the experimental values which is considered as a good fit of experimental data. The variation in enhancement factor with wall sub cooling temperature for different integral fin tubes is drawn in Fig. 7. The enhancement factor (EF) is defined as the ratio of the heat transfer coefficient of finned tube to that for a plain tube at the same value of wall sub cooling temperature. Since it is difficult to generate same wall sub cooling temperature for plain and finned tube during experimentation, hence heat transfer coefficient for plain tube is calculated by Nusselt’s equation, Eq. (5) for same wall sub cooling temperature which is generated in finned tube during experimentation. Fig. 8 draws a bar chart for the performance comparison of different integral fin tubes. It is clear from Figs. 7 and 8 that enhancement factors are in the same order in which their heat transfer characteristics are shown in Figs. 3–5. Fig. 9 shows a
Fig. 7. Variation in enhancement factor with wall sub cooling temperature for different fin tubes.
Fig. 8. Performance comparison of different integral fin-tubes.
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Fig. 9. Comparison between experimental results of different fin-tubes and different theoretical models.
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comparison between experimental results of different fin-tubes and different theoretical models. Fig. 9 also shows % deviations of theoretical models from the experimental values for different fin-densities. Although, % deviations are different for different fin-densities, Fig. 9(a)–(e) illustrate the same trend that Rudy– Webb and Webb–Rudy–Kedzierski models overpredict the experimental results whereas Beatty–Katz and Owen et al. models underpredict the experimental values. However, there are two major reasons behind this. The first reason is that the density of R-600a is low, whereas surface tension is high; hence surface tension effects are more dominating than gravitational effects. There are two effects of surface tension: first is the surface tension drainage effect which thins the condensate-film, therefore this is an enhancing factor for heat transfer; the second is surface tension condensate retention effect which reduces the effective surface area, hence this is a depreciating factor for heat transfer. In Beatty– Katz model, only gravitational effects (condensate drainage by gravity) are considered. However, Owen et al. extended Beatty and Kazt model to include the condensate retention-effect which is a depreciating factor for heat transfer. Hence, heat transfer rates given by Owen et al. model are lower than those given by Beatty and Katz model. In Rudy–Webb and Webb–Rudy– Kedzierski models, in addition to gravity-drainage mechanism, surface tension-drainage mechanism (an enhancing factor for heat transfer) and surface tension condensate-retention (a depreciating factor for heat transfer) are also considered. The surface tension-drainage mechanism is more dominating over the surface tension condensate-retention, hence the net result is an enhancement in heat transfer rate. In Rudy–Webb model, heat transfer by the flooded region is neglected whereas in Webb–Rudy–Kedzi erski model, heat transfer by the flooded region is also considered. Hence, heat transfer rates given by Webb–Rudy–Kedzierski model is higher than those given by Rudy–Webb model. The second reason is that Beatty–Katz and Owen et al. models are based upon the Nusselt equation, Eq. (5) for film condensation over horizontal tube in which film flow is assumed to be in laminar flow regime, but in real, even at low Reynold numbers, formation of waves occurs creating turbulence. These waves lead to an improvement in the heat transfer rate. Therefore, Beatty–Katz and Owen et al. models underpredict the experimental values. 5. Conclusions On the basis of the experimental results, following conclusions have been drawn: 1. Heat flux is directly proportional to ‘‘b’’th power of wall subcooling temperature, DTf where b lies between 0.797 to 0.698 depending upon fin density. 2. HTC is inversely proportional to (DTf)n where n lies between 0.302 to 0.203 depending upon fin density. 3. HTC decreases as heat flux increases with a increment in DTf. 4. 1102 fpm integral fin tube shows the highest heat transfer characteristics among all tubes with EF = 5.1 whereas 1260 fpm integral fin tube shows the lowest with EF = 4.1. 5. Rudy–Webb and Webb–Rudy–Keidersky models overpredict the experimental results whereas Beatty–Katz and Owen et al. models underpredict the experimental values.
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