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ORIGINAL Heat transfer characteristics of a new helically coiled crimped spiral fi nned tube heat exchanger Kwanchanok Srisawad Somchai Wongwises Received: 26 March 2007/Accepted: 27 August 2008/Published online: 27 September 2008 ? Springer-Verlag 2008 AbstractIn the present study, the heat transfer charac- teristics in dry surface conditions of a new type of heat exchanger, namely a helically coiled fi nned tube heat exchanger, is experimentally investigated. The test section, which is a helically coiled fi ned tube heat exchanger, consists of a shell and a helical coil unit. The helical coil unit consists of four concentric helically coiled tubes of different diameters. Each tube is constructed by bending straight copper tube into a helical coil. Aluminium crimped spiral fi ns with thickness of 0.5 mm and outer diameter of 28.25 mm are placed around the tube. The edge of fi n at the inner diameter is corrugated. Ambient air is used as a working fl uid in the shell side while hot water is used for the tube-side. The test runs are done at air mass fl ow rates ranging between 0.04 and 0.13 kg/s. The water mass fl ow rates are between 0.2 and 0.4 kg/s. The water temperatures are between 40 and 50?C. The effects of the inlet condi- tions of both working fl uids fl owing through the heat exchanger on the heat transfer coeffi cients are discussed. The air-side heat transfer coeffi cient presented in term of the Colburn J factor is proportional to inlet-water temper- ature and water mass fl ow rate. The heat exchanger effectiveness tends to increase with increasing water mass fl ow rate and also slightly increases with increasing inlet water temperature. List of symbols Aarea (m2) Cp specifi c heat kJ/(kg K) dtube diameter (m) Ddiameter of the curvature (m) Dcdiameter of the coil (m) ffriction factor Fcorrection factor G mass fl ux kg/(m2s) h heat transfer coeffi cient W/(m2K) ienthalpy (kJ/kg) Io modifi ed Bessel function solution of the fi rst kind, order 0 I1 modifi ed Bessel function solution of the fi rst kind, order 1 jColburn j factor Ko modifi ed Bessel function solution of the second kind, order 0 K1 modifi ed Bessel function solution of the second kind, order 1 kthermal conductivity W/(m K) Ltube length (m) m mass fl ow rate (kg/s) NuNusselt number Ppitch of the helical coil (m) PrPrandtl number Qheat transfer rate (W) rtube radius (m) ReReynolds number Ttemperature (?C) U overall heat transfer coeffi cient W/(m2K) Vaverage velocity (m/s) dthickness (m) g fi n effectiveness gooverall surface effectiveness K. Srisawad ? S. Wongwises ( |Qw- Qa|/Qaveis less than 0.05, are used in the analysis. The total heat transfer rate, Qave, is averaged from the air-side heat transfer rate, Qa, and the water-side heat transfer rate, Qw. Experiments were con- ducted with various fl ow rates of air and hot water entering the test section. The hot water fl ow rate was increased in small increments while the air fl ow rate, inlet hot water temperatures were kept constant. The hot water tempera- ture was adjusted to achieve the desired level by using electric heaters controlled by temperature controllers. Before any data were recorded, the system was allowed to approach the steady state. The range of experimental conditions in this study and uncertainty of the measurement are given in Tables 2 and 3, respectively. 3 Data reduction In order to determine the heat transfer characteristic of the heat exchangers from the data recorded at steady state conditions during each test run, the Correction factor- Logarithmic-meantemperaturedifferencemethodis applied to determine the UA product. The air-side heat transfer rate can be given as 8.6 mm 9.4 mm 28.25 mm Section A-A 0.5 mm 2 mm AA Fig. 4 Schematic diagram of crimped spiral fi n Table 3 Uncertainty of measurement InstrumentsAccuracy (%)Uncertainty Orifi ce meter (air velocity, m/s)2.00.23 Rotameter (water mass fl ow rate, kg/s)0.20.003 Thermocouple T-type,0.10.03 Data Logger (K)0.04 Humidity transmitter (%RH)0.50.22 Table 1 Dimensions of the helically coiled fi nnedtube heat exchanger ParametersDimensions Outer diameter of tube (mm)9.4 Inner diameter of tube (mm)8.6 Diameter of spiral coil 1 (mm)115.0 Diameter of spiral coil 2 (mm)205.0 Diameter of spiral coil 3 (mm)285.0 Diameter of spiral coil 4 (mm)365.0 Helical coil pitch (mm)16.38 Diameter of shell (mm)430 Number of coil turns7 Number of helical coils4 Distance between each coil (mm)42 Length of shell (mm)355 Diameter of hole at air inlet (mm)298 Number of fi ns per metre500 Fin height (mm)18.64 Fin outside diameter (mm)28.25 Fin pitch (mm)2 Fin thickness (mm)0.5 Table 2 Experimental conditions VariablesRange Inlet-air temperatureAmbient Inlet-water temperature (K)313323 (4050?C) Air mass fl ow rate (kg/s)0.040.13 Water mass fl ow rate (kg/s)0.200.40 Heat Mass Transfer (2009) 45:381391385 123 Qa maia;out? ia;in ? 1 where ma is the air mass fl ow rate, ia,inis the enthalpy of the inlet air and ia,outis the enthalpy of the outlet air. The water-side heat transfer rate can be given as Qw mwCp;wTw;in? Tw;out ? 2 where mw is the mass fl ow rate of water, Cp,w is the specifi c heat of water, Tw,inand Tw,outare the inlet and outlet-water temperature, respectively. The total rate of heat transfer used in the calculation is averaged from the air-side and the water-side as follows Qave Qa Qw 2 3 The air-side heat transfer coeffi cient, ho, of the heat exchanger is determined from the overall heat transfer resistance relationship 1 UA 1 gohoAo lnro=ri 2pktLt 1 hiAi 4 where the overall heat transfer coeffi cient can be then determined from UA Qave FDTLM 5 where the logarithmic-mean temperature difference, DTLM, is determined from DTLM Tw;in? Ta;out ? ? Tw;out? Ta;in ? lnTw;in? Ta;out ? Tw;out? Ta;in ?6 and F is the correction factor. The tube-side heat transfer coeffi cient, hi, is evaluated from the Nusselt number obtained from the Gnielinski semi-empirical correlation 16. Nu hid kw fi=8RePr 1 12:7 ffi ffi ffi ffi ffi ffi ffiffi fi=8 p Pr2=3? 1 Pr Prwall ?0:14 7 The Prandtl number, Pr, is evaluated at the mean fl uid temperature and Prwallis evaluated at the wall temperature. The factor Pr Prwall ?0:14 was introduced into the original equation by Schmidt 17 to take into account the temperature dependence of the physical properties. The friction factor for turbulent fl ow in helically coiled tubes, fi, is given by Mishra and Gupta 18 as fi 0:3164 Re0:25 0:03 d D ? ?0:5 “# lwall l ?0:27 8 where the diameter of the curvature, D, is related to the coil diameter Dcand the pitch, P, of the helical coil by D Dc1 P pDc ?2 “# 9 The dynamic viscosity, l, is of water estimated at the mean water temperature and the dynamic viscosity, lwallis of water evaluated at the wall temperature.The Reynolds number is calculated from Re Rew qwVwd=lw where qwis the density of water, lwis the dynamic vis- cosity of water, d is the inner diameter of the helical coil (8.6 mm) and Vwis the average velocity of water in the helical coil. The overall surface effectiveness, go , which is defi ned as the ratio of the effective heat transfer area to the total heat transfer area, can be expressed in terms of fi n effectiveness, g, fi n surface area, Af, and total surface area, Atotal, as follows: go 1 ? Af Atotal 1 ? g10 where Atotal= Af? Ab, Ab is the base area. The fi n effectiveness, g, is determined by the method proposed by Wang et al. 19 as follows: g 2rf;i MTr2 f;o? r 2 f;i ? ? K1MTrf;i ?I 1MTrf;o ? ? K1MTrf;o ?I 1MTrf;i ? K1MTrf;o ?I 0MTrf;i ? K0MTrf;i ?I 1MTrf;o ? “# 11 where rf,i is the distance from the center of the tube to the fi n base, rf,o is the distance from the center of the tube to the fi n tip, I0 is the modifi ed Bessel function solution of the fi rst kind, order 0, I1 is the modifi ed Bessel function solution of the fi rst kind, order 1, K0 is the modifi ed Bessel function solution of the second kind, order 0, K1 is the modifi ed Bessel function solution of the second kind, order 1 MTis determined from MT ffi ffi ffi ffi ffi ffi ffi ffi 2ho kfdf r 12 where kf is the thermal conductivity of fi n and df is the fi n thickness. To obtain the air-side heat transfer coeffi cient, ho, an iterative procedure is employed to solve Eqs. (4)(12). The 386Heat Mass Transfer (2009) 45:381391 123 air-side heat transfer characteristics of the heat exchanger is presented in term of the Colburn j-factor as follows: j StPr2=313 where the Stanton number, St, is determined from St ho GaCp;a 14 The effectiveness used to evaluate the performance of the helically coiled heat exchanger is determined from e Qave Qmax Qave mCpminTw;in? Ta;in ?15 where (mCp)minis the smaller mCp of the two fl uids. 4 Results and discussion Figure 5 shows the water temperature and tube wall tem- perature at various positions in the helical coils at Tw,in= 46.8?C,Ta,in= 34.4?C,mw= 0.21 kg/sand ma = 0.085 kg/s. Coil number shown in the fi gure is used to identify the coil considered e.g. Coil numbers 1 and 4 are represented as the innermost coil and outermost coil respectively. The water and tube wall temperatures are measuredateachcoilattheuppermostlayer(layer1)andthe lowermost layer (layer 7). The hot water enters the lower- mostlayerisseparatedtoeachcoil,fl owsalongeachcoiland fl ows out at the uppermost layer (layer 1). The air enters the heat exchanger at the top and center of the shell and fl ows axially across the water fl owing in the coils before leaving theheatexchangerattheairoutletsectionatthebottomofthe heat exchanger. As expected, at the same position, the water temperatures are always higher than tube wall temperatures. During the hot water fl ows along each coil from lower layer to upper layer, heat will be gradually transferred from the watertotheair,whichresultsinthedecreaseofthewaterand tube wall temperatures at upper layer. Figure 6 shows the water temperature and tube wall temperature at layer 1 of each helical coil at Ta,in= 32.8?C, mw= 0.37 kg/s and ma= 0.085 kg/s for the different inlet water temperature of 42, 46?C. Itcan be clearly seen that the water temperature and tube wall temperature at each coil increase with an increase in inlet water temperature. They also gradually decrease from the inner coil to outer coil. Figure 7 shows the water temperature and tube wall temperature at layer 1 of each helical coil at Tw,in= 41.6?C, Ta,in= 30.5?C, ma= 0.097 kg/s for the different water mass fl ow rate of 0.33, 0.37 kg/s. It should be noted that when inlet water temperature, inlet air temperature, air mass fl ow rate are kept constant, the water and tube wall temperatures at lower water mass fl ow rates are lower than at higher ones. Fig. 5 Variation of the water temperature and tube wall temperature at layer 1 and layer 7 with coil number Fig. 6 Variation of the water temperature and tube wall temperature at layer 1 with coil number for different inlet-water temperatures Fig. 7 Variation of the water temperature and tube wall temperature at layer 1 with coil number for different water mass fl ow rates Heat Mass Transfer (2009) 45:381391387 123 Figure 8 shows the water temperature and tube wall temperatureatlayer1ofeachhelicalcoilat Tw,in= 41.8?C, Ta,in= 31?C, mw= 0.37 kg/s for the dif- ferent air mass fl ow rate of 0.035, 0.071, 0.11 kg/s. The water temperature and tube wall temperature tend to decrease with increasing air mass fl ow rate. However, it can be seen that the effect of the air mass fl ow rate on the water temperature and tube wall temperature is very low. Figure 9 shows the variation of the outlet air tempera- ture with air mass fl ow rate at Ta,in= 32?C, mw= 0.21 kg/s for the different inlet water temperature of 40, 45, 50?C. At a specifi c inlet air temperature, inlet water temperature, water mass fl ow rate and the results obtained from Fig. 8 that the air mass fl ow rate only slightly affects the water temperature, one way of keeping the heat transfer rate equal to the water side while the air mass fl ow rate is increased is by decreasing the outlet air temperature. Therefore, it can be clearly seen that for a given water mass fl ow rate, inlet water temperature and inlet air temperature, the outlet air temperature tends to decrease with increasing air mass fl ow rate. In addition, at the same air mass fl ow rate, the outlet air temperature at the higher inlet water temperature is higher than that at the lower one across the range of air mass fl ow rates. Figure 10 shows the relation between the outlet air tem- peratureandairmassfl owrateatTa,in= 32?C,Tw,in= 50?C forthedifferentwatermassfl owrateof0.21,0.25,0.29,0.33, 0.37 kg/s. At the same air mass fl ow rate, the outlet air temperature at the higher water mass fl ow rate is higher than that at the lower one across the rage of air mass fl ow rate. Figure 11 shows the variation in the outlet water tem- perature as the air mass fl ow rate changes at Ta,in= 32?C, mw= 0.21 kg/s for the different inlet water temperature of 40, 45, 50?C . The results shown in this fi gure corresponds with those in Fig. 4. The outlet water temperature tends to decrease slightly with an increase in air mass fl ow rate. Figure 12 shows the average heat transfer rate plotted against air mass fl ow rate at Ta,in= 32?C, Tw,in= 45?C for the different water mass fl ow rate of 0.21, 0.25, 0.29, 0.33, Fig. 8 Variation of the water temperature and tube wall temperature at layer 1 with coil number for different air mass fl ow rates Fig. 9 Variation of the outlet-air temperature with air mass fl ow rate for different inlet-water temperatures Fig. 10 Variation of the outlet-air temperature with air mass fl ow rate for different water mass fl ow rates Fig. 11 Variation of the outlet-water temperature with air mass fl ow rate for different inlet-water temperatures 388Heat Mass Transfer (2009) 45:381391 123 0.37 kg/s. As expected, the heat transfer rate is directly proportional to both the air mass fl ow rate and water mass fl ow rate. The effect of water mass fl ow rate on the heat transfer rate can be clearly seen at higher air mass fl ow rate. Figure 13 shows the variation of the average tube-side heat transfer coeffi cient calculated from the data obtained from the present experiment with water mass fl ow rate at various inlet water temperature. As expected, the average tube-side heat transfer coeffi cient increases with increasing water mass fl ow rate. At a given water mass fl ow rate, the average tube-side heat transfer coeffi cient for higher inlet water temperature is higher than that for the lower ones. Moreover, our experimental results show that there is no effect of air mass fl ow rate on the tube-side heat transfer coeffi cient. Figures 14 and 15 illustrate the variation of the out-side heat transfer coeffi cient with air mass fl ow rate for different inlet-water temperatures and water mass fl ow rates, respectively. The out-side heat transfer coeffi cient increases rapidly with air mass fl ow rate. The inlet-water temperature and water mass fl ow rate show a signifi cant effect on the out-side heat transfer coeffi cient. Figures 16, 17 and 18 show the variation of the Colburn j factor with air side Reynolds number. The air-side Rey- nolds number is calculated from Rea= qaVaD/lawhere qa is the density of air, lais the dynamic viscosity of air. Both density and dynamic viscosity are determined based on the measured air temperature. D is the diameter of inlet section of the heat exchanger (D = 0.298 m). Vais the average velocity of air fl owing through the inlet of the heat exchanger. As shown, the Colburn j factors decrease with increasing air-side Reynolds number over the range of examined water side Reynolds numbers. From the fi gure, it is observed that the water mass fl ow rate and inlet water temperature have a signifi cant effect on the heat transfer characteristics. It can be seen from this fi gure that as the air side Reynolds number increases, all curves become fl atter and tend to approach a specifi c Colburn j factor. Fig. 13 Variation of the tube-side heat transfer coeffi cient with water mass fl ow rate for different inlet-water temperatures Fig. 14 Variation of the air-side heat transfer coeffi cient with air mass fl ow rate for different inlet-water temperatures Fig. 12 Variation of the average heat transfer rate with air mass fl ow rate for different water mass fl ow rates Fig. 15 Variation of the air-side heat transfer coeffi cient with air mass fl ow rate for different water mass fl ow rates Heat Mass Transfer (2009) 45:381391389 123 Fig. 17 Variation of the Colburn factor with air-side Reynolds number for different inlet-water temperatures Fig. 18 Variation of the Colburn factor with air-side Reynolds number for different water mass fl ow rates Fig. 19 Variation of the heat exchanger effectiveness with air-side Reynolds number for different inlet-water temperatures Fig. 20 Variation of the heat exchanger effectiveness with air-side Reynolds number for different water mass fl ow rates Fig. 21 Variation of the heat exchanger effectiveness with air-side Reynolds number for different water mass fl ow rates Fig. 16 Variation of the Colburn factor with air-side Reynolds number for different inlet-water temperatures 390Heat Mass Transfer (2009) 45:381391 123 Figures 19, 20, 21 and 22 show the variation of the effectiveness with air side Reynolds number. The effec- tiveness used to estimate the performance of the helically coiled heat exchanger is determined from Eq. (15). Fromthewholerangeofwatermassfl owrateandairmass fl ow rate used in the present study, the capacity rate of hot water, (mCp)wis generally higher than that of the air (mCp)a. Therefore, the capacity rate of the hot water is the minimum capacityrate,(mCp)mininEq. (15).Itcanbeclearlyseenfrom this fi gure that the effectiveness decreases with increasing air side Reynol