HEAT TRANSFER IN SERRATED-FIN TUBE BUNDLES WITH STAGGERED TUBE LAYOUTS

Transcription

1 HEAT TRANSFER IN SERRATED-FIN TUBE BUNDLES WITH STAGGERED TUBE LAYOUTS Erling Næss Norwegian University of Science and Technology N-7491 Trondheim Norway Paper presented at the 9 th U.K. National Heat Transfer Conference Manchester 5 th 6 th September, 2005

2 HEAT TRANSFER IN SERRATED-FIN TUBE BUNDLES WITH STAGGERED TUBE LAYOUTS Erling Næss Norwegian University of Science and Technology N-7491 Trondheim Norway ABSTRACT An experimental investigation of the heat transfer performance of ten finned tube bundles using serrated fins is presented. All bundles had staggered arrangements, and the influence on varying tube bundle layout, tube and fin parameters on the heat transfer is discussed and compared to published correlations. The heat transfer coefficient undergoes a maximum when the flow areas in the transversal and diagonal planes are equal. An increase in the fin pitch increased the heat transfer coefficient; the same was observed with an increase in fin height. The tube bundle layout effect was satisfactory reproduced by the Weierman correlation when the flow area in the transversal plane was smaller; however no correlations were able to reproduce the experimental data when the flow area in the diagonal plane was smaller. The fin pitch effect was successfully reproduced by the Weierman correlation, but fin height effect was not well predicted by any of the correlations. INTRODUCTION In heat recovery from high temperature flue gases, externally finned heat transfer surfaces are frequently used in order to compensate for the low gas-side heat transfer coefficient. Among the large variety of fin types, the most commonly used for high temperature heat recovery applications are the annular or helically wound solid fins and the serrated (or pin) fins, both shown in Figure 1. Figure 1 (a) (b) Solid fin tubes (a) and serrated fin tubes (b). From Technitube Röhrehrenwerke Gmbh ( For equal tube and fin dimensions, solid fin tubes possess a larger heat transfer surface than serrated fins per unit tube length. On the other hand, the cut geometry of the serrated fins leads to frequent boundary layer breakup and a potentially higher heat transfer coefficient, combined with 1

3 serrated fins having higher fin efficiencies. A comparison of heat transfer and pressure drop performance for serrated and solid fin tubes with identical parameters (tube and fin dimensions, tube layout etc) using the frequently recommended correlations of Weierman [1] and PFR [3], both having correlated heat transfer and pressure loss for solid fin and serrated fin tube bundles, gave nonconclusive results. The Weierman correlations predicted equal thermal performance (in W/K m tube length) and pressure drop for low fins (h f less than ca. 10 mm), and a slightly better performance for solid fin tubes for higher fins. The PFR correlations, on the other hand, predicted a moderately higher thermal performance (20-30% increased heat duty per unit tube length) with only a 5-10% increase in pressure drop for serrated finned tubes with moderate fin heights (h f up to ca. 15 mm), and a lower thermal performance for higher fins. Further, in a weight optimization study on waste heat recovery units, Sæther [17] concluded that serrated finned tube bundles would yield less heavy units than solid fin units designed for the same thermal-hydraulic performance. In the same study, Sæther found that the principal parameters for weight minimization was using small diameter tubes with relatively low fins, and a tube bundle layout pattern with high P t /P l -ratio. Sæther based his calculations on the heat transfer and pressure drop correlations of Weierman. In view of this, serrated fin tubes seemed attractive for heat recovery applications, but the selection of tube bundle layout and fin parameters were unclear. Additionally, the published experimental data were limited, covering only the range of P t /P l -ratios where the highest fluid velocity is obtained in the transversal plane. Hence, a set of experiments were performed with the objective of providing guidelines to the optimum choice of parameters for compact heat recovery units, as well as to extend the data range for the evaluation of existing predictive correlations.. The present study is limited to heat transfer in tube bundles with staggered layouts, since inline layouts have shown a significantly lower heat transfer performance ([1], [3], [13], [15]), and are less compact than staggered layouts. AVAILABLE HEAT TRANSFER DATA AND CORRELATIONS Serrated fins may be in the form of L-foot fins (Figure 2 a), where the serrations penetrate all the way to the fin root, or as I-foot fins (Figure 2 b), where the innermost region close to the tube wall have a solid-fin geometry. Another alternative is stud-fins, which consist of individual studs of various shapes welded to the tube surface in a regular pattern, yielding geometries similar to the L- foot fin type. For high temperature applications, the tubes and fins are normally made from carbon steel, and the fin assembly is welded to the tube surface. The available body of experimental data on heat transfer in tube bundles in staggered arrangements using serrated fins seems limited. Results on L-foot type fins were reported by Rabas and Eckels [13] and Schryber [14], and results from experiments using I-foot fins were presented by Hashizume [12], Weierman et al [15] and recently by Kawaguchi et al [6]. Cox [9] performed experiments on aluminum tubes with integral serrated fins, i.e. fins carved from the tube surface, resembling L-foot fins. Results on stud-fin tubes were reported by Ackerman and Brunsvold [8], Vampola [16] and Worley and Ross [4], who performed an extensive experimental program using a variety of stud shapes, tube dimensions and tube bundle layouts. Worley and Ross concluded from their work that the stud geometry had little, if any influence on the heat transfer performance. Therefore, it may be argued that results from both L-foot, I-foot and stud fins may be representative for serrated-fin tubes. Available predictive correlations are shown in Table 1. Also shown are the data sources used for developing the correlations. The correlations of Weierman, PFR and Nir are derived assuming similarity in behavior for serrated-fin and annular (or helically) finned tubes. 2

4 Figure 2 L-foot fins I-foot fins (a) (b) L-foot and I-foot serrated fins (from GEA Spiro-Gills Ltd). Table 1 Heat transfer correlations, length scale in Nu and Re is effective tube O.D., d e. Reference Correlation Data sources Weierman 1) [1],[10] hf /3 s f Nu 0.25Re Pr e 0.25 P 2 l D 0.15Nl P t f T b e e de Tw Not specified PFR [3] 0.7 1/ Nu 0.195Re Pr Ar [9],[13],[15],[16] Mieth [5] Nu Re Pr s s /3 f f h f t f Not specified Worley and Ross 2) 0.7 1/3 [4] Nu 0.125Re Pr [4] /3 A' o F D t f Nir [2] Nu 1.0Re Pr [12],[13],[14],[15] F t F f de 1) The constant in Weiermans original correlation was 0.23, but was later changed to 0.25 in the ESCOA Engineering Manual. The ESCOA recommendation is used here. 2 ) It should be pointed out that Worley and Ross measured and commented a dependency of Nu with Pt, but did not include this in their correlation. EXPERIMENTAL SETUP Experimental setup The experimental setup is shown in Figure 3. Hot air was used on the fin side, and city water or a water/glycol mixture was used as coolant. Upstream the test section (pos. 12), the air passed through a calming section equipped with flow straighteners and several fine wire meshes (pos. 3-10) in order to reduce the large-scale turbulence and provide a uniform velocity profile at the test 2 section entrance. The turbulence level at the test section entrance, defined as Tu u ' 100 u 3

5 where u is the turbulent velocity fluctuation component in the mean flow direction, and u is the mean (time averaged) fluid velocity. The turbulence level was measured to approximately 5%. Downstream the test section the air was rejected to the atmosphere. Figure 3 Test rig for heat transfer measurements The air inlet temperature was maintained at approximately 100 C for all experiments by means of an electric heater. In the initial experiments city water was used as coolant, but due to the low coolant inlet temperature, some indications of moisture condensation from the air was detected. The cooling circuit was therefore modified to consist of a closed circuit system using water/glycol as coolant and rejecting the heat through a separate heat exchanger. In this manner the coolant inlet temperature could be maintained above the air dew-point temperature. Flow rates were measured using orifice plates on both the air (pos. 2) and coolant (pos. 15) sides, and thermocouples at the air and coolant inlet and outlet ends were used to register the fluid temperatures. The air side temperatures (pos. 7 and 14) were measured by sucking off a small flow rate from several grid points in the flow cross-sectional area, and measuring the mixing-cup temperature. In this manner a representative air mixing-cup temperature was obtained. The coolant flow was mixed in a mixing chamber at the exit from the test section, providing a representative mixing-cup temperature measurement. The heat balance deviations for the air and coolant sides had a 95% confidence level of approximately 2.5%. A sketch of the test section is shown in Figure 4. The test section consisted of 32 active tubes for heat transfer (4 transversal and 8 longitudinal tube rows) with dummy half-tubes at the section walls in order to obtain hydraulic similitude. The coolant was passing in parallel in each of the transversal tuberows. The transversal rows were connected in series, providing an overall countercurrent arrangement for the air/coolant flow. The test section width (i.e. the active tube length) was 500 mm, and the section height was 4.5 times the transversal pitch. 4

6 Figure 4 Test section Data Reduction The heat duty was calculated from the measured mass flow rates and overall temperature changes, and the overall heat transfer coefficient was then calculated from Eq.(1), using the arithmetic average of the air and coolant heat duties. U Q A LMTD tot (1) From this, the gas-side heat transfer coefficient was extracted using Eq.(2) d A ln e tot 1 A d tot i Atot o U A 2N N L A A 1 i i l t t t f f t, net (2) Fully turbulent flow was assured on the tube side, and the tube side heat transfer coefficient (α i ) was calculated using the Petukhov et al correlation, see e.g. [18]. The appropriate fin efficiency, which compensates for the finite conductance in the fins can, under the assumption of a uniform gas side heat transfer coefficient be expressed as [11] th tanh M h M h e e (3) where the parameter M was given by M 2o tf wf t w f f f (4) However, as pointed out by several investigators ([1], [3], [7]), the heat transfer coefficient distribution is not uniform, yielding lower actual fin efficiencies than predicted by Eq.(3). In the present analysis, an empirical correction factor to the theoretical fin efficiency proposed by [1] was used, shown in Eq.(5). The magnitude of the correction introduced by using Eq.(5) instead of Eq.(3) is relatively small (less than 7%) for all experiments. 5

7 0,9 0,1 (5) f th th Test Geometries The test tubes all had L-foot fins, as shown in Figure 5. Tubes and fins were made from carbon steel. The fin foot was resistance-welded to the tubes, providing negligible thermal contact resistance between the fin and tube outer surface. The fin thickness and segment width were kept constant for all test geometries, with t f =0.91 mm and w f =3.97 mm. The main features of the test geometries are shown in Table 2, with the geometric variables explained in Figure 5. High compactness requires that the fin-tip clearance between neighboring tubes are kept as small as possible. However, a certain minimum clearance is normally required in order to accommodate production tolerances, tube vibrations, servicing requirements etc. Therefore, a common minimum fin-tip clearance of 8.0 mm was used for all of the test geometries, with the exception of geometry 10, which had identical tube layout as geometries 6 and 9, but with higher fins. Figure 5 Tube geometry and tube bundle layouts Table 2 Main geometry data for test bundles Geometry no. d e =d o +2t f [mm] P t [mm] P l [mm] h e =h f -t f [mm] s f [mm] t f [mm] w f [mm]

8 A total of 10 tube bundles were tested. Tube bundles 1-8 basically consisted of tubes with different tube outside diameters, but with identical fin geometries. The main geometric parameter varied for these bundles (aside from the tube diameter) was the tube bundle layout, i.e. P t /P l. Tube bundles 9 and 10 explored the effect of fin pitch and fin height for a tube bundle layout where the flow areas in the transversal and diagonal planes were approximately equal. RESULTS AND DISCUSSION The non-dimensional heat transfer coefficient (Nusselt number) dependency on the nondimensional mass flux (Reynolds number) can generally be expressed as Nu=CRe m Pr 1/3, where C is a geometry-specific constant. In the data reduction, the common convention of using the base tube effective outside diameter (d e ) as length scale in Nu and Re, and the mass flux in the narrowest flow area (i.e. transversal area for geometries 1, 2, 5 and 8, and diagonal flow area for the other geometries) was applied. The experimentally obtained exponent m varied between 0.63 and 0.68, with an arithmetic average value of This dependency was in good agreement with the published correlations shown in Table 1, where m varied in the range The geometry-specific constants C were established by regression analysis, fitting the experimental data to Eq.(6), and are shown Table 3. Nu de C Re Pr (6) /3 de Table 3 Constants in Eq. (6) for the tested geometries Geometry no. C 95% confidence interval Re-range min/max Influence of tube bundle layout The tube bundle layout effect on the heat transfer performance is demonstrated in Figure 6, showing the Nusselt number for the geometries with identical fin geometries relative to the geometries with equilateral tube layouts (geometries 1 and 5) as function of the ratio of transversal to diagonal free flow areas. Also shown are the data of Ackerman and Brunsvold [8], and the predicted dependency of the correlations in Table 1. As the figure shows, the Nusselt number increases with increasing F t /F d up to maximum of ca at F t /F d =1.0, from where it decreases monotonically. When the flow area in the transversal plane was smaller than the flow area in the diagonal plane, the heat transfer dependency followed the predictions from Weierman, except for one of the Ackerman/Brunsvold data sets. Inspection of the data of Ackerman and Brunsvold indicate that Nu was independent of P l, which was also confirmed by data of Rabas and Eckels [13] (tube banks 3 and 4) and Worley and Ross [4]. Hence, at present the best representation of the bundle layout influence is to use the ratio (P t /d e ) rather than (P t /P l ) or (F t /F d ). Comparison of the data of [8] and 7

9 [13] as well as Geometry 1 and 2 of the present study showed that the ratio P / d accurately reproduced the tube bundle layout dependency. t 0.35 e 1,3 1,2 1,1 Exp. Ø20.87 mm O.D. Exp. Ø27.22 mm O.D. Ackerman/Brunsvold data Weierman [1] Present study Nu/Nu Eq 1 PFR [3], Worley/Ross [4], Mieth [5] 0,9 Nir [2] 0,8 0,7 0,25 0,5 0,75 1 1,25 1,5 Ft/F d [-] Figure 6 Tube bundle layout effect on Nu relative to Nu Eq When the transversal flow area was larger than the diagonal flow area, the heat transfer coefficient dropped markedly. None of the correlations of Table 1 were able to reproduce this behaviour. This is not unexpected, however, since none of the correlations are valid in the region where F t /F d >1. Numerous investigators (e.g. [1], [3], [8], [13], [15]) have pointed out that in-line layouts experience significantly lower apparent heat transfer coefficients than staggered layouts, ranging from 25% [8] to approximately 75% [15] reduction in heat transfer relative to equilateral tube layouts. From this it is expected that the heat transfer at some point should start decreasing with increasing P t /P l -ratios, in this study found to be the interception point where F t and F d are equal. Based on the limited data shown in Figure 6, the presently suggested representation of the tube bundle layout effect on heat transfer in the region where F t /F d >1: Nu Nu Eq F 3.23 t Fd e (7) where Nu Eq is the Nusselt number for an equilateral layout. The expression has an asymptotic value of 0.6 as F t /F d approaches infinity, which may be taken as a representative value for in-line layouts [3]. Further experiments are required in order to evaluate other variables (such as P t and P l ) influence on the heat transfer coefficient in this region. Influence of tube diameter The most frequently adopted length scale in Re and Nu is the (effective) tube O.D., d e. However, several other length scales are possible, such as the hydraulic diameter [2], [3], the equivalent tube diameter [6] and the fin diameter [2]. Inspection of the constants C in Table 3 show that the equilateral tube layouts with identical fin geometries (Geo 1, 5 and 8) are dependent on the tube diameter, as shown in Figure 7. This dependency is well correlated by the term (D f /d e ) -0.35, 8

10 which is equivalent to replacing d e with D f as length scale in (6). The data of Rabas and Eckels [13] with D f /d o =82.6mm/34.2mm (tube bundle 4) and 101.6mm/53.2mm (tube bundle 7) are also shown, and are reasonably well reproduced by (D f /d e ) -0.44, equivalent to replacing d e with D f as length scale in their expression for Nu. Nirs correlation includes a similar term, effectively making D f the length scale. However, the the data of Worley and Ross [4] contradict this observation, since their results were reported to be well reproduced by using the tube outside diameter as length scale. Therefore, the correct choice of length scale needs further investigation. 0,48 C 0,46 0,44 0,42 0,4 0,38 0,36 0,34 0,32 0,3 0,28 0,26 R/E: Bundle 4 C~(D f /d e ) R/E: Bundle 7 0,24 0,22 0,2 0,18 Geo 8 C~(D f /d e ) Geo 5 Geo 1 Present study: Nu de =C Re de 0.65 Pr 1/3 Rabas/Eckels: Nu de =C Re de 0.56 Pr 1/3 1,4 1,5 1,6 1,7 1,8 1,9 2 2,1 2,2 2,3 2,4 2,5 D f /d e Figure 7 Dependency of Nusselt number (Nu de ) with the ratio of fin diameter to tube diameter. Influence of fin spacing and fin height Geometries 6, 9 and 10 had various fin pitches and fin heights, but were arranged in identical tube bundle layouts. For these geometries, the effect of fin parameters could be investigated with comparative bundle arrangements. It should be noted that (F t /F d ) >1 in these tests, hence the available correlations are strictly not valid. However, (F t /F d ) was only slightly higher than unity (in the range ), so it was unlikely that the flow pattern had changed significantly from the region F t /F d <1. Figure 8 shows the dependency of the normalized Nusselt number (Nu/Nu Geo6 ) on the fin pitch. Also shown are predictions from the correlations in Table 1. As shown, the measured dependency is reasonably well reproduced by most correlations, and accurately reproduced by the correlation of Weierman. The influence of the fin height on the normalized Nusselt number is shown in Figure 9. As observed, the observed Nusselt number increases with increased fin height, whereas the predictions show constant or decreasing Nusselt numbers. It may be speculated that the difference in behaviour may be attributed to the fact that most of the correlations are based on the assumption of similar behaviour with annular fins, where fluid may not penetrate as efficiently to the fin root as in serrated fin tubes, possibly also more efficient fluid mixing between the serrated fins. The observed discrepancy between measurements and predictions is however moderate (less than 7%) for the correlations showing no h e -dependency. 9

11 Nu (normalized) [-] 1,25 1,20 1,15 1,10 1,05 1,00 0,95 0,90 0,85 0,80 0,75 Figure 8 Experimental (Geo 6 & 10) Worley/Ross PFR Weierman Nir Mieth Worley/Ross PFR Weierman Nir Mieth Geo 10 Geo S f [mm] Effect of fin pitch on the Nusselt number. Nu (normalized) [-] 1,25 1,20 1,15 1,10 1,05 1,00 0,95 0,90 0,85 0,80 Experimental (Geo 9 & 10) Worley/Ross Weierman Nir Mieth PFR Geo 10 Geo 9 0,75 Figure 9 8,0 8,5 9,0 9,5 10,0 10,5 11,0 11,5 12,0 h e [mm] Effect of fin height on the Nusselt number Overall comparison with correlations It is concluded from the above that none of the available correlations can reproduce the tube bundle layout effects for F t /F d >1.0. Hence, a comparison of the experimental results with the correlations is limited to the geometries where Ft/Fd<1.0, i.e. geometries 1, 2, 5 and 6, all having identical fin geometries. Figure 10 shows the comparison, and the main statistics are shown in 10

12 Table 4. Due to the limited range of parameters tested, the data spread is relatively small. It is interesting to note, however, that the discrepancy between the different correlations is unacceptably large. Taking into consideration published data on serrated/stud fins from other sources, i.e. [4],[8],[9],[12],[14],[15] in addition to the present data, the variation in geometry parameters is much larger. A comparison with these data and the correlations is shown in Figure 11, with the main statistics given in Table 5. Based purely on statistics, the performance of the correlations is acceptable. It should however be noted that the data spread is significant, and that none of the correlations seem to reproduce consistently the effect of geometry variations. The correlations of Weierman [1], PFR [3] and Worley and Ross [4] seem to give the best overall accuracy. 2,0 1,8 1,6 Mieth Nu Pred /Nu Exp [-] 1,4 1,2 1,0 0,8 0,6 0,4 0,2 0,0 Figure 10 Mieth [5] Weierman [1] PFR [3] Worley/Ross [4 Nir [2] Weierman Worley/Ross Re de [-] PFR Comparison of measured Nusselt numbers for geometries 1, 2, 5 and 6 and correlations of Table 1. Nir Table 4 Comparison of measured Nusselt numbers for geometries 1, 2, 5 and 6 and correlations of Table 1. Weierman PFR Mieth Worley/Ross Nir Min Max Average Standard deviation [%]

13 Nu pred /Nu exp 3,0 2,5 2,0 1,5 1,0 0,5 Weierman Worley/Ross Weierman PFR Mieth Worley/Ross Nir Mieth PFR Nir 0, Re d Figure 11 Comparison of measured Nusselt numbers for present data and data of [4],[8],[9],[12],[14],[15] with correlations of Table 1. F t /F d <1.0 for all geometries shown. Table 5 Comparison of measured Nusselt numbers for present data and data of [4],[8],[9],[12],[14],[15] with correlations of Table 1. F t /F d <1.0 for all geometries. Weierman PFR Mieth Worley/Ross Nir Min Max Average Standard deviation [%] % data point within ±20% CONCLUSIONS An experimental investigation of heat transfer to serrated fin tube bundles in staggered layout has been performed, and the results have been compared to available correlations from the literature. Based on the results, the following conclusions may be drawn: - The Nusselt number undergoes a maximum when flow areas in the transversal and diagonal planes are equal. - For F t /F d <1.0, The tube layout influence on Nu is best reproduced by Weiemans correlation, although experimental data suggest that it is not correct. - For Ft/Fd>1.0, no available correlations reproduce the observed behaviour. - Observations indicate that the fin diameter is a representative length scale in Nu and Re. - The fin pitch effect is adequately predicted by the Weierman correlation. - The fin height effect is small, but not reproduced by any of the correlations. Based on the experimental results, some guidance towards the development of an improved heat transfer correlation is given. 12

14 Furthermore, a comparison of the available correlations with published data from the literature show that the overall prediction accuracy is best using the correlations of Weierman, PFR and Worley and Ross. NOMENCLATURE A Heat transfer surface (m 2 ) A o Heat transfer surface for one tube row (m 2 ) A t,net Heat transfer surface of base tube between fins (m 2 ) Ar Area extension ratio (A tot /A bt ) (-) C Constant (-) c p Specific heat capacity (J/kg K) d Tube diameter (m) Tube effective outside diameter (d o for I-foot fins, do+2t f for L-foot fins) (m) d e D f Fin diameter (m) F d Free flow area in diagonal plane (between two tube rows) (m 2 ) F f Free flow area between fins for one tube row (m 2 ) F t Free flow area in transversal plane (m 2 ) h e Effective fin height (h f for I-foot fins, h f -t f for L-foot fins) (m) h f Fin height from base tube (m) L Tube length (m) LMTD Logarithmic mean temperature difference (K) m Mass flux in narrow free flow area (kg/m 2 s) N l Number of tube rows in flow direction (longitudinal) (m) N t Number of tube rows perpendicular to flow direction (transversal) (m) P f Net open gap between fins (s f -t f ) (m) P l Longitudinal pitch (m) P t Transversal pitch (m) Q Heat duty (W) s f Fin pitch (m) T Temperature (K) t f Fin thickness (m) U Overall heat transfer coefficient (W/m 2 K) w f Fin segment width (m) Greek symbols α Heat transfer coefficient (W/m 2 K) η Dynamic viscosity (kg/m s) λ Thermal conductivity (W/m K) ψ Fin efficiency (-) Dimensionless numbers de Nud Nusselt number m" de Red Reynolds number c Pr p Prandtl number 13

15 Subscripts b bulk bt base tube i Inner o outer f fin t tube th theoretical tot total w wall REFERENCES 1. C. Weierman, Correlations Ease the Selection of Finned Tubes, Oil and Gas Journal, pp , Sept A. Nir, Heat Transfer and Friction Factor Correlations for Crossflow over Staggered Finned Tube Banks, Heat Transfer Engineering, vol. 12, No. 1, pp.43-58, PFR Engineering Systems, Heat Transfer and Pressure Drop Characteristics of Dry Tower Extended Surfaces, PFR Report BNWL-PFR-7 100, PFR Engineering Systems Inc, N.G. Worley and W. Ross, Heat Transfer and Pressure Loss Characteristics of Crossflow Tubular Arrangements with Studded Surfaces, Inst. Mech. Engrs.,pp 15-26, Nov H. C. Mieth, Method for Heat Transfer Calculation of Helical-Wound Fin Tubes, ASME-70,Pet 4, K. Kawaguchi, K. Okui and T. Kashi, Heat Transfer and Pressure Drop Characteristics of Finned Tube Banks in Forced Convection (Comparison of Heat Transfer Characteristics between Spiral Fin and Serrated Fin), Heat Transfer - Asian Research, vol. 34, No. 2, pp , K. Hashizume,, R. Morikawa, T. Koyama and T. Matsue, Fin Efficiency of Serrated Fins, Heat Transfer Engineering, vol.23, No. 2, pp. 7-14, J.W. Ackerman and A.R. Brunsvold, Heat Transfer and Draft Loss Performance of Extended Surface Tube Banks, J. Heat Transfer, vol.92, pp , May B. Cox, Heat Tansfer and Pumping Power Performance in Tube Banks - Finned and Bare, ASME Paper 73-HT-27, G. Breber, Heat Transfer and Pressure Drop of Stud Finned Tubes, AIChE Symp. Ser, vo. 87, no.283, pp , K.A. Gardner, Efficiency of Extended Surfaces, Trans ASME, vol. 67, pp , K. Hashizume, Heat Transfer and Pressure Drop Characteristics of Finned Tubes in Crossflow, Heat Transfer Engineering, vol.3, No. 2, pp.15-20, T.J. Rabas and P.W. Eckels, Heat Transfer and Pressure Drop Performance of Segmented Extended Surface Tube Bundles, ASME Paper 75-HT-45, E.A. Schryber, Heat-Transfer Coefficients and Other Data of Individual Serrated-Fin Surfaces, Trans ASME, vol.67, No.8, pp , Nov C: Weierman, J. Taborek and W.J. Marner, Comparison of the Performance of In-Line and Staggered Banks of Tubes With Segmented Fins, AIChE Symp. Ser., vol.74, pp.39-46, J. Vampola, --, Strojirestvi, vol. 16, pp , 1966 (In russian). 17. S. Sæther, Combined Cycles with Compact Heat Recovery Steam Generators, Sintef Report STF15 A93111, M. S. Bhatti and R.K. Shah, Turbulent and Transition Flow Convective Heat Transfer in Ducts, in S. Kakac, R.K. Shah and W. Aung (eds), Handbook of Single Phase Convective Heat Transfer, John Wiley & sons,