Jurnal f Electrnics Cling and Thermal Cntrl, 01,, 1-16 http://dx.di.rg/10.436/jectc.01.1001 Published Online March 01 (http://www.scirp.rg/jurnal/jectc) 1 Experimental Study f Heat Transfer t Flwing Air inside a Circular Tube with Lngitudinal Cntinuus and Interrupted Fins Saad A. El-Sayed *, Sayed A. EL-Sayed and Mhamed M. Saadun Department f Mechanical Pwer Engineering, Zagazig University, El-Sharkia, Egypt Email: * shamad53@htmail.cm Received January 3, 01; revised February 1, 01; accepted February 8, 01 ABSTRACT Experimental investigatins have been perfrmed t determine the detailed mdule-by-mdule pressure drp and heat transfer cefficient f turbulent flw inside a circular finned tube. The tubes are prvided with lngitudinal fins cntinuus r interrupted in the stream wise directin by arranging them bth in a staggered and in-line manner. Experiments are carried ut fr tw different fin gemetries, with tw numbers f fins (N = 6 and 1). All tested finned tubes have 16 mdules each with length equal t the tube diameter (L = D = 30 mm). The thermal bundary cnditin cnsidered here, is a unifrm heat flux. The mdule-by-mdule heat transfer cefficient is fund t vary nly in the first mdules, and then attained a cnstant thermally peridic fully develped value after eight t twelve mdules. The results als shwed that in the peridic hydrdynamic fully develped regin, the value f the pressure drp alng the tube with cntinuus fins is greater than that f the in-line arrangement, and lwer than that f the staggered arrangement. Furthermre, the results shwed that in the peridic fully develped regin, the tube with cntinuus fins prduces a greater value f the heat transfer cefficients than that the tube with interrupted fins, especially thrugh a high range f Reynlds number (5 10 4 > Re > 10 4 ). The tube with Staggered arrangement f fins prduces a greater value f the heat transfer cefficient than the tube with cntinuus fins and the in-line arrangement finned tube at lw Reynlds number (Re < 1. 10 4 ).). It was fund that the fins efficiency is greater than 90 percent; in the wrst case (maximum Reynlds number with cntinuus fins tube). Keywrds: Internal Flw; Turbulent Flw; Heat Transfer; Interrupted and Cntinuus Fins; Fin Analysis 1. Intrductin The demand fr high-perfrmance heat exchange devices having small spatial dimensins is increasing due t their need in applicatins such as aerspace and autmbile vehicles, cling f electrnic equipment, and s n. This has led t varius designs f a cmpact heat exchanger. Internal fins are the mst cmmnly used technique fr enhancing the rate f heat transfer between the surface and a flwing fluid. It has been recgnized fr sme time that higher heat transfer rates can be btained when the internal fin surfaces f circular tubes are peridically interrupted in the stream wise directin, resemble the ffset-fin heat exchanger. Heat transfer enhancement is accmpanied by an increase in a pressure drp due t the increase f the frictin factr. Since the frictin pwer, expenditure is equally very imprtant fr the exchanger surfaces, it is therefre, f interest, t study the heat-transfer perfrmance f an internally finned cir- * Crrespnding authr. cular tube with fin surface interrupted in the stream wise directin. Numerical predictins f the laminar fluid flw and the frced cnvectin heat transfer in the entrance regin f internal lngitudinal finned tubes have been investigated by varius researchers. Rustum and Sliman [1] as well as Camp and Mrales [] cnducted numerical studies based n standard finite differences fr the thermal develpment f a fluid flw thrugh tubes with fully develped hydrdynamics. Prakash and Liu [3] and Chudhary and Patankar [4] have been independently examined, the prblem f simultaneusly develping flw and heat transfer in a tube. They used a mdified cntrl vlume technique fr slving the gverning cnservatin equatins numerically. Hu and Chang [5] studied theretically the case f fully develped velcity and temperature simultaneusly f an internally cntinuus finned tube at cnstant heat flux. Masliyah and Nandakumar [6] cnsidered the fins f a triangular shape with finite thickness. Sliman et al. [7] have been investigated Cpyright 01 SciRes.
S. A. EL-SAYED ET AL. the laminar heat transfer in an internally finned tube with unifrm utside wall temperature. Patankar et al. [8] used a mixing length mdel t predict numerically the fully develped turbulent flw and heat transfer characteristics f circular tubes and annuli equipped with lngitudinal internal fins. Kim and Webb [9] develped an analytical treatment fr the frictin factr and heat transfer cefficient in rectangular and circular channels with internal cntinuus lngitudinal fins. Sparrw et al. [10] have been presented a numerical investigatin f fluid flw and heat transfer in a tw-dimensinal staggered ffsetfin array. Sparrw and Liu [11] have been made a perfrmance cmparisn fr tw dimensinal in-line and staggered fin arrays. Lndn and Shah [1] as well as Jshi and Webb [13] have been investigated experimentally ffset-fin arrays. Patakar and Prakash [14] have been studied numerically the effect f plate thickness n heat transfer f tw-dimensinal staggered fin arrays. Kelkar and Patankar [15] have been analyzed a three-dimensinal flw and a heat transfer in ffset-fin arrays. Analytical mdels t predict laminar and turbulent flw and heat transfer ffset-been arrays have been investigated by Jshi and Webb [16]. Kelkar and Patankar [17] investigated the perfrmance f an internal lngitudinal finned circular tube with fin surface interrupted in the stream wise directin by arranging them bth in the staggered and in-line manner fr laminar flw. Xiayue and Michael [18] presented a parametric study n a turbulent and heat transfer in internally finned tubes. Three fin prfiles-rectangle, triangle, and rund crest-with the same fin heights, widths, and helix angles were cmpared. Saha and Langille [19] studied heat transfer and pressure drp characteristics in a circular tube fitted with full-length strip, shrt-length strip, and regularly spaced strip elements. Zeitn and Hegazy [0] presented an analysis study fr a fully develped laminar cnvective heat transfer in a pipe prvided with internal lngitudinal fins, and with unifrm utside wall temperature. The fins are arranged in tw grups f different heights. The numerical results shwed that the height f the fin effects greatly flw and heat transfer characteristics. The present wrk is carried ut experimentally t study a heat transfer fr turbulent flw inside circular tubes equipped with internal lngitudinal interrupted (staggered and in-line) fins. The plain tube and the tube with cntinuus fins are als investigated mainly fr cmparisn with the interrupted finned tubes. Tw main gemetries: 1) (N = 6, with Hr = 0.5), and ) (N = 1, with Hr = 0.3) have been used in this study. The simultaneus develpment f velcity and temperature fields are cnsidered, when the fluid enters the tested finned tubes with unifrm inlet velcity and unifrm temperature. The thermal bundary cnditin is being a unifrm heat input per unit area (cnstant surface heat flux). The radial and axial heat cnductin thrugh the tube wall is neglected. Air is the wrking fluid in all experiments with assuming cnstant prperties. The Reynlds number range extends frm 5 10 3 t 5 10 4 based n the hydraulic diameter f the tested finned tubes.. Experimental Apparatus and Prcedure The main bjective f the present experimental wrk was defined, that is t determine the detailed mdule-bymdule pressure drp and heat transfer cefficient f the turbulent flw inside circular tubes with internal lngitudinal fins that are cntinuus and interrupted. The interrupted fins are arranged in a staggered and an in-line manner. The apparatus cnsists mainly f air passage, heating unit, and measuring instruments, as shwn in Figure 1. Air is sucked frm the labratry atmsphere and blws int the tested tube. A mtr-driven fan, running at a cnstant speeds, draws air thrugh a cntrl valve (gate valve), and delivers it int a U-shaped tube f 75 mm internal diameter t the tested tube thrugh a cnical nzzle. The cnical cnvergent nzzle gives nearly a unifrm velcity distributin at the inlet f the tested tube. A British standard rifice plate f 40 mm diameter was installed in the apparatus t measure the air flw rate. It was calibrated by integrating the velcity prfile in a fully develped regin f a plain circular tube with 3.6 mm diameter. The tested tubes were made f a brass plain tube (uter diameter = 31.8 mm, and inner diameter = 30.5 mm) in which axial slts were machined n its surfaces t insert 0.6 mm thick fins made als f brass strips. The plain tubes slts were made cntinuusly and interrupted by using 0.6 mm thick cutter n a milling machine. The strips were sheared by CNC shearing machine. Special cres were used fr fins insertin t ensure that 1) all fins inside the tube have the same height, and ) all the recgnized extensins f the fins passing thrugh the centerline (see Figure ). All tested tubes with interrupted fins have 16 mdules, each f length equal t a tube diameter ( 30 mm). The cntinuus fins tube has fins f a length equal t 36 times a tube diameter. All tested tubes with interrupted fins have a distance equal t tw and three tube diameter length free f fins at the tube entrance and exit respectively. On the ther side, the tube with cntinuus fins has a distance equal t ne and fur tube diameter length free f fins at the tube entrance and exit respectively. Axial pressure distributin was measured with aid f 9 static taps (0.5 mm inner diameter) fr the interrupted finned tubes, and 37 static taps fr the cntinuus fins Cpyright 01 SciRes.
S. A. EL-SAYED ET AL. 3 1 D 14 D Figure 1. Schematic diagram f experimental apparatus. (a) Flw directin H L L (in-line arrangement) Flw directin L H L (staggered arrangement) (b) Figure. (a) Fins insertin in the tube and cre; (b) Schematic f different gemetries in this study. tube distributed alng the tube uter surface. Taps were installed alng the line lies in the middle between tw fins. The pressure signals frm the taps are cnveyed t the pressure selectr switch via plastic tubes. The utput signals f the pressure selectr switch are sensed by a micr manmeter with accuracy ± 0.01 mm f H O. 3. Heating Units and temperature Aspects The tested finned tube was heated by an Ohmic dissipatin in an electric resistance tape ( mm width, and 0. mm thickness). The tape heater pwer f 1900 Watts at 65 Vlt, and 7.3 Ampere, was wund unifrmly n the uter surface f the tube. The pwer f the heater was Cpyright 01 SciRes.
4 S. A. EL-SAYED ET AL. cntrlled by a variac transfrmer, which prvides a cntrllable cnstant heat flux alng the surface f the tested tubes. The electric pwer input t the heater was measured by an in-line digital wattmeter (accuracy ± 0.5%). Over the range f test cnditins; the utput-input air temperature difference was kept cnstant at apprximately 3 C. A 1.5 mm thick layer f asbests insulated the uter surfaces f the tested finned tubes electrically. The uter surface f the heater was insulated thermally by a 35 mm thick glass wl (k = 0.041 W/m k). The insulatin layer and the heater tape cvered all the uter surface f the tested tube except a tw diameter length frm the tube entrance. Cpper-cnstantan calibrated thermcuples f 0.4 mm diameters were embedded at 0.5 mm depth frm the uter surface f the tested finned tube t measure the lcal surface temperatures. Three thermcuples, distributed circumferentially, were used fr each mdule at ne traverse crss-sectinal area. They were at the exit f the finned mdule as well as a distance equal t 60 percent f the un-finned mdule length as shwn in Figure 3. Eighteen thermcuples at a six traverse crss-sectinal areas (distributed unifrmly and axially) fr a ne finned mdule in the peridic fully develped regin were used t determine the lcal heat transfer cefficient f the mdule. Eighteen thermcuples were als distributed alng the un-finned successive mdule f the in-line arrangements. Six f them are used t give the lcal fin base temperatures. The details f all thermcuples psitins fr bth arrangements are shwn in Figure 4. Six thermcuples were unifrmly distrib- Figure 3. Schematic lcatins f the thermcuples junctins n the surface f the tested finned tubes. Figure 4. Schematic lcatins f the thermcuples junctins alng the mdule fr in-line and staggered arrangements. Cpyright 01 SciRes.
S. A. EL-SAYED ET AL. 5 uted alng the inner and the uter surfaces f the insulat) was distributed int the heat transferred by cnvectin t tin (glass wl) t determine the radial cnductin lsses. The reading f the thermcuples was taken ut by a digital thermmeter f accuracy ± 0.4 C. A standard mercury thermmeter was used t read the inlet temperature f the flwing air stream. Anther five thermcuples were distributed at the tested finned tube exit t read the utlet temperature f the flwing air stream. The ttal rate f heat generated frm the heater (q the flwing air (q c ), and heat lsses t the utside f the tested tubes. The heat transferred by cnvectin t the air stream is given by: q c qt q cd,i q cd,e q q (1) q t = The ttal input pwer t the heater, W q cd,i = The heat lst by cnductin thrugh the insulatin in the axial and radial directins, and it is given by: f,c cd,i ins ins i cd,a q πk LT ln D D () k ins = The thermal cnductivity f the insulatin, W/m K. L = The length f the insulated sectin f tube, m. D i = Inner diameter f the insulatin, m. D = Outer diameter f the insulatin, m. ΔT ins = The average temperature difference between the inner and the uter surfaces f the insulatin and it is given by: T T T T T5 T6 3, K. 1 3 4 It was fund that it represents abut 7.6% f the ttal heat input fr the maximum case at minimum Reynlds number. q cd,e = The heat lst by cnductin thrugh the tube wall in the insulated entrance regin retarded the flw. It is given by: qcd,e w w ka T x (3) A he crss-sectinal area f the tube wall, m W = T. ΔT w = The wall temperature difference per ne md- length in the entrance regin withut heating, K. ule Δx = The mdule length in the entrance regin withut heating, m. k = The thermal cnductivity f the tube material, W/m K. It was fund that it represents abut 0.03% f the ttal heat input fr the maximum case at minimum Reynlds number. q f,c = The heat lst by free cnvectin frm the rear face f the tested finned tube (W). It is given by: q h A T T f,c f w r,f a (4) h f = The heat transfer cefficient W/m K. by free cnvectin, T r,f = The rear face surface temperature, K. T a = The surrunding air temperature, K. It was fund that it des nt exceed 0.018 percent f the ttal heat input. q cd,a is the heat lst by axial cnductin thrugh the tested finned tube wall. In ur study, the Peclet number (Pe = Re Pr) was typically greater than 1000. Therefre, the axial heat cnductin lss thrugh cnvectin air is neglected as nted in [1]. Except q cd,i, the ther heat lsses can be neglected due t their small values as cmpared with the ttal heat input value. The investigated parametric variatins are: fins number (N), relative fin height ( Hr), and the arrangement manner. The arrangement may be classified int tw gemetries as shwn in Table 1. Fr a certain required rate f air discharge f air in the tested tube, the pressure difference acrss the rifice meter was determined. The gate valve pining was adjusted t giving that pressure difference. Thrughut the experiment, this pressure difference was kept cnstant. The flw was characterized by Reynlds number based n hydraulic diameter (Re h ), and n a velcity via the minimum crss-sectinal area f the tested finned tube. The range f the hydraulic Reynlds number based n the plain tube diameter (Re) was 10 4 t 10 5 apprximately. Fr each tested tube, grups f experiments were perfrmed t determine the heat transfer cefficient per mdule. Bth the velcity and the temperature distributins at tw diameter lengths frm the tube entrance were determined t check the unifrmity f bth the velcity and the temperature prfiles. 4. Methd f Calculatin The essential quantities, which were determined in this study, include the mass flw rate f air ( m a ), wall tem- t the heater. The air peratures, and electric pwer input mass flw rate was calculated frm the measured values f pressure difference acrss the standard rifice plate (C d = 0.64 ± 0.005), and the density f the flwing air Table 1. Arrangements f fins inside the tested tubes. Gemetry 1 Fin Relative Arrangement Hydraulic number N height Hr manner diameter D h, m 6 0.5 Cntinuus 6 0.5 Staggered 6 0.5 In-Line 1 1 0.3 0.3 Staggered In-Line 14.86 13.46 Cpyright 01 SciRes.
6 S. A. EL-SAYED ET AL. and v m accrding t its inlet tempe rature. The bulk velcity can als be calculated frm the cn- tinu ity equatin as: a b aa (5) c 4D A π NHt (6) c Fr internal flw, the equivalent hydraulic diameter D h is ften used as the characteristic length. It is defined as D 4 h π 4 D NHt πd NH (7) The hydraulic Reynlds number Re h based n the D h is defined as: Re v D (8) h a b h a Using the plain tube diameter, D, as the characteristic length, the R eynlds number based n it is defined as: h Re v D a b a The mdule-averaged frictin factr based n the hydraulic diameter (f ) can be defined as f p LDh h a b (9) (10) v while the mdule-averaged frictin factr based n the plain tube diameter is defined as a b p L D f (11) v where Δp = The ttal pressure drp acrss a mdule length (L). The perfrmance f the tested finned tubes is cmpared with the Blasius frmula f the plain tube [] f 0.5 0.3164Re (1) als, the pressure distributin alng the tested finned tubes is cnsidered in the dimensinless frm as P P P i x (13) avb P = The dimensinless pressure drp. P i = The pressure at the tube entrance, N/m. P e pressure at an axial statin x, N/m x = Th. The pressure is measured at a distance equal t the m dule length, starting frm the entrance f the first mdule. The Nusselt number was calculated frm the measured values f the wall temperatures. The wall temperatures were als measured at the mdules exit as well as at a distance equal t 0.6 L f the un-finned mdules, as shwn in Figure 4. At these psitins, it was fund that the value f the lcal Nusselt numbers is nearly equal t the value f the mdule averaged Nusselt numbers, alng the mdules. The mdule averaged Nusselt number can be btained frm the integratin f the lcal Nusselt number alng the mdule. Then, the mdule-averaged Nusselt number based n the hydraulic diameter can be defined as: Nuh h t,adh ka (14) where (h t,a ) is the cnvective heat transfer cefficient based n the ttal heat transfer area (plain and finned area), and it is calculated as ht,a qm PL Tw Tb (15) k a = The thermal cnductivity f the air. It is taken at the average temperature f the air stream Ti T. q m = The rate f heat transfer per unit area fr ne mdule, W. P = πd NH, the wetted perimeter, m. It is a cmmn practice in applicatins invlving fins t de-rate the fin surface area by efficiency η [3] as we can see in the wetted perimeter equatin. Based n the diam eter f the plain tube (D as the characteristics length), then the Nusselt number (Nu) can be given by: Nu hd k a (16) where (h) can be calculated frm the fllwing equatin as h q πdl T m Tw = The wall temperature f the mdule which is determined frm taking the average f the three thermcircumference, K. cuple readings thse distributed unifrmly n the tube T b = The bulk temperature f air which was btained frm assuming a linear distributin f the air temperature rise alng the tube [3] as: w T b b i a P (17) T T qpx m C (18) T i = Inlet air temperature, K. c p = Specific heat f air at cnstant pressure, J/kg K. q = Rate f heat transfer per unit area, W/m. The perfrmance f the tested finned tubes was cmpared with that f the plain tube. The mdule-averaged Nusselt number has been cmpared with respect t the mdified Dittus-Blter Equatin [4]: 0.8 0.3 Nu 0.03Re Pr (19) Cpyright 01 SciRes.
S. A. EL-SAYED ET AL. 7 Fin Efficiency (η) Tw appraches were emplyed t evaluate η. One was t set η = 1, and the ther was t use the cnventinal ne-dimensinal fin mdel. The efficiency f the fin is given by c tanh mh mh (0) m c h kt (1) and Hc Ht H () H c = Crrected fin height, m. t = Fin thickness, m. An iterative prcedure was required t implement the secnd apprach. Since, the calculatin f η frm Equatins (16) t (18) necessitates that (h) must be knwn. Starting with η = 1.0, the heat transfer area (PL) was determined frm Equatin (15), and (h) was evaluated frm Equatin (13), using the values f (q L ) and (T w T b ) frm the experiments. Substituting (h) in the equatin f wetted perimeter, (η) can be calculated, and thus enabling successive re-evaluatins f (PL) and (h). The new value f (h) was used t initiate anther cycle f the iteratin, and this prcess was cntinued until cnvergence, prduced bth (h) and (η). 5. Uncertainty Analysis The minimum inlet temperature during the experiments was 3 C, and the accuracy f the mercury thermmeter was ±0.5 C. Therefre, the relative uncertainty ( uti T i ) was 1.56%. The minimum measured temperature by the thermcuple thermmeter during experiments was 5 C. The accuracy f the thermcuple thermmeter was ±0.4 C. Therefre, the maximum relative uncertainty ( ut T ) in measuring temperature was 1.6%. The relative uncertainty in the bulk velcity ( uv V) was 1.84%. The relative uncertainty in the mass flw rate f air ( um,a m a ) was 1.84%. The relative uncertainty in the frictin factr ( uf f ) was 4.97%. The relative uncertainty in the Reynlds number ( ure Re ) was 1.84%. The relative uncertainty in Nusselt number ( unu Nu ) was 5%. 6. Results and Discussin Presentatin f the experimental results and their analy- grups: ses will be divided int the fllwing A: The frictin factr in hydrdynamic peridic fully develped flw regin. B: The pressure drp distributin alng the tested finned tubes. C: The averaged Nusselt number in thermally peridic fully develped regin fr all tested finned tubes. D: The variatin f the averaged Nusselt number with the number f mdules in the fully develped flw regin fr all tested finned tubes. E: The lcal Nusselt number alng the mdule fr all tested interrupted finned tubes. F: The fin efficiency as a functin f Reynlds number (i.e. fin perfrmance). Regarding t (A), Figure 5 shws the mdule-aver- Figure 5. Mdule-averaged frictin factr in the peridic fully develped regin as a functin f the hydraulic Reynlds number fr all tested finned tubes. Cpyright 01 SciRes.
8 S. A. EL-SAYED ET AL. aged frictin factr in the peridic fully develped regin fr all tested tubes. The value f (f h ) fr the tubes with staggered arrangement is highly higher than that fr tubes with in-line arrangement. This is because f increasing the area available fr frictin as well as increasing the number f leading and trailing edges f the fins, fr tw successive mdules. The value f (f h ) fr the tubes with the staggered arrangement is higher than that fr the tubes with cntinuus fins. Because staggering f the fins causes extra frictin n the fin surface at the starting f each mdule. As the number f fins increases, the available area fr frictin increases and s the values f (f h ) increase. Figure 6 shws the mdule-averaged frictin factr based n the plain tube diameter fr all tested finned and plain tubes. It is fund that the values f (f) are 1.6,.0, and.8 f that fr the plain tube fr inline, cntinuus and staggered arrangement, respectively. Regarding t (B), Figures 7 t 9 shw the dimensinless pressure drp against the dimensinless axial distance ( xd) fr all tested finned tubes. The flw characteristics exhibit a peridically repeating behavir after sme initial develping regin. Fr peridic gemetube versus axial distance tries f the type cnsidered here, the fully develped pressure distributin alng the is nt a straight line as fr cnventinal duct flws. The pressure distributin lies n a straight line in the fully develped regin at axial statins x, (x + L), (x + 4L), etc. Since the average frictin, factr decreases with increasing Re, s the pressure increases. Except fr the first mdule, the pressure at the successive mdule ends decrease linearly alng the tested interrupted finned tubes. Fr all tested finned tubes, it can be seen that the pres- sure drp fr the staggered arrangement is larger than that fr the in-line arrangement, while the cntinuus fins tube lies in between. Regarding t (C), the augmentatin f heat transfer caused by the additinal f cntinuus fins n the inside f a circular tube surface, is significant. The mdule-averaged Nusselt number fr all tested interrupted finned tubes is always lwer than that fr cntinuus fins tube. This may be attributed t the effect that the additin f fins with mre interruptins causes the axial flw t escape frm the tube wall and fin surface t the cre regin and thus reduces the washing flw n these surfaces. Figure 10 shws the mdule-averaged Nusselt number (based n hydraulic diameter) as a functin f hydraulic Reynlds number in the thermally peridic fully develped regin fr all tested finned tubes. The slid lines represent the fin efficiency f the analytical cnventinal mdel (η < 1), while the dashed lines represent the fin efficiency mdel (η = 1). Frm the experimental results, it is fund that the Nusselt number versus Reynlds number fr each tested finned tube can be represented by straight line, in a lglg scale s that the pwer-lw can be used as fllws; Nu n cre (3) where (c) and (n) may be determined frm the least square fit. Further mre, fr each arrangement (staggered r in-line) the straight lines fr tw test gemetries are nearly parallel. The cnstant n and c in the pwer-lw representatin differ slightly fr η =1 and η < 1 mdels as shwn in Table. Fr cmparisn with the plain tube, the mdule-aver- Figure 6. Mdule-averaged frictin factr in the peridic fully tested finned tubes. develped regin as a functin f Reynlds number fr all Cpyright 01 SciRes.
S. A. EL-SAYED ET AL. 9 Figure 7. Axial variatin f the mdule-averaged dimensinless pressure drp (In-line arrangement: N = 6, and Hr= 0.5). Figure 8. Axial variatin f the mdule-averaged dimensinless pressure drp (Staggered arrangement: N = 6, and Hr= 0.5). Table. Values f cnstants (c) and (n) f Equatin (3). Type f arrangement N = 6, and Hr = 0.5 N = 1, and H r = 0.3 Cntinuus Staggered In-Line Staggered In-Line η = 1 η <1 N c N C 0.800 0.449 0.67 0.58 0.67 0.0166 0.45 0.045 0.156 0.037 0.785 0.446 0.663 0.57 0.668 0.0186 0.458 0.048 0.158 0.039 aged Nusselt number is calculated based n the plain tube diameter. Figure 11 shws the mdule-averaged Nusselt number (based n the plain tube diameter) in the peridic thermally fully develped regin fr all tested finned tubes. The values f mdule-averaged Nusselt number fr the in-line arrangement tubes are higher than thse fr the staggered arrangement tubes, at high Reynlds number, (Re h > 3. 10 4 ) fr (N = 6, and Hr = Figure 9. Axial variatin f dimensinless pressure drp (cntinuus fins: N = 6, and Hr= 0.5). 0.5) and (Re h > 10 4 ) fr (N = 1, and Hr = 0.3). On the ther hand, the values f the mdule-averaged Nusselt number fr staggered arrangement tubes are higher than thse fr a tube with cntinuus fins at lw Reynlds number (Re h > 1. 10 4 ) fr (N = 6, and Hr = 0.5). Als, gemetry 1) fr bth arrangements (staggered and in-line) have higher values f mdule averaged Nusselt number than that fr gemetry ). The effective values f mdule-averaged Nusselt number fr the inline arrangement, which can be cmpared with the crrespnding values fr the thers arrangements are btained by averaging the values f tw successive mdules with and withut fins. Regarding t (D), the mdule-by-mdule heat transfer results are presented in Figures 1 t 16 fr all tested finned tubes. In these figures several general characteristics f the results are evident. It is nticed that fr all tested interrupted finned tubes, the mdule-averaged Nusselt number decreases frm mdule t mdule in the stream wise directin until it reaches an asympttic value, then it remains cnstant regardless f the mdule number. It is als shwn that the value f Nusselt number increases with increasing the value f Reynlds number. Tw cnflicting factrs may be identified, which influence the variatin f Nusselt number in the thermal e ntrance regin. One f these factrs is resulting frm the mdule-by-mdule develpment f pattern f flw acceleratin, wake shedding and impingement, which augment the heat transfer. The t her fact r is resul ting frm the migratin f flw frm the relative cnstrained in- ter-fin regin t the cre regin. This migratin ccurs in the initial part f the fins array and then ceases as the flw becmes peridic thermally fully develped. Thus, the cnflicting ef fects f the tw f actrs discussed here are clear; ne tends t increase the heat transfer, and the ther tends t decrease it. The number f mdules, in the thermal entrance regin, Cpyright 01 SciRes.
10 S. A. EL-SAYED ET AL. Figure 10. Mdule-averaged Nusselt number in the peridic fully develped regin as a functin f Reynlds number fr all tested finned tubes. Figure 11. Mdule-averaged Nusselt number in the peridic fully develped regin as a functin f Reynlds number fr all tested finned tubes. required t make the flw peridic thermally fully develped depends n the fin height, the number f fins, the arrangement manner, and the Reynlds number. It is desired t have an verall indicatin f the thermal entrance regin that will serve fr all tested finned tubes investigated. The number f mdules required fr the flw t be peridical, thermally fully develped extends frm abut 8 t 1 mdules. Fr the in-line arrangement, the value f the mdule-averaged Nusselt number is av- eraged ver tw successive mdules, s that the value f (Nu) at even values f (M) nly is meaningful. Regarding t (E), the lcal Nusselt number alng the mdule in the stream wise directin is shwn fr five values f the Reynlds numbers in Figures 17 and 18 as an example fr the staggered and in-line arrangements fr gemetry 1) (N = 6, and Hr= 0.5). In the in-line arrangement as shwn in Figure 17, the lcal Nusselt number alng the mdule is calculated fr tw successive mdules (finned and un-finned). The results shw that, the value f the lcal Nusselt number in the finned mdule is slightly higher than that in the un-finned mdule. Mrever, if the Nusselt number is calculated based n the hydraulic diameter, the increase in Nusselt number in the finned mdule becmes larger than that in the un- Cpyright 01 SciRes.
S. A. EL-SAYED ET AL. 11 Figure 1. variatins f the mdule-averaged f Nusselt number with number f mdules. Figure 13. Variatins f the mdule-averaged f Nusselt number with number f mdules. finned mdule. The value f the Nusselt number at the finned mdule entrance is slightly higher than that at the finned mdule exit. This is because the thermal bundary layer thickness is very thin at the leading edge f the fins. The value f the Nusselt number after the finned mdule exit is decreased suddenly, due t the absence f the fins in the un-finned mdule. Finally, the Nusselt number can be cnsidered almst unifrm alng the finned mdule, and then drpped t anther value in the un-finned mdule. This unifrmity cmes frm the fact that in a shrt mdule, the grwth f the thermal bundary layer thickness may nt reach t large values alng its length. In the staggered arrangement as shwn in Figure 18, the values f lcal Nusselt numbers at bth f the mdule entrance and exit are higher than that at the middle f the mdule. Because the mdule has mre heat transfer area at bth the mdule entrance and exit. Als, bth the mdule entrance and exit have high level f the turbulence due t increasing the number f fins cuts. Regarding t (F), fin efficiency measurements are difficult t be btained. Because the temperature measurements within the fin r n its surface are inherently difficult, using the available techniques, t be made withut disruptin f the heat transfer behavir. Thermcuples n the surface can significantly alter the flw and heat transfer ver the surface, and thermcuples within the fin alter its heat cnductin behavir. Anaused t predict lytical mdels f heat exchanger can be the efficiency with suitable accuracy. These mdels incrprate several simplifying assumptin. The mainly Cpyright 01 SciRes.
1 S. A. EL-SAYED ET AL. Figure 14. variatins f the mdule-averaged f Nusselt number with number f mdules. Figure 15. Variatins f the mdule-averaged f Nusselt number with number f mdules. ne cnsidered that the temperature distributin within the fin is ne-dimensinal in the directin f heat flw. In additin, the expressins fr evaluating the fin efficiency ignre the existence f wall and the ther resistance affecting the heat flw. Figure 19 presents the fin efficiency, calculated frm the iterative methd, as a functin f Reynlds number based n the plain tube diameter, fr all tested finned tubes. Figure 0 cnveys the fin temperature distributins which are pltted in the T T T T versus the dimensinless frm fin b fin,w b dimensinless distance r r H. As expected, the values f efficiency are substantially lwer fr the lnger fins. In particular, the value f efficiency fr fins with Hr = 0.3 generally exceeded 98 percent, while values as high as 94 percent btained fr fins with Hr= 0.5, fr bth arrangements at the maximum Reynlds number. The cntinuus fins tube has lwer values f η than that f the interrupted finned tubes, because its fins efficiency is calculated in the fully develped regin. But fr interrupted finned tubes, each fin can be dealt as if it is in the entrance regins. It is seen that the fin efficiency decreases with increasing Reynlds number. This is due t the increase in the air mass flw rate that increases the heat transfer cefficient. 7. Cnclusins The heat transfer fr turbulent flw in a circular tube with staggered and in-line arrangements f lngitudinal Cpyright 01 SciRes.
S. A. EL-SAYED ET AL. 13 Figure 16. Variatins f Nusselt number with the dimensinless axial length. Figure 17. Variatins f the lcal Nusselt number with the dimensinless axial mdule length. cntinuus and interrupted fins n the inside surface f the tube is investigated experimentally. The experiments are perfrmed t determine the detailed mdule-bymdule heat transfer characteristics. Detailed temperature measurements are made, frm which the mduleaveraged Nusselt number are determined. As results f the present study, the fllwing cnclusins are derived: 1) The results shwed that in the peridic hydrdynamic fully develped regin, the value f the pressure drp alng a tube with cntinuus fins is higher than that f the in-line arrangement, and lwer than that f the staggered arrangement. ) After a certain initial length, the flw characteristics Figure 18. Variatins f the lcal Nusselt number with the dimensinless Axial mdule length. shw peridically repeating behavir due t the peridicity in the gemetry. Results shwed that the mduleaveraged Nusselt number starts with a high value and then decreases gradually twards an a symptmatic value, which relates t the thermal peridic fully develped flw. The number f mdules required fr the flw t becme thermally peridic fully develped extends frm abut 8 t 1 mdules. 3) The values f the mdule-averaged Nusselt number fr the tube with in-line arrangement fins are higher than that f the staggered arrangement, at high Reynlds numbers, (5 10 4 > Re h > 3. 10 4 ) fr gemetry (1) (n = 6, Hr= 0.5) and (5 10 4 > Re h > 10 4 ) fr ge- Cpyright 01 SciRes.
14 S. A. EL-SAYED ET AL. Figure 19. Fin efficiency fr all tested finned tubes with Reynlds number. Figure 0. Fin temperature distributins in the radial directin fr all tested finned tubes fr Re = 1.1 10 5. metry () (N = 1, and Hr= 0.5). 4) The values f mdule-averaged Nusselt number fr staggered arrangement tubes are higher than that fr a tube with cntinuus fins at lw Reynlds numbers (Re h > 1. 10 4 ) fr gemetry (1) (N = 6, and Hr= 0.5). 5) Fr bth arrangements (staggered and in-line), gemetry (1) (N = 6, and Hr= 0. 5) has higher values f the Nusselt number than that fr gemetry () (N = 1, and Hr = 0.3). 6) The augmentatin f heat transfer caused by the ad- fins is abut ne and ditin f cntinuus fins inside a circular plain tube is significant. The value f the mdule-averaged Nusselt number, fr a tube with cntinuus half that fr the plain tube. The tested interrupted finned tubes have mdule-averaged Nusselt number equal t abut ne and third that fr the plain tube. REFERENCES [1] I. M. Rustm and H. M. Sliman, Numerical Analysis f Laminar Frced Cnvectin in the Entrance Regin f Tubes with Lngitudinal Internal Fins, ASME Jurnal f Heat Transfer, Vl. 110, N., 1988, pp. 310-313. di:10.1115/1.350485 [] A. Camp and J. C. Mrales, Analysis/Numerical Predictin f the Three-Dimensinal Temperature Variatin in Tube Having Stream Wise Internal Fins, Jurnal f Numerical Heat Transfer, Part A: An Internatinal Jurnal f Cmputatin and Methdlgy, Vl. 3, N. 3, 1993, pp. 319-339. di:10.1080/10407789308913675 [3] C. Prakash and Y. D. Liu, Analysis f Laminar Flw and Heat Transfer in the Entrance Regin f an Internally Finned Circular Tubes, ASME Jurnal f Heat Transfer, Vl. 107, N. 1, 1985, pp. 84-91. di:10.1115/1.347407 [4] D. Chudhury and S. V. Patankar, Analysis f Laminar Flw and Heat Transfer in Tubes with Radial Internal Fins, Prceedings f the 3rd Natinal Heat Transfer Cnference, Denver, 1985, pp. 57-64. [5] N. H. Hu and Y. P. Chang, Optimizatin f Finned Tubes fr Heat Transfer in Laminar Flw, ASME Jurnal f Heat Transfer, Vl. 95, N. 3, 1973, pp. 33-338. di:10.1115/1.3450060 [6] J. H. Masliyah and K. N. Nandakumer, Heat Transfer in Internally Finned Tubes, ASME Jurnal f Heat Transfer, Vl. 98, N. 5, 1976, pp. 57-61. di:10.1115/1.345058 [7] H. M. Sliman, T. S. Chau and A. C. Trupp, Analysis f Laminar Heat Transfer in Internally Finned Tubes with Unifrm utside Wall Temperature, ASME Jurnal f Heat Transfer, Vl. 10, N. 4, 1980, pp. 598-604. di:10.1115/1.344358 [8] S. V. Patankar, M. Ivanvic and E. M. Sparrw, Analysis f Turbulent Flw and Heat Transfer in Internally Fin- Cpyright 01 SciRes.
S. A. EL-SAYED ET AL. 15 ned Tubes and Annuli, ASME Jurnal f Heat Transfer, Vl. 101, N. 1, 1979, pp. 9-37. di:10.1115/1.345095 [9] N.-H. Kim and R. L. Webb, Analytic Predictin f the Frictin and Heat Transfer fr Turbulent Flw in Axial Internal Fin Tubes, ASME Jurnal f Heat Transfer, Vl. 115, N. 3, 1993, pp. 553-559. di:10.1115/1.91073 [10] E. M. Sparrw, B. R. Baliga and S. V. Patankar, Heat Transfer and Fluid Analyses f Interrupted Wall Channels, with Applicatin t Heat Exchangers, ASME Jurnal f Heat Transfer, Vl. 99, N. 1, 1977, pp. 4-11. di:10.1115/1.3450654 [11] E. M. Sparrw and C. H. Liu, Heat Transfer, Pressure Drp and Perfrmance Relatinships fr In-Line, Staggered, and Cntinuus Plate Heat Exchangers, Internatinal Jurnal f Heat and Mass Transfer, Vl., N. 1, 1979, pp. 1613-165. di:10.1016/0017-9310(79)90078-4 [1] A. L. Lndn and R. K. Shah, Offset Rectangular Plate- Fin Surface-Heat Transfer and Flw Frictin Characteristics, ASME Jurnal f Engineering fr Pwer, Vl. 90, 1968, pp. 18-8. [13] H. M. Jshi and R. L. Webb, Heat Transfer and Frictin in the Offset Stripfin Heat Exchanger, Internatinal Jurnal f Heat and Mass Transfer, Vl. 30, N. 1, 1987, pp. 69-84. di:10.1016/0017-9310(87)90061-5 [14] S. V. Patankar and C. Prakash, An analysis f the Effect f Plate Thickness n Laminar Flw and Heat Transfer in Interrupted-Plate Passage, Internatinal Jurnal f Heat and Mass Transfer, Vl. 4, N. 11, 1981, pp. 1801-1810. di:10.1016/0017-9310(81)90146-0 [15] K. M. Kelkar and S. V. Patankar, Numerical Predictin f Heat Transfer and Fluid Flw in Rectangular Off- set-fin Arrays, Jurnal f Numerical Heat Transfer, Part A: Applicatins: An Internatinal Jurnal f Cmputatin and Methdlgy, Vl. 15, N., 1989, pp. 149-164. di:10.1080/1040778890894468 [16] H. M. Jshi and R. L. Webb, Heat Transfer and Frictin in the Offset Strip-Fin Heat Exchanger, Internatinal Jurnal f Heat and Mass Transfer, Vl. 30, N. 1, 1987, pp. 69-84. di:10.1016/0017-9310(87)90061-5 [17] K. M. Kelkar and S. V. Patankar, Numerical Predictin f Fluid Flw and Heat Transfer in a Circular Tube with Lngitudinal Fins Interrupted in Stream Wise Directin, ASME Jurnal f Heat Transfer, Vl. 11, N., 1990, pp. 34-348. di:10.1115/1.910383 [18] X. Liu and M. K. Jensen, Gemetry Effects n Turbulent Flw and Heat Transfer in Internally Finned Tubes, ASME Jurnal f Heat Transfer, Vl. 13, N. 6, 001, pp. 1035-1044. di:10.1115/1.140967 [19] S. K. Saha and P. Langille, Heat Transfer and Pressure Drp Characteristics f Laminar Flw thrugh a Circular Tube with Lngitudinal Strip Inserts under Unifrm Wall Heat Flux, ASME Jurnal f Heat Transfer, Vl. 14, N. 3, 00, pp. 41-43. di:10.1115/1.143907 [0] O. Zeitun and A. S. Hegazy, Heat Transfer fr Laminar Flw Internally Finned Pipes with Different Fin Heights and Unifrm Wall Temperature, Jurnal f Heat and Mass Transfer, Vl. 40, N. 3-4, 004, pp. 53-59. di:10.1007/s0031-003-0446-8 [1] W. M. Kays, Cnvective Heat and Mass Transfer, Mc- Graw-Hill, Bstn, 1966. [] W. M. Kays and H. G. Perkins, Handbk f Heat Transfer, McGraw-Hill, Bstn, 197. [3] M. N. Ozisik, Basic Heat Transfer, McGraw-Hill, Bstn, 1977. [4] F. M. White, Heat Transfer, Addisn-Wesley, Bstn, 1984. Cpyright 01 SciRes.
16 S. A. EL-SAYED ET AL. Nmenclature A = Area, m. A c = Minimum crss-sectinal area f the tested fin- ter. ned tubes, m. C d = Discharge cefficient f rifice meter. c p = Specific heat f the air at cnstant pressure, J/Kg k. D = Inner diameter f the tested finned tubes, m. D h = Hydraulic diameter f the tested finned tube, m. h = Lcal heat transfer cefficient, W/m K. H = Height f the fin, m. M = Number f mdules. N = Number f fins. Nu = Nusselt number based n the plain tube diameter. Nu h = Nusselt number based n the hydraulic diame- P = Wetted perimeter (m). Pe = Peclet number (Pe = Re Pr). Pr = Prandtl number. q c = Cnvectin heat transfer, W. r = Radial crdinate. r = Inner radius f the tested finned tubes, m. Re = Reynlds number based n the plain tube diameter. Re h = Reynlds number based n the hydraulic diameter. T = Temperature, K. v = Velcity, m/s. x = Axial crdinate. Greek Letters η = efficiency f the fin. μ = Viscsity, kg/m s. ρ = Density, kg/m 3. Subscripts and Superscripts a = Air. b = Bulk. e = Entrance/exit cnditins. Fin, lc. = Fin lcal. Fin, w = at the fin base. i = Inlet cnditin. L = Mdule. = Outlet cnditin. w = Wall. Cpyright 01 SciRes.