Heat Transfer Enhancement in Swirl Annulus Flows

Transcription

1 5th WSEAS Int. Conf. on ENIRONMENT, ECOSYSTEMS and DEELOPMENT, Tenefe, Span, Decembe 14-16, Heat Tansfe Enhancement n Swl Annulus Flows ALI M. JAWARNEH Depatment of Mechancal Engneeng The Hashemte Unvesty, Zaqa 13115, Jodan E-mal: jawaneh@hu.edu.jo Abstact: The chaactestcs of decayng swlng flows and foced convectve heat tansfe on the condton of tubulent flow n a naow concentc annulus wee smulated. The govenng equatons ae solved numecally va a fnte volume method. Unfom wall tempeatue at the nne wall and adabatc wall at the oute wall ae consdeed as themal bounday condtons. Solutons fo the axal and swl velocty dstbutons and the Nusselt numbe ae obtaned fo dffeent values of the nlet swl numbe and the Reynolds numbe. Smulatons show that the nlet swl numbe have geat nfluences on the heat tansfe chaactestcs. Unde developed tubulent flow condtons, the nceases of nlet swl numbe wll enhance the heat tansfe. When the nlet swl numbe nceases t nceases the axal velocty nea the wall and educes t at the md-gap to acheve the consevaton of mass due to the exstence of seconday flows n the annulus due to centfugal foces. The ncease of the nea-wall velocty, n tun, poduces lage tempeatue gadents and hghe heat tansfe ate. The swl velocty pofles decay gadually downsteam as a esult of fcton whch leads to damp the tangental velocty. The compason between pedcted and expemental data of aveage Nusselt numbes was found to be n good ageement. Keywods: Swl Flow; Nusselt Numbe; Tubulence; Naow Annulus 1 Intoducton Foced convecton n an annulus between two hozontal concentc cylndes has been nvestgated extensvely n the lteatue [1-3] because of ts wde vaety of pactcal and techncal applcatons such as heat exchanges. The poducton of small sze and nexpensve but effectve heat exchanges to tansfe moe heat fom the sufaces of heat exchanges s a vey mpotant subject n heat tansfe. Swl flows ae found n natue, such as tonadoes, and ae utlzed n a vey wde ange of applcatons, such as cyclone sepaatos, agcultual spayng machnes, heat exchanges, gasolne engnes, desel engnes, gas tubnes and many othe pactcal heatng devces [4]. A Swl flow devces ae desgned to mpat a otatonal moton about an axs paallel to the flow decton to the bul flow and s one of the passve enhancement technques used fo nceasng the ate of heat tansfe [5]. The use of decayng swl flow s one of most pomsng technques fo enhancng the mass and heat tansfe. The swlng effect to the flud s gven upsteam secton, and then allowed to decay along the length of a tube [6]. The pesence of swl wll ncease the flow path, decease the fee aea and ntoduce an angula acceleaton to the flud flow [7]. Swlng flows can be mpated to the flow by use of vaous swl-geneatng methods [8-10] whee pat of flud entes axally whle the emnde s njected tangentally usng a votex geneato. Dffeent swl ntenstes can be acheved by vayng the flud flow ate at the axal and tangental nlets. Matemanov and Oulov [11] poposed theoetcal model of the heat tansfe n the axsymmetc swl ppe flows. The study shows that wae-le swl flows wll ncease the heat tansfe compason wth the axal flow whle the jet-le swl flows can dmnsh the heat tansfe. Zeng et al [1] nvestgated the chaactestcs of the flow and convectve heat tansfe on the condtons of both developed lamna and tubulent flow n blateally heat naow annul. The convectve heat tansfe depends on the combnaton effect of the heat-flux ato and the Reynolds numbe. Unde lamna flow condton, the deceases of the gap sze wll lead to the heat tansfe deteoaton both on the nne and oute walls. Howeve wth espect to the case of the tubulent flow condtons, t s qute dffeent. The decease of the gap sze wll yeld heat tansfe deteoaton on the nne wall, but t wll enhance the heat tansfe coeffcent on the oute wall. Apna and Bce [13] nvestgated the effect of swl geneato on heat tansfe ates, swl geneato wee placed at the entance secton of nne ppe of heat exchange. Expements wee caed out fo both paallel and counte flow models of the fluds at dffeent Reynolds numbes. It was obseved that the Nusselt numbe could ncease up to 130% by gvng otaton to the a wth the help of the swl elements. Seveal studes have ndcated that helcally coled tubes ae supeo to staght tubes when employed n heat tansfe applcatons [14-16]. The centfugal foce due to the cuvatue of the tube esults n the development of seconday flows (flows pependcula to the axal decton) whch assst n mxng the flud

2 5th WSEAS Int. Conf. on ENIRONMENT, ECOSYSTEMS and DEELOPMENT, Tenefe, Span, Decembe 14-16, and enhance the heat tansfe. These stuatons can ase n the food pocessng ndusty fo the heatng and coolng of ethe hghly vscous lqud food, such as pastes o puees, o fo poducts that ae senstve to hgh shea stesses. Lu and Wang [17] have nvestgated expementally the convecton heat tansfe chaactestcs of wate flow n a naow annulus wthout swl. Expemental esults show that the heat tansfe chaactestcs of sngle-phase wate flow n the naow annulus ae dffeent fom those n ccula tubes. The tanston fom the lamna to tubulent heat tansfe n the naow annulus s eale than that n ccula tubes. When the Reynolds numbe s lowe than 150, the heat tansfe deteoates, and the axal heat conducton has an mpotant nfluence on the oveall heat tansfe. The tanston fom lamna to tubulent heat tansfe s n the Reynolds numbe ange fom 800 to 100. In the tubulent flow aea, a naow annulus can acheve the enhancement of heat tansfe. De and Meye [18] conducted expements of heat tansfe coeffcents at the nne wall of smooth concentc annul fo tubulent flow of wate wth wde ange of damete atos and the Wlson plot technque was used to develop a convecton heat tansfe coelaton. It was found the convecton heat tansfe coelaton fo an annulus was dependent on the annula damete atos. The deduced coelaton pedcted Nusselt numbes accuately wthn 3% of measued values fo a Reynolds numbe ange, based on the hydaulc damete, fom 4000 to 30,000. Ichmya et al. [19] caed out expements of foced convecton heat tansfe n a naow concentc annulus by tubulence pomotes to examne the effects of pomotes. An expemental study of a double-ppe helcal heat exchange was pefomed usng two dffeently szed heat exchanges has been expementally done by [0]. Oveall heat tansfe coeffcents wee calculated and heat tansfe coeffcents n the nne tube and the annulus wee detemned usng Wlson plots. The effect of swl n axal flow though a naow gap has been studed by [1]. The chaactestcs of tubulent swlng flow n an axsymmetc annul usng the PI technque has been studed by []. Numecal study has been pefomed by [3] to estmate the hydodynamcs of an annula swlng decayng flow nduced by means of a sngle tangental nlet n lamna flow egme. The mean swl ntensty n the whole annula gap thcness has been found to decease fom the entance secton. The methodology of calculatng the Nusselt numbe and velocty components n the annulus of the heat exchange s qute ncomplete n the open lteatue fo decayng votex flow. Theefoe, ths pape concens a numecal study of tubulent flow of an ncompessble vscous flud confned between two statonay tubes wth a small gap usng a fnte volume method. The man pupose n the pesent wo s to show the effect of nlet swl numbe on heat tansfe n the fom of Nusselt numbe fo developed tubulent flow wthn the annulus. Analyss.1 Govenng Equatons Fg.1 shows the schematc of the annulus and coodnates system. The flow unde study s steady, tubulent, ncompessble and axsymmetc. The oute and nne ad of the concentc annulus ae o and, espectvely. The flud entes the cylndes gap unfomly wth two velocty components (, U) n z,θ dectons, whee and U denote the axal and tangental nlet velocty components, espectvely. The themo physcal popetes of flud ae assumed constant except densty fo whch the Boussnesq appoxmaton s employed such that the vaaton of densty wth tempeatue has been neglected. The basc equatons govenng flud flow and heat tansfe n annula geomety ae the laws of consevaton of mass, momentum, enegy, tubulent netc enegy and ts dsspaton ate. The equatons wll be solved by assumng that the gap between the two cylndes s small, and the adal velocty s also assumed to be zeo snce t doesn t have the space and tme to develop. The govenng equatons n the annulus ae wtten as: Fg.1: Swlng flow between two concentc cylndes Contnuty: ( ρu ) = 0 x Momentum: p u u ( ρ ) = + [ µ ( j u u + δ l u j j )] + x j x x j x j x 3 x l Enegy: / / ( ρ uu j ) x j T [ u ( ρe + p)] = [ eff + u ( τj ) eff ] x x j x j (1) () (3) whee E s the total enegy and ( τ j ) eff epesents the vscous heatng, defned as u j u ( τ ) = µ ( + u ) µ j eff eff eff δj x x j 3 x (4) the effectve themal conductvty s eff =α C pµ eff (5) The nvese effectve Pandtl numbes, α, s set to be fo hgh Reynolds numbe. The enomalzaton goup (RNG) model s

3 5th WSEAS Int. Conf. on ENIRONMENT, ECOSYSTEMS and DEELOPMENT, Tenefe, Span, Decembe 14-16, smla n fom to the standad model, but t has shown consdeable mpovements ove the standad model whee the flow featues of stong steamlne cuvatue, votces, and otaton ae ncluded. Tanspot equatons fo the RNG model ae ( ρ u ) / / u j = ( eff ) uu j ( x ) ( x j ) x j x α µ ρ ρ ( ρ u ) / / u j = ( α µ eff ) + C1 ( ρ uu j ) ( x ) ( x j ) x j x C ρ + R (6) (7) The quanttes α and α ae the nvese effectve Pandtl numbes fo and and fo hgh Reynolds numbe the values aeα = α The effectve scosty µ eff s the sum of the lamnaµ and tubulent vscostesµ t, t = µ µ ρ C (8) The model constants; C 1, C and C µ ae 1.4, 1.68 and , espectvely. The man dffeence between the RNG and standad model les n the addtonal tem n the equaton gven by 3 C µ ρη (1 η / η0) R = 3 1+ βη (9) whee η = S n /, η 0 = 4.38, β = The swl numbe S n s defned as the ato of the axal flux of angula momentum to the axal flux of axal S n zθ d o z d (10) o o momentum: = ρ /( ) ρ whee z and θ denote the axal velocty and swl velocty components. Tubulence s affected by the swl n the mean flow. The RNG model povdes an opton to account fo the effects of swl by modfyng the tubulent vscosty appopately. The modfcaton taes the followng functonal fom, µ t = µ to ( Ψ, n, ) f S (11) wheeµ to s the value of the tubulent vscosty calculated wthout the swl modfcaton usng Eq.(8), and Ψ s a swl constant that taes on dffeent values dependng on whethe the flow s swl-domnated o only mldly swlng. Fo stongly swlng flows as n the pesent wo a value of 0.08 was used.. Mateals and Bounday Condtons Smulatons have been done fo dffeent Reynolds numbes and dffeent nlet swl numbes. In the pesent smulatons, the Reynolds numbe ange, based on the annula hydaulc damete Dh = ( o ), of s coveed and the nlet swl numbe ange of 0-3 s coveed. The Reynolds numbe Re and nlet swl numbe S, whch measues the ato of the ate of the njected tangental momentum flux to the ate of axal momentum flux, ae defned as Re= ρ D h (1) µ S = U We defne non-dmensonal quanttes as follows: z = z, = θ θ, Z U = z, L =, α = o o, θ (13), (14) whee z, Z,, and α ae the dmensonless axal velocty, dmensonless swl velocty, dmensonless axal coodnate, dmensonless adal coodnate, and adus ato, espectvely. The specfc heat C p, densty ρ, dynamc vscosty µ, and Pandtl numbe P of the wate as the wong flud wee constant wth values of 4178 J g 1 K 1, 996 g m 3, g m 1 s 1, and 5.4 espectvely. The oute adus of the annulus was o =0.05 mm, whle the nne adus was =15.93 mm, theeby fomng an annula gap of 4.1 mm and a adus ato of α= / o =0.8. The length of the annulus was equal to L=1500 mm. The bounday condtons ae the no slp at the sold walls, unfom velocty and tempeatue pofles at the nlet and developed flow at the outlet. At the outlet bounday thee s no nfomaton about the vaables and some assumptons have to be made. The dffuson fluxes n the decton nomal to the ext plane ae assumed to be zeo. The pessue at the outlet bounday s calculated fom the assumpton that adal velocty at the ext s neglected, so that the pessue gadent fom -momentum s gven by: p ρ = θ (15) Due to memoy lmtatons, axs-symmetc solutons wee obtaned. The cente-lne bounday was consdeed axs of symmety. Unfom wall tempeatue (T w =constant) as a themal bounday condton s assumed fo the nne wall. The oute wall s assumed to be pefectly nsulated (q w =0). Fo unfom wall tempeatue bounday condton, ϕ gven by: T T ϕ = w Tn Tw (16) whee T w s the nne wall tempeatue and T n s the nlet flud tempeatue. Fo the case of unfom nne wall tempeatue, the Nusselt numbe s gven by: h D (1 α) ϕ Nu = h = ϕb = α whee h s the heat tansfe coeffcent and (17)

4 5th WSEAS Int. Conf. on ENIRONMENT, ECOSYSTEMS and DEELOPMENT, Tenefe, Span, Decembe 14-16, T ϕ = b Tw b Tn Tw (18) s the dmensonless bul tempeatue. The bul tempeatue, T b, s gven by: o o Tb ut d / u d = (19) Inlet boundaes fo and : The tubulence ntensty, I, can be estmated fom the followng fomula deved fom an empcal coelaton fo ppe flows: u I = = 0.16(Re) 1/8 (0) An appoxmate elatonshp between the tubulence length scale, L o, and the physcal sze of the annulus hydaulc damete D h s Lo = 0.07D h (1) The elatonshp between the tubulent netc enegy,, and tubulence ntensty, I, s 3 ( ) = I () The tubulence dsspaton ate can be detemned as 3/ 4 = C µ 3/ Lo (3) Wall boundaes fo and : In ths study, the standad wall functons [4] ae mplemented. The bounday condton fo mposed at the wall s = 0 n (4) whee n s the local coodnate nomal to the wall. The tubulence dsspaton ate s computed fom = C K κ y (5) 3/ 4 3/ µ 4 / p whee κs von Kámán constant (= ), and y p s dstance fom pont p to the wall..3 Soluton Pocedue The govenng equatons fo mass, momentum, enegy, tubulent netc enegy and ts dsspaton ate wee solved usng the contol-volume method descbed by Patana [5]. The convectve and dffusve tems wee dscetzed usng powe law scheme and the SIMPLER algothm [5] was used to esolve the pessue-velocty couplng. Fo all the smulatons pefomed n ths study, conveged solutons wee usually acheved wth esduals as low as 10-6 fo all govenng equatons. The gd ponts ae not dstbuted unfomly ove the computatonal doman. They have geate densty n the adal decton and have a lowe densty n the axal decton. The -D axsymmetc case wth quadlateal gd cells s chosen and an unstuctued gd was used fo the pesent smulaton. The mesh s suffcently efned n ode to esolve the expected lage flow paamete gadents. The unde-elaxaton paametes on the veloctes wee selected fo the adal and axal, and 0.9 fo the swl velocty components. Segegated, mplct solve has been appled though annulus. When usng the pesent tubulent model t s necessay to un the smulaton fo a sgnfcant numbe of teatons, beyond nomal convegence ctea. Expeence has shown that typcally 4000 teatons needed befoe the pea tangental velocty n the smulaton stablzes. In ode to ensue the accuacy of the esults and the ndependence wth espect to the numbe of nodes used n the dscetzaton pocess, seveal gds wee tested. A gd ndependent soluton study was made by pefomng the smulatons fo thee dffeent gds consstng of 50000, , and nodes. A mesh efnement study showed a gd of nodes to be fne enough to captue all the flow featues. 3 Results and Dscusson The poblem of foced convecton between two concentc hozontal cylndes s studed expementally by Lu and Wang [17] fo dffeent Reynolds numbe. In ode to gan confdence and undestand the modelng methodology that s equed to adequately smulate the heat tansfe n the annulus, the expemental wo of Lu and Wang [17] s used as a case study to valdate the modelng appoach pesented n ths pape. Computatons wee fstly pefomed fo ths geomety wthout swl to valdate the accuacy of the numecal esults by compang wth the expemental esults. Table 1 compaes the pedcted and the measued aveage Nusselt numbes fo dffeent Reynolds numbes, the mean Nusselt numbe s obtaned by ntegatng the local Nusselt numbe ove the nne cylnde. The esult pesented n Table 1 fo Reynolds numbe angng fom 5000 to Results ae shown n Table 1 epesent good ageement between the pesent computatons and expements of Lu and Wang [17]. The pedcted values of Nusselt numbes compae well wth the measued values wth maxmum pecentage eo less than 5%. Table 1: The compason between pedcted and expemental data of aveage Nusselt numbes Re Nu m, expement Nu m, pesent smulaton % eo The chaactestcs of the swlng flow and foced convectve heat tansfe on the condtons of developed tubulent flow n naow annul ae now pesented and dscussed. The solutons wee caed out fo dffeent nlet swl numbes S. The entance length effect can be neglected; the flow s hydodynamcally fully developed and somewhat flatte n tubulent flow as expected. The stength of votex flow has a geat nfluence on the axal velocty pofle. Fg. shows the developed axal velocty pofles n the annulus n tubulent flow, Re=5000, fo nlet swl numbe of S=0, and 3. It can be seen fom Fg. and that when the

5 5th WSEAS Int. Conf. on ENIRONMENT, ECOSYSTEMS and DEELOPMENT, Tenefe, Span, Decembe 14-16, nlet swl numbe nceases t nceases the axal velocty nea the wall and educes t at the md-gap to acheve the consevaton of mass due to the exstence of the ecculaton zone, eddy moton, mxng n adal decton and centfugal foces. Fg. 3 shows the development of the non-dmensonal swl velocty n the annulus n tubulent flow at dffeent axal postons Z =0.07, 0.13, 0.33, 0.5, 0.67, and In geneal, at specfed nlet swl numbe and Reynolds numbe, as an example S= and R e = 5000, the swl velocty pofles decay along the annulus due to vscous effects at the wall whch leads to damp the tangental velocty. The maxmum tangental velocty does not occu at the md-gap but occus close to the oute wall, especally fo the entance egon due to stong centfugal foce. The local Nusselt numbe at the lowe wall fo the hozontal flow n the annulus fo tubulent flow s smulated and plotted fo dffeent nlet swl numbes n Fg. 4. Smulatons show that the nlet swl numbes have geat nfluences on the heat tansfe chaactestcs. The vaaton of local Nusselt numbe along the annulus n tubulent flow, themally developed flow, fo unfom suface tempeatue s gven n Fg. 4, the local Nusselt numbe was plotted as a functon of the dmensonless axal locaton Z fo Re=5000 and fo the ange of swl numbes of S=0, and 3. The Nusselt numbe deceased appoxmately up to ten annulus hydaulc dametes, and then t emaned nealy constant at specfed nlet swl numbe because of the themally developed flow. The last fgue ndcated that the Nusselt numbe of tubulent flow n the annulus wth swl s hghe than that wthout swl fo the same Reynolds numbes. The enhancement n the local Nusselt numbes compaed to values obtaned n the axal flow was hghe at hghe swl numbe because of the hghe swl ntensty. The centfugal foce esults n the development of seconday flows whch help n mxng the flud and enhance the heat tansfe. In addton, the Nusselt numbes and thus the convecton heat tansfe coeffcents ae much hghe n the entance egon. It can be also obseved that as the swl numbe nceases, the Nusselt numbe nceases. Ths behavo s elated to the wall velocty gadent, whch ncease wth the wdenng of the axal velocty aound the md-gap. In ealy wo [6] the exstence of the ecculaton zone has been mentoned as a possble mechansm of heat tansfe enhancement n the swl flows. Indeed, the ecculaton zone mpoves the convectve heat tansfe because t nceases the axal velocty nea the wall. The ncease of the nea-wall velocty, n tun, poduces lage tempeatue gadents and hghe heat tansfe ate. It was shown expementally [6] that one of the majo mechansms of the heat tansfe enhancement s a hgh axal velocty nea the wall. Fo swlng flow, the local Nusselt numbe decayed along the annulus n the axal decton as the axal dstance nceased, but the effect of swl was stll consdeably evdent at the end of the annulus. As the flud flows along the annulus, the angula momentum and tangental velocty decay due to fcton losses at the wall. Some nvestgatos, ncludng Bae and Saye [7] and Keth and Sonju [8], obseved that the decay pocess showed an exponental behavo. z S=0 S= S=3 Re= Fg. : The axal velocty pofles n the annulus n tubulent flow at dffeent swl numbes θ Re=5000 S= Z= Fg. 3: Swl velocty pofles n the annulus n tubulent flow Nu S= S=3 S=0 Re= Z Fg.4: aaton of local Nusselt numbe along annulus n tubulent flow fo unfom suface tempeatue 4 Conclusons

6 5th WSEAS Int. Conf. on ENIRONMENT, ECOSYSTEMS and DEELOPMENT, Tenefe, Span, Decembe 14-16, The chaactestcs of the tubulent swlng flow and convectve heat tansfe on the n naow annula wee solved by means of a fnte volume technque. The pedcted aveage Nusselt numbes wee found to be n good ageement wth expemental data. Smulatons n the pesent studes evealed that the nlet swl numbe has geat nfluences on the heat tansfe chaactestcs. Nusselt numbes wee seen to ncease wth mposng swl to the entance of the annulus. When the nlet swl numbe nceases t nceases the axal velocty nea the wall and educes t at the md-gap due to centfugal foces. The ncease of the nea-wall velocty poduces lage tempeatue gadents and hghe heat tansfe ate. The swl velocty pofles decay along the annulus as a esult of wall fcton whch leads to damp the swl velocty. Refeences: [1] R.K. Shah, A.L. London, Lamna Flow Foced Convecton n Ducts, Advances n Heat Tansfe, Academc Pess, New Yo, [] S. Kaac, R.K. Shah, W. Aung, Handboo of Sngle- Phase Convectve Heat Tansfe, John Wley, New Yo; [3] Yunus A. Cengel, Heat and Mass Tansfe, A pactcal Appoach, 3 d Ed., McGaw Hlls Inc., USA; 006. [4] AK. Gupta, DG. Llley, N. Syed, Swl flows, Ohu: Abacus Pess; [5] F. Keth, MS Bohn, Pncples of heat tansfe, St. Paul: West Publshng Company; [6] R. Razgats, JP. Holman, A suvey of heat tansfe n confned swl flows, Heat Mass Tansfe Pocesses, 1976; : [7] T.H. Kuhen and R.J. Goldsten, An expemental and theoetcal study of natual convecton n the annulus between hozontal concentc cylndes, J. Flud Mech., 74, 1979, [8] A.M. Jawaneh, P. Saas, and G.H. atstas, Expemental and analytcal study of the pessue dop acoss a doubleoutlet votex chambe, Tansacton of ASME, Jounal of Fluds Engneeng, ol. 19, ssue 1, 007, [9] A.M. Jawaneh, G.H. atstas G.H. and H. Hong, On the flow development n jet-dven votex chambes, AIAA, Jounal of Populson and Powe, ol. 1, No. 3, 005, [10] M. Ylmaz, S. Yapc, O. Jomal, and O.N. Saa, Enegy coelaton of heat tansfe and enhancement effcency n decayng swl flow, Heat Mass Tansfe, 38, 00, [11] S. Matemanov,.L. Oulov, On heat tansfe enhancement n swl ppe flows, Int. J. of heat and Mass Tansfe, 47 (004), [1] H.Y Zeng, S.Z Qu, D.N Ja, Investgaton on the chaactestcs of the flow and heat tansfe n blateally heated annul, Int. J. of Heat and Mass Tansfe 50 (007) [13] E.K. Apna, Y. Bce, C. Yldz, and D. Pehlvan, Heat Tansfe Enhancement n a concentc double ppe exchange equpped wth swl element, Int. Comm. Heat Mass Tansfe, ol. 31, No. 6, 004, [14] S.A. Bege, L. Talbot, L.S. Yao, Flow n cuved ppes, Annual Revew of Flud Mechancs 15 (1983) [15] L.A.M. Janssen, C.J. Hoogendoon, Lamna convectve heat tansfe n helcal coled tubes, Intenatonal Jounal of Heat and Mass Tansfe 1 (1978) [16] D.G. Pabhanjan, G.S.. Raghavan, T.J. Renne, Compason of heat tansfe ates between a staght tube heat exchange and a helcally coled heat exchange, Intenatonal Communcatons n Heat and Mass Tansfe 9 () (00) [17] G. Lu, J. Wang, Expemental nvestgaton on heat tansfe chaactestcs of wate flow n a naow annulus, Appled Themal Engneeng xxx (007) xxx xxx. In Pess, Coected Poof, Avalable onlne 0 Mach 007 [18] J. De, J.P. Meye, Heat tansfe coeffcents n concentc annul, Jounal of Heat Tansfe 14 (00) [19] Ichmya, Koch, Hasegawa, Enhancement foced convectve heat tansfe n naow concentc annulus by tubulence pomotes, Jounal of the Atomc Enegy Socety of Japan 6 (8) (1984) [0] T.J. Renne,.G.S. Raghavan, Expemental studes of a double-ppe helcal heat exchange, Expemental Themal and Flud Scence 9 (005) [1] D. Mateescu, M.P. Padousss, Unsteady vscous effects on the annula-flow-nduced nstabltes of a gd cylnde body n a naow duct, J. of Flud and Stuctues 1, 1987, [] T.H. Chang, Expemental study on tubulent swlng flow n a cylndcal annul by usng the PI technque, Intenatonal Jounal of Automotve Technology, ol. 5, No. 1, 004, 17. [3] R. De Paas Neto, P. Legentlhomme, and J. Legand, Fnte-element smulaton of lamna swlng decayng flow nduced by means of a tangental nlet n an annulus, Compute Methods n Appled Mechancs and Engneeng, ol. 165, 1998, [4] B. E. Launde and D. B. Spaldng, The Numecal Computaton of Tubulent Flows, Compute Methods n Appled Mechancs and Engneeng, 1974, 3: [5]. Patana, Numecal Heat Tansfe and Flud Flow, Hemsphee, New Yo, [6] F. Chang,.K. Dh, Mechansms of heat tansfe enhancement and slow decay of swl n tubes usng tangental njecton, Int. J. Heat Flud Flow 16 () (1995) [7] DW Bae, Saye J CL. In: Dowdell RB, edto. Poceedngs of Symposum on Flow: Its Measuement and Contol n Scence and Industy, vol. 1, p [8] F Keth, OK Sonju, The decay of a tubulent swl n a ppe. J Flud Mech 1965;:57 71.