Natural Convection Heat Transfer in Horizontal Concentric Annulus between Outer Cylinder and Inner Flat Tube

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1 Anba Jounal fo Engineeing Sciences Natual Convection Heat Tansfe in Hoizontal Concentic Annulus between Oute Cylinde and Inne Flat Tube Waleed Mohammed Abed Instucto Ame Jameel Shaeef Asst. Instucto Univesity of Anba /Engineeing College -Mechanical Engineeing Dept. Received on : 11/5/0 Accepted on : 8/1/0 Ahmed Ali Najeeb Asst. Instucto Abstact. Natual convection heat tansfe in two-dimensional egion fomed by constant heat flux hoizontal flat tube concentically located in cooled hoizontal cylinde studied numeically. The model solved using the FLUENT CFD package. The numeical simulations coveed a ange of hydaulic adius atio (5, 7.5, and ) at oientation angles fom (0 o up to 90 o ). The esults showed that the aveage Nusselt numbe inceases with hydaulic adius atio, oientation angles and Rayleigh numbe. As well as enhancement atio fo Nusselt numbe at oientation angle 90 o and hydaulic adius atio 7.5 equal 4.87%. Both the fluid flow and heat tansfe chaacteistics fo diffeent cases ae illustated velocity vectos and tempeatue contous that obtained fom the CFD code. The esults fo the aveage Nusselt numbes ae compaed with pevious woks and show good ageement. Key wods: Natual Convection, Hoizontal Annulus, Flat Tube, Aspect Ratio, Oientation Angle. 1. Intoduction. Natual convection in an annulus concentic cylinde has been extensively investigated due to the vaiety of technical applications and pacticality such as heat tansfe in heat exchange device, sola collectos, nuclea eacto, cooling of electical and electonic components, themal stoage system, electical tansmission cables, etc. Among the poblems elated to natual convection, many eseaches focused thei investigation on the heat tansfe and fluid flow behavio fom diffeentially heated walls in a squae o cubic cavity. Howeve, the heat tansfe mechanism and fluid flow behavio in a concentic annulus cylinde ae stongly depended on the aspect atio which is defined as a atio of the diamete of the oute to the inne cylinde. The tempeatue diffeent between the heated inne cylinde and cold oute cylinde contibutes the density gadient and ciculate the fluid in the annulus. The next impotant dimensionless paametes ae the Rayleigh and Pandtl numbes, which affect the heat tansfe mechanism, the flow patten and the stability of the tansitions of flow in the system [1,]. One of the fist, well documented studies of heat tansfe in hoizontal annula enclosues was pesented by Beckmann [3]. He pefomed expeimental measuements fo thee diffeent gases, ai; H and CO, fo the anges of aspect atio and G Di whee Do/Di 8.1 and G Di Kuehn and Goldstein [4] studied natual convection in annula cavities filled with pessuized nitogen ove a Rayleigh numbe ange of. Ra and fo adii atio.6. The esults showed that the flow is unstable in the plume egion fo Ra= 5 and that the flow becomes tubulent as Ra is inceased. Also, they epoted that ove the inne cylinde the flow is tubulent and that unde the inne cylinde the flow is lamina. Compaatively, fewe publications wee noticed fo natual convection in non-cicula domain, Rayleigh numbe ange of 7 Ra 4 and fo adii atio 1.3, Lee and Lee [5] attempted to fomulate the fee convection poblem in tems of 31

2 Anba Jounal fo Engineeing Sciences elliptical coodinates fo the symmetical cases of oblate and polate elliptical annuli and have pefomed expeiments fo this geomety. The poblem of fee convection heat tansfe fom hoizontal elliptic cylinde placed with its majo axis vetical in a fluid of infinite extent is investigated by Bade and Shamshe [6]. Thei poblem was solved fo Rayleigh numbe vaies fom to 3, P=0.7, and the cylinde axis atio (mino/majo) vaies fom 0.1 to Bade [7] studied the effect of elliptic cylinde oientation. The cylinde oientation vaies hoizontal to vetical majo axis while the axis atio anges fom (0.4 to 0.98) at two Rayleigh numbes of 3 and 4. Teetsta et al. [8] developed an analytical model fo natual convection in the two dimensional egion fomed by an isothemal. The model is compised of a combination of thee solutions, the diffusive limit, the lamina bounday laye limit, and the tansition flow limit, and is applicable to a wide ange of aspect atios and inne and oute bounday shapes. The model and data ae in good ageement, with an aveage RMS diffeence of 6% fo the cicula annulus and less than 9% fo the othe geometies. Djezza et al. [9] expessed the Boussinesq equations of the lamina themal and natual convection, in the case of pemanent and flow, in an annula space between two concentic elliptic cylindes. They use a new calculation code with the finite volumes with the pimitive functions (velocity-pessue fomulation) and the elliptic coodinates system. The Pandtl numbe is constant at 0.7 and intenal elliptic tube (e 1 = 0.999, 0.9, and 0.83) the eccenticity of the extenal elliptic tube is maintained constant (e = 0.75) with vaying the Gashof numbe (G = 3, 4, 5 and 5 ). The authos examined effect of the geomety of the inteio elliptic cylinde on the esults. Eid [] studied natual convection heat tansfe in elliptic annuli with diffeent aspect atios expeimentally and numeically. Fou test specimens having elliptic annuli coss sections with diffeent aspect atios of 0.5 to 1 and an annulus diamete atio of wee tested expeimentally. The model was solved numeically using the FLUENT CFD package. The esults show that the otation of the elliptic annuli with small aspect atio by a ight angle wheneve the specimens ae hoizontal o inclined impoves the fee convective heat tansfe chaacteistics. The numeical pedictions show that the annulus diamete atio has moe significant effect on the esults athe than the oientation mode. Sak et al. [11] investigated expeimental and numeical of natual convection heat tansfe in hoizontal elliptic annuli. Expeiments wee caied out fo Rayleigh numbe anges fom up to 4.9 7, the elliptic tube oientation angle, θ, vaies fom 0 to 90 and the hydaulic adius atio of 6.4. These expeiments wee caied out fo axis atio of elliptic tube (mino/majo=b/c) of 1:3. The numeical simulation fo the poblem is caied out by using commecial CFD code. The numeical simulations coveed a ange of elliptic tube axis atio fom 0.1 to 0.98 and fo hydaulic adius atio fom 1.5 to 6.4. Both the aveage and local Nusselt numbe fom the expeimental esults ae compaed with those obtained fom the CFD code. Both the fluid flow and heat tansfe chaacteistics fo diffeent opeating and geometic conditions ae illustated velocity vectos and isothems contous that obtained fom the CFD code. Padilla and Silveia-Neto [1] ae pefomed lage-eddy simulations of tansition to tubulence in a hoizontal annula cavity. Solutions fo Pandtl numbe of (0.707), hydaulic adius atio of () and Rayleigh numbe up to ae obtained. The influences of tansitional and tubulent flows on local and mean Nusselt numbe ae also investigated. Nada [13] investigated expeimental natual convection heat tansfe in hoizontal and inclined annula fluid layes. The annulus inne suface is maintained at high tempeatue by applying heat flux to the inne tube while the annulus oute suface is maintained at low tempeatue by ciculating cooling wate at high mass flow ate aound the oute tube. The expeiments wee caied out at a wide ange of Rayleigh numbe (5 4 up to 5 5 ) fo 3

3 Anba Jounal fo Engineeing Sciences diffeent annulus gap widths (L/D o = 0.3, 0.3, and 0.37) and diffeent inclination of the annulus (θ= 0, 30 and 60 ). The esults showed that: (1) Inceasing the annulus gap width stongly inceases the heat tansfe ate. () The heat tansfe ate slightly deceases with inceasing the inclination of the annulus fom the hoizontal. Azmi and Azwadi [14] pesented numeical study of flow behavio fom a heated concentic annulus cylinde at vaious Rayleigh numbe (.38 3 Ra ), Pandtl numbe (0.716, and 0.718) and aspect atio of the oute and inne cylindes (.6, 3.6, 4.6 and 5). The finite diffeent lattice Boltzmann method (FDLBM) numeical scheme is poposed to impove the computational efficiency and numeical stability of the conventional method. Cuent investigation concluded that the FDLBM is an efficient appoach fo the cuent poblem in hand and good ageement with the published papes in liteatue solution. The above suvey, of hoizontal annulus studies and data as summaized in table (1). In the pesent wok, the pesent contibution pesents a simulation of the poblem as a mathematical model which was solved numeically using the FLUENT-CFD package. The pesent poblem to investigate the effect of Rayleigh numbe, aspect atio (hydaulic adius atio), and diffeent oientation angle of the heated flat tube placed in an isothemal cooled cicula cylinde on the natual convection heat tansfe.. Mathematical model. Conside an annula space anging fom a flat tube placed at the cente of a cicula cylinde filled with ai. The intenal wall of the annula space (flat tube suface) heate unde constant heat flux q H, and the extenal wall of the annula space (cicula cylinde suface) keep isothemally at tempeatue Tc. The inne flat tube is allowed to be inclined to the hoizontal axis by an oientation angle; θ. The physical model of the pesent poblem is illustated in Fig. (1-a). The natual convection heat tansfe between oute cylinde and inne flat tube esults in a buoyancy-diven flow in a vetical - θ plane. The space coodinates ae, measued fom the cente of the cylinde and, θ, measued anti-clockwise fom the downwad vetical symmety line. The two-dimensional govening equations wee summaized as follows unde the following assumptions, [15, 16]: a) Steady state. b) Two dimensional heat tansfe. c) The lamina flow. d) The fluid is incompessible. e) Constant popeties except change in density, accoding to Boussinesq appoximation. f) The viscous dissipation is negligible. The pesent poblem is govened equations of continuity, momentum and enegy. These equations can be witten in the fom: Continuity equation: V V 1 V 0 (1) -momentum equation: V V V V V θ -momentum equation: p 1 1 V V ( ) V F () 33

4 Anba Jounal fo Engineeing Sciences V V V V VV p 1 1 ( V 1 ) V V F (3) Enegy equation: T V T 1 T 1 T V ( ) (4) The buoyancy foces in and θ diections ae witten as: F g ( T Tc) sin F g ( T Tc) sin The bounday conditions T At the suface of the flat tube, ( = Ri; 0 ), V =V =0, const. At the suface of the oute cylinde, ( = Ro; 0 ), V =V =0, T=Tc 3. Numeical method. The govening equations wee solved using FLUENT-CFD code; vesion 6. is employed fo all numeical simulations [17]. Gambit, Vesion..30, is used fo the development of the computational gid. Fig. (1-b) shows the computational gid. The computational domain esulted fom the subtaction of the flat tube section fom the cicula cylinde section. The gid is made up of tiangula elements to impove the quality of the numeical pediction nea the cuved sufaces. The continuity is satisfied using a semiimplicit method fo pessue linked equations, which is efeed to as the SIMPLE pocedue. To educe numeical eos, second ode upwind discimination schemes ae used in the calculations. Each computational iteation is solved implicitly. The convegence of the computational solution is detemined on scaled esiduals fo the continuity, enegy equations and fo many of the pedicted vaiables. The total esidual fo a given vaiable is based on the imbalance in an equation fo consevation of that vaiable summed ove all computational cells. Less than 00 iteations ae geneally needed fo convegence. 4. Results and discussions. Figs. (, 3, 4) show the vaiation of the aveage Nusselt numbe with Rayleigh numbe fo diffeent hydaulic adius atio (5, 7.5, and ) at oientation angles, (0,45, and 90 ). The Nusselt numbe inceases with inceasing Rayleigh numbe. This is because the Nusselt numbe depends on the heat tansfe ate. In addition, figues show the effect of hydaulic adius atio on the Nusselt numbe. It can be seen clealy fom the figues that the Nusselt numbes at highe hydaulic adius atio ae highe than those at lowe ones. The incease of hydaulic adius atio causes highe fluid e-ciculation and highe swil flow ai in the annula space due to the gadient in density, and consequently, the Nusselt numbe incease with inceasing hydaulic adius atio. It is also found fom these figues. the enhancement in Nusselt Numbe at hydaulic adius atio. (), oientation angle fom 0 to 45 (19.8%), as fom θ=0 to θ=90 (4.3%).While, enhancement in Nusselt Numbe at (Ro/Ri=7.5) fom θ=0 to θ=45 (19.4%) and fom θ=0 to θ=90 (4.87%). (Ro/Ri=) fom θ=0 to θ=45 (18.98%), fom θ=0 to θ=90 (4.%). 34

5 Anba Jounal fo Engineeing Sciences The effect of the oientation angle on the flow and themal fields contous ae illustated in Figs. (5, 6). It is obseved that both the velocity vectos and tempeatue (isothems) contous ae symmetic about the vetical axis of the flat tube fo oientation angle 90. A themal plume above the flat tube is obseved fo all inclination angles. Also, it is obseved that as the oientation angle inceases the tempeatue gadient deceases, indicating that moe cooling fo the flat tube suface. The themal plume size incease with heat flux at all oientation diffeent angles. Figs. (7, 8, 9) show the vaiation of the aveage Nusselt numbe with Rayleigh numbe fo oientation angles, (0,45, and 90 ) at diffeent hydaulic adius atio (5, 7.5, and ). The aveage Nusselt numbe inceases with inceasing oientation angles at the same value of Rayleigh numbe. In the othe wod, the maximum heat tansfe ate occus at 90 oientation angle. Fig. () show the velocity vecto and tempeatue contous fo to at oientation angle of 45 and q H =400W/m. Figs. (11, 1) show the vaiation of the aveage Nusselt numbe with oientation angles fo diffeent hydaulic adius atio (5, 7.5, and ) at heat flux, 800W/m espectively. The aveage Nusselt numbe inceases with inceasing oientation angles. In the othe wod, the maximum heat tansfe ate occus at hydaulic adius atio. In othe wise, it is obseved that fom the these Figs. the apid incease in the aveage Nusselt numbe in the ange of oientation angles (0º to 45º) afte this oientation angles ange the incease in the aveage Nusselt numbe fowad to fixed. The incease of the hydaulic adius atio leads to incease in the aveage Nusselt numbe fo diffeent oientation angles based on the equivalent hydaulic adius of the flat tube. This is may be attibuted to the longe annuli (path) of the ai fluid laye with highe velocity at highe hydaulic adius atio. The best enhancement in Nusselt Numbe at =90 and Ro/Ri=7.5 which is (4.87%). As well as the pevious wok Sak et al. [11], see Fig. (13) this figue shows that the pesent esults ae good ageement with the pevious wok. 5. Conclusions. Natual convection heat tansfe between oute cylinde and inne flat tube was investigated numeically using the FLUENT CFD package. 1. The aveage Nusselt numbe inceases with the incease of the flat tube oientation angle.. Both the velocity vecto and tempeatue contous ae symmetic about the majo axis of the flat tube only at an angles of oientation of 0 o, and 90 o, which coesponding to maximum ate of heat tansfe condition. 3. The aveage Nusselt numbe inceases with the incease of Rayleigh numbe. 4. The aveage Nusselt numbe inceases with the incease of the hydaulic adius atio. 6. Refeences. [1] Jaluia Y.," Natual Convection Heat and Mass Tansfe Volume 5 ", William Clowes (Beccles) Limited, Beccles and London, Fist Edition, [] Kays W. M. and Cawfod M. E.," Convective Heat and Mass Tansfe ", McGaw-Hill, Inc., Thid Edition, [3] Teetsta P. and Yovanovich M.M.," Compehensive eview of natual convection in hoizontal cicula annuli ", 7th AIAA/ASME Joint Themophsics and heat tansfe confeence, Albuqueque, NM, June 15-18, [4] Kuehn T.H. and Goldstein R.J., " An Expeimental and Theoetical Study of Natual Convection Heat Tansfe in Concentic and Eccentic Hoizontal Cylindical Annuli " ASME J. of Heat Tansfe, Vol. 0, pp ,

6 Anba Jounal fo Engineeing Sciences [5] Lee J.H. and Lee T.S., " Natual Convection in the Annuli between Hoizontal Confocal Elliptical Cylindes" Int. J. Heat and Mass Tansfe, Vol. 4, pp , [6] Bade H.M. and Shamshe K., "Fee Convection fom an Elliptic Cylinde with Majo Axis Vetical" Int. J. Heat and Mass Tansfe, Vol. 36, No. 14, pp , [7] Bade, H.M., " Lamina Natual Convection fom an Elliptic Tube with Diffeent Oientations" ASME J. of Heat Tansfe, Vol. 119, pp , [8] Teetsta P., Yovanovich M. M., Culham J. R.," Analytical Modeling of Natual Convection in Hoizontal Annuli" Published by the Ameican Institute of Aeonautics and Astonautics (AIAA- 0959), 005. [9] Djezza M., Chake A., and Daguenet M.," Numeical Study of Bidimensional Steady Natual Convection in a Space Annulus Between Two Elliptic Confocal Ducts Influence of the Intenal Eccenticity ", Rev. Eneg. Ren. J., Vol. 8, pp. 63-7, 005. [] Eid E. I.," Natual Convection Heat Tansfe in Elliptic Annuli with Diffeent Aspect Ratios", Alexandia Engineeing Jounal, Vol. 44, No., pp , 005. [11] Sak R.Y., Bebish N.S., Abd-Alziz A.A. and Hanafi A.S.," Expeimental and Numeical Investigation of Natual Convection Heat Tansfe in hoizontal Elliptic Annuli " Jounal of Applied Sciences Reseach, Vol.4, No., pp , 008. [1] Padilla E. L. M. and Silveia-Neto A.," Lage-eddy Simulations of Tansition to Tubulence in a Hoizontal Annula Cavity ", Int. J. of Heat and Mass Tansfe, Vol. 51, pp , 008. [13] Nada S. A.," Expeimental Investigation of Natual Convection Heat Tansfe in Hoizontal and Inclined Annula Fluid Layes", Int. J. of Heat and Mass Tansfe, Vol. 44, No. 8, pp , 008. [14] Azmi O. Shahul and Azwadi C. S. No," UTOPIA Finite Diffeent Lattice Boltzmann Method fo Simulation Natual Convection Heat Tansfe fom a Heated Concentic Annulus Cylinde" Euopean Jounal of Scientific Reseach -ISSN X, Vol.38, No.1, pp.63-71, 009. [15] Patanka S.V., "Numeical Heat Tansfe and Fluid Flow ", McGaw-Hill Book Company, New Yok, [16] Vesteeg H.K. and Malalasekea W.," An Intoduction to Computation Fluid Dynamics, The Finite Volume Method ", John Wiley, Sons Inc., 605 Thid Avenue, New Yok, USA, [17] Fluent," FLUENT-CFD use s guide ", Lebanon, Fluent Inc., USA, Nomenclatue. F Foce (N) T Tempeatue ( C) g Gavity acceleation (m/s ) V Velocity (m/s) h Heat tansfe coefficient (W/m. C) Geek Samples k Themal conductivity (W/m. C) Themal diffusivity (m /s) L Length (m) Volume coefficient of expansion (K -1 ) Nu Nusselt numbe Oientation angle ( ) P Peimete (m) Dynamic viscosity (N.s/m ) P Pandtl numbe Density (kg/m 3 ) p Pessue (Pa.) Subscipt Q Heat tansfe ate (W) c cold q H Heat flux (W/m ) h hot R Radius (m) o oute Ra Rayleigh numbe adial coodinate (m) Ro/Ri Hydaulic adius atio tangential diection 36

7 Anba Jounal fo Engineeing Sciences Kuehn and Goldstein [4] Table 1: Review of hoizontal annulus studies and data. Authos Test Range of independent paametes Geomety Hoizontal Expeimental and. Ra 7.7 7, Po/Pi=.6 cicula Theoetical annulus Lee and Lee [5] Bade and Shamshe [6] Bade [7] Teetsta et al. [8] Djezza et al. [9] Eid [] Expeimental 7 Ra 4 Po/Pi= 1.3 Expeimental Expeimental Ra 3, P=0.7, (mino/majo) vaies fom 0.1 to Ra 4, P=0.7, (mino/majo) vaies fom 0.4 to 0.98 Numeical Po/Pi=.1 to 6.37 Numeical Expeimental and Numeical P= 0.7, (e 1 = 0.999, 0.9, and 0.83) (e = 0.75) (G = 3, 4, 5 and 5 ) 1 5 Ra Po/Pi= 0.5 to 1 Elliptic cylinde Elliptic annulus Elliptic annulus Cicula annulus Elliptic cylinde Elliptic and cicula annulus Sak et al. [11] Padilla and Silveia-Neto [1] Nada [13] Azmi and Azwadi [14] Expeimental and Numeical Numeical Expeimental Numeical Ra 4.9 7, annulus inclination (θ, 0 to 90 ), Po/Pi=6.4 Hoizontal elliptic tube Hoizontal P=0.707, Po/Pi= Ra cicula annulus 5 4 Ra 5 5 Hoizontal (L/D o = 0.3, 0.3, and 0.37) cicula annulus inclination (θ = 0, 30 annulus and 60 ) Ra 1.0 5, P=0.716,0.717, Po/Pi=.6, 3.6, 4.6 and 5 Hoizontal cicula annulus 37

8 Nu Nu Anba Jounal fo Engineeing Sciences Tc Ai q H θ a- Physical domain b- Computational gid Fig. (1): Physical domain and computational gid. 5 θ=0º Ro/Ri= Ro/Ri= Ra 5 Fig. (): The vaiation of aveage (Nu) with (Ra) at oientation angle, 0, fo diffeent (Ro/Ri). 30 θ=45º Ro/Ri= Ro/Ri= Ra 5 Fig. (3): The vaiation of aveage (Nu) with (Ra) at oientation angle, 45, fo diffeent (Ro/Ri). 38

9 Nu Anba Jounal fo Engineeing Sciences 30 θ=90º Ro/Ri= Ro/Ri= Ra 5 Fig. (4): The vaiation of aveage (Nu) with (Ra) at oientation angle, 90, fo diffeent (Ro/Ri). θ=90 θ=0 θ=45 Fig. (5): Velocity vectos and tempeatue contous fo diffeent oientation angle, q H =W/m. 39

10 Nu Anba Jounal fo Engineeing Sciences θ=90 θ=0 θ=45 Fig. (6): Velocity vectos and tempeatue contous fo diffeent oientation angle, q H =800W/m θ=90º θ=45º θ=0º Ra 5 Fig. (7): The vaiation of the aveage (Nu) with the (Ra) fo diffeent oientation angle at (Ro/Ri =5). 40

11 Nu Nu Anba Jounal fo Engineeing Sciences 30 Ro/Ri= θ=90º θ=45º θ=0º Ra 5 Fig. (8): The vaiation of the aveage (Nu) with the (Ra) fo diffeent oientation angle at (Ro/Ri =7.5). 30 Ro/Ri= θ=90º θ=45º θ=0º Ra 5 Fig. (9): The vaiation of the aveage (Nu) with the (Ra) fo diffeent oientation angle at (Ro/Ri =). 41

12 Anba Jounal fo Engineeing Sciences Ro/Ri=7.5 Ro/Ri= Fig. (): Velocity vectos and tempeatue contous fo θ=45, q H =400W/m. 4

13 Nu Nu Anba Jounal fo Engineeing Sciences.08 q H = W/m Ro/Ri=7.5 Ro/Ri= θº Fig. (11): The vaiation of the Nu with θº fo diffeent Ro/Ri at q H =W/m. q H =800 W/m Ro/Ri=7.5 Ro/Ri= θº Fig. (1): The vaiation of the Nu with θº fo diffeent Ro/Ri at q H =800W/m. 43

14 Nu Anba Jounal fo Engineeing Sciences q H =800W/m q H =400W/m Pesent study Pesent study Sak et al. [11] Sak et al. [11] θº Fig. (13): Compaison between the pesent numeical pedictions with the pevious wok. 44

15 Anba Jounal fo Engineeing Sciences وليد محمد عبد مدرس/ كلية الهندسة جامعة االنبار عامر جميل شريف مدرس مساعد / كلية الهندسة جامعة االنبار احمد علي نجيب مدرس مساعد / كلية الهندسة جامعة االنبار الخالصة. FLUENT CFD package (4.87%)