Int. J. Mec. Eng. & Rob. Res. 05 Ansar Ali S K et al., 05 Researc Paper LAMIAR FORCED COVECTIO TO FLUIDS I COILED PIPE SUBMERGED I AGITATED VESSEL Ansar Ali S K *, L P Sing and S Gupta 3 ISS 78 049 www.ijmerr.com Vol. 4, o., January 05 05 IJMERR. All Rigts Reserved *Corresponding Autor: Ansar Ali S K, ansnil@gmail.com Laminar forced convection in curved pipe placed in agitated vessel as been studied experimentally for te flow of bot ewtonian fluid (water) and power law non-ewtonian fluids (5%, % and % aqueous CMC solutions. Te eat transfer as been calculated using modified Wilson metod. It is found tat te usselt number is function of Dean and Prandtl numbers. Te following correlation is found for flow of ewtonian and power law non-ewtonian fluids flowing troug elical coils. 0.066 / D 0. Re Keywords: Agitated vessel, ewtonian, on-newtonian power law, Wilson metod ITRODUCTIO Laminar forced convection in curved pipes as received considerable attention. From te work of Kubair and Kuloor (966), Rajsekaran et al. (966 and 970), Akiyama and Ceng (97) and Dravid et al. (97), it is found tat not muc work as been done for non-ewtonian fluids in curved pipes. Te existing eat transfer data in te literature for fully developed laminar forced convection in curved pipe wit uniform wall temperature are rater limited and incomplete. For ewtonian fluids, perturbation metod was applied by Maekawa for extremely low Dean umber. Te boundary layer approximation near te wall was presented by Akiyama and Ceng (97) for ig dean number of order one. Dravid et al. (97) presented te numerical results in te termal entrance region for Dean umber less tan 5 and Pr = 5. Te improved later work of Akiyama and Ceng (97) sows tat te ratio of eat transfer coefficient in coil and in straigt pipe is a function of Dean umber as well as Prandtl number. Tus tere is a possibility of obtaining a suitable correlation of te following form Researc Scolar, Mecanical Engineering Department, SHIATS, Allaabad, India. Professor, Mecanical Engineering Department, SHIATS, Allaabad, India. 3 Professor, Mecanical Engineering Department, HIET, Gaziabad, India (Rtd. HOD, Department of Mecanical Engineering, ITBHU).
Int. J. Mec. Eng. & Rob. Res. 05 Ansar Ali S K et al., 05 = Ø ( D, Pr )...() Te advantage of te above form of correlation is tat for small D, te Equation () satisfies te condition tat = for very small D. may be calculated for isotermal laminar eat transfer in straigt tube for te case of uniform wall temperature and te parabolic velity distribution by following correlation as suggested by Mujawar and Raja Rao (997). / 3.75...() Gz For non-ewtonian fluids te above equation takes te form 3n 4n.75 / 3 Gz...(3) Here again it is important to note tat dean number contain Reynolds number and te viscosity term appears in bot Reynolds and Prandtl numbers. It is suggested tat te effective viscosity at te sear stress prevailing at te wall sould be used for evaluating te Reynolds and Prandtl numbers. From te above discussion it may be concluded tat te correlation may be written as follows b5 b6 C3DPr...(4) Te fluid eat transfer coefficient were calculated from overall coefficient U using Wilson grapical metod. U versus / 3 plot for water gives y c equal to 0.000. For different combinations of aqueous CMC solutions in te agitated vessel and flowing troug te coils is plotted against 3 / 3 U n yeieled separate straigt lines for different blade diameters. Te respective y c values were found to be 0.000445, 0.000575 and 0.000905 respectively. Te outside eat transfer coefficient of te coil tube from te coil side over all eat transfer coefficient U oe was calculated by following relation. U were Y and Yc...(5) c D c xdc dirt resistance ic D t K md...(6) tm 3n / 3 Y...(7) c Te calculated values of and for U 0.5% CMC, % CMC, % CMC tat of 4% CMC solution and tat of water for blade diameter 7.5 cm,.7 cm and 8.35 cm ave been used in te present work. Te liquid film coefficient inside te coiled tube, i.e., ic was calculated by te relation ic U Dt D o...(8) For a set of observation te fluid flow rate in te coil was varied at a constant rotational speed of te agitator and for tat set of readings was maintained constant. Te value of was obtained from te Wilson plot according to te relation Yc U...(9) 5
Int. J. Mec. Eng. & Rob. Res. 05 Ansar Ali S K et al., 05 EXPERIMETAL PROCEDURE Te experimental setup consisted of a flat bottomed cylindrical test vessel of 45.5 cm inner diameter and 60 cm. eigts made from /8 inc tick copper seet. Te vessel was jacketed by providing annular space surrounding it wit anoter cylinder of 44 cm eigt and made from /8 inc tick G.I seet. Te jacket and vessel assembly was adequately insulated from outside. A elical coil aving 34 cm mean coil diameter and made from.898 cm internal diameter and.5 cm outer diameter copper tubing was placed in te centre of te test vessel. A rectangular tank of about 300 litre capacity filled wit eaters was used to eat te water to a pre-determined temperature wic in turn was circulated troug te jacket (annular space around te test vessel) wit te elp of a centrifugal pump. Te fluid in te test vessel was agitated by marine type agitator fitted in te centre of te coil. Te agitator saft was driven at a known speed by a HP electric motor troug a reduction gear assembly. Provision was made for replacement of impeller of desired sape and size. Te water in te ot water tank was eated and te temperature of fluid was brougt to te desired level. Te temperature was controlled to a pre determined value wit te elp of temperature controller. Te water circulation was ten started in te coil as well as in te jacket and adjusted by means of regulating values and bypasses. Te agitator was ten started at a fixed rpm. At steady state condition te inlet and outlet water temperatures in te jacket, mass rate of water flow troug jacket and tat of fluid in te coil, rpm of te agitator and temperatures of fluid in te agitated vessel and tat of water in te storage tank were noted. Te test fluid side wall temperatures of te test vessel were noted at different lations and at different eigts from its bottom wit te elp of copper constantan termouples. Te readings were duplicated to ensure te steady state and to eliminate any error in measurement. Similar measurements were made by varying te flow rate in te coil and ten by varying te rotational speed of te agitator. Te above predure was repeated for all te fluids. Te eat transfer caracteristics of five fluids, viz., water and four aqueous CMC solutions of concentration 0.5,, and 4% by weigt ave been investigated. Te reological properties were determined wit te elp of capillary tube viscometer. All te CMC solutions were found to be psuedoplastic in nature obeying power law relation. Te flow beavior indices were found to be 0.937, 0.85, 0.793, and 0.698 for 0.5%, %, % and 4% aqueous CMC solutions respectively. Termal conductivity of CMC solutions were determined by comparative concentric cylinders and were found to be equal to tat of water. Specific eats of te solutions, as measured by calorimetric metod, were found to be nearly equal to tat of water. RESULTS AD DISCUSSIO In order to obtain exponent b 5 and b 6 and constant C 3 in Equation (4) te proposed form of correlation for laminar forced convection to non-ewtonian fluids in elical coils 0.5, and 6
Int. J. Mec. Eng. & Rob. Res. 05 Ansar Ali S K et al., 05 % CMC solutions were investigated in a elical coil of 34 cm diameter made from a tube of diameter.898 cm. Before conducting te eat transfer runs, pressure drop measurements were made to verify te fitness of te coil. Coil flow is compared wit capillary sear flow in Figure. Friction factor f c is sown Figure 3: Laminar Flow Friction Factor in Helical Coils as a Function of Dean umber for on-ewtonial Fuids in Figure against Reynolds number Re defined by te following equation. D t U p Re...(0) Figure : Flow Diagram for 0.5%, % and % CMCA Troug HT Test Coil Te ratio of friction factor, f c, for coil to tat of straigt pipe, f SL evaluated at Reynolds number, Re, from equation f SL = 6/ Re plotted against D in Figure 3. is f f c sl 4. 0 0.33 log D...() Figure : Variation of Friction Factor wit Reynolds umber for Water, %, % and 0.5% CMCA Troug HT Test Coil Te Equation () proposed by Berger et al. (983) is also sown in tis figure. Te excellent agreement of te data wit above equation indicates te fitness of te coil and te eat transfer data obtained in tis coil could be placed for its accuracy. Tree non-ewtonian fluids: 0.5% (n = 0.937), % (n = 0.85) and % (n = 0.793) CMC in water, representative of pseudo plastic fluids obeying power law, and water, a ewtonian fluids were investigated. Most of te data, obtained, were in laminar region and only a few non-ewtonian data could fall in turbulent region. Om Prakas et al. ave sown tat te fluid flow data in elical coils over wide range of coil diameter and fluid beavior can 7
Int. J. Mec. Eng. & Rob. Res. 05 Ansar Ali S K et al., 05 successfully be correlated by te use of apparent viscosity µ z evaluated at te wall sear stress in Reynolds number Re. Tis suggests te possibility of analogous Figure 5: Variation of [( / ) ] wit D for Heat Transfer to on-ewtonian Fluids correlation in terms of te ratio was evaluated by Equation (3).. Effect of Dean umber In order to find te effect on te ratio of eat transfer in coil to eat transfer in straigt pipe, te first attempt was to plot te ratio against D on a logaritmic scale as sown in Figure 4. Figure 4: Variation of / wit D for Heat Transfer to on-ewtonian Fluids o direct relationsip is seen between te two variables in tis manner. At very low Dean umber or very small curvature, effect of secondary flow will be negligible and ten will be equal to. Terefore, te next attempt was to plot Tis plot is sown in Figure 5. against D. o net conclusion could be drawn even from tis figure except for some qualitative ones. Te eat transfer coefficient in coil is always iger tan in straigt pipe as it is seen tat is always greater tan unity. Te ratio ic / is increases wit Dean number, D. Tese data do not follow any particular trend. Tis may be explained by te fact tat due to non ewtonian beavior Prandtl number canges by cange of flow rate affecting te eat transfer rate. Data plotted for tree fluids in Figure 5 ave wide range of Prandtl number. However, an exponent of Dean umber ½ correlated te data muc better. Tis trial as been made on te basis of teoretical results presented by previous investigators. Effect of Prandtl umber Prandtl number pr was calculated by using apparent viscosity, evaluated at wall sear stress, w, obtained from te measured pressure drop. Te may be evaluated by te following derived expression k w / k n n 8
D e a n u m b e r Int. J. Mec. Eng. & Rob. Res. 05 Ansar Ali S K et al., 05 Subsequently Re = DtU/ and D = Re (D t /D c ) / In order to understand te effect of pr on Figure 7: Laminar Flow Heat Transfer Correlation for on-ewtonian Fuids Troug Coils te ratio ic / is, a logaritmic plot of / D versus pr is sown in Figure 6. Figure 6 clearly sows te effect of pr. Many oter trails were made by canging te exponent of Dean number D Figure 6., in te ordinate variable of Figure 6: Laminar Flow Heat Transfer Correlation for on-ewtonian Fuids Troug Coils: Effect of Prandtl umber 0. 0.066 / D pr...() Figure 8 compares te experimental usselt number wit corresponding values calculated from Equation (). It is found tat tat laminar flow eat transfer data in te range 4 < D < 000, pr < 5 and 0.793 < n < can successfully be correlated using Equation () wit a standard deviation of 5.5%. Values of exponent oter tan ½ on D tend to increase te scatter of data points. Te slope of mean line sown represents te exponent of pr and was estimated to be 0. for Prandtl number range of 4.9 to 5. Finally Figure 8: Comparison Between Experimental and Calculated Values of Laminar usselt umber UIC (Heat Transfer to on-ewtonian Fluids Troug Coil) 0. pr is plotted against D in Figure 7 to verify te exponent of D. Te mean line passing troug data points sow an exponent equal to ½. Te resulting correlation is obtained as: 9
Int. J. Mec. Eng. & Rob. Res. 05 Ansar Ali S K et al., 05 According to Ozisik and Topa kaglu s teoretical approac (08), tere is possibly of two regions to exist, namely te eated and cooled region in te fluid space and tat too depends upon Prandtl number. Tis equation is similar to te equation suggested by Mori and akjayama (09) for flow of ewtonian fluids across tube banks were te ratio and D. REFERECES is te function of pr. Akiyama M and Ceng K C (97), Boundary Vorticity Metod for Laminar Forced Convected Heat Transfer in Curved Pipe, Int. J. Heat Mass Trans., Vol. 4, Pt., p. 659.. Akiyama M and Ceng K C (97), Int. J. Heat Mass Trans., Vol. 5, o. 7, p. 46. 3. Berger S A, Talbot L and Yao L S (983), Flow in Curved Pipes, Annual Review Fluid Mecanics, Vol. 5, p. 46. 4. Cioncolini A and Santini L (006), An Experimental Investigation Regarding te Laminar to Turbulent Flow in Helically Coiled Pipes, Experimental Termal & Fluid Science, Vol. 30, p. 367. 5. Dravid A, Smit K A, Merrill E W and Brian P L T (97), Effect of Secondary Fluids on Laminar Flow Heat Transfer in Helical Coiled Tubes, A.I.C.E.J., Vol. 7, p. 4. 6. Kaya O and Teke I (005), Turbulent Forced Convection in Helically Coiled Square Duct wit One Uniform Temperature and Tree Adiabatic Walls, Heat Mass Transf., Vol. 4, pp. 9-37. 7. Kubair V and Kuloor R (966), Flow of ewtonian Fluids in Arcimedian Spiral Tube Coils: Correlation of te Laminar, Transition and Turbulent Flows, Ind. J. Tec., Vol. 4, p. 3. 8. Kumar V, Faizee B, Mrida M and igam K D P (008), umerical Studies of a Tube-in-Tube Helically Coiled Heat Excanger, Cem. Eng. Press, Vol. 47, pp. 87-95. 9. Kumar V, Gupta P and igam K D P (007), Fluid Flow and Heat Transfer in Curved Tubes wit Temperature Dependent Properties, Ind. Eng. Cem. Res., Vol. 46, pp. 36-336. 0. Kurnia J C, Sasmito A P and Mujumdar A S (0), Evaluation of Heat Transfer Performance of Helical Coils of on- Circular Tubes, J. Zejiang Univ. Sci. A, Vol., pp. 63-70.. Liou T M (99), Flow Visualization and LDV Measurement of Fully Developed Laminar Flow in Helically Coiled Tubes, Exp. Fluids, Vol., pp. 33-338.. Mandal M M and igam K D P (009), Experimental Study of Pressure Drop and Heat Transfer of Turbulent Flow in Tube Helical Heat Excanger, Ind. Eng. Cem. Res., Vol. 48, pp. 938-934. 3. Mandal M M, Kumar V and igam K D P (00), Augmentattion of Heat Transfer Performance in Coiled Flow Inverter visa-vis Conventional Heat Excanger, Cem. Eng. Sci., Vol. 65, pp. 999-007. 4. Metzner A B and Reed J C (955), Flow of on-ewtonian Fluids Correlation of Laminar, Transition and Turbulent Flow 30
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Int. J. Mec. Eng. & Rob. Res. 05 Ansar Ali S K et al., 05 omenclature b 5, b 6 constant in Equations (4) C 3 constant in Equation (4) D c D t D o f sl f c diameter of te coil elix, cm inner diameter of te straigt or coil tube outer diameter of te straigt or coil tube laminar flow friction factor in straigt pipe friction factot in coil ic coil inside eat transfer coefficient, kcal/r m C coil outside eat transfer coefficient, kcal/r m C k consistency index, gm sec n -/cm speed (r.p.m) pr Prandtl number UIC usselt number, ic D t /k UIS usselt number, is D t /k D GZ Dean number Graetz number, wc p /kl speed (r.p.m) n generalized flow beavior index U OC coil overall eat transfer coefficient, Kcal/r m C OC coil outside eat transfer coefficient, Kcal/r m C ic coil inside eat transfer coefficient, Kcal/r m C Y C X resistance of te jacket side fluid and te wall widt of te agitated vessel wall, cm Re Reynolds number defined by Equation (0) U average velity, cm P density, gm/cm 3 effective or pseudo sear viscosity, gm/cm W sear stress, gm(f)/cm e effective viscosity APPEDIX a apparent viscosity at te impeller tip 3