Experimental analysis of natural convection over a vertical cylinder

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Experimental analysis of natural convection over a vertical cylinder

  1. 1. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 3, May - June (2013) © IAEME54EXPERIMENTAL ANALYSIS OF NATURAL CONVECTION OVER AVERTICAL CYLINDER AT UNIFORM TEMFERATURED. Subramanyam 1M. Chandrasekhar 2R. Lokanadham 31Professor, Department of Mechanical Engg, CREC, Tirupati, India2Associate Professor, Department of Mechanical Engg, CREC, Tirupati, India3Associate Professor, Department of Mechanical Engg, CREC, Tirupati, IndiaABSTRACTIn the present work, an experimental study of natural convection heat transfer invertical circular cylinders immersed in air at uniform wall temperature has beenpresented. The outcome of the study is summarized with practical correlation equationslinking to the Nusselt number to the Rayleigh number and Prandtl number. The proposedregression model was good agreement with the regression models given by previousauthors.Keywords: Vertical Cylinder, Natural Convection, Uniform Temperature1 INTRODUCTIONStudy of natural convection from over vertical heated cylinders is important inmany applications like vertical tubes of HVAC systems in resistive heating of electroniccomponents, space shuttle launch pads, wasted nuclear rods stored in repositories,refrigerating coils and hot radiators etc. To facilitate approximate solution of the set ofcoupled conservation equations descriptive of natural convection from a vertical cylinder,various assumptions need to be implemented, such as uniform surface temperature oruniform surface heat flux, unidirectional heat transfer, geometrically similar boundarylayer flows etc. Sparrow and Gregg [14] provided the first approximate solution for thelaminar buoyant flow of air bathing a vertical cylinder heated with a prescribed surfaceINTERNATIONAL JOURNAL OF MECHANICAL ENGINEERINGAND TECHNOLOGY (IJMET)ISSN 0976 – 6340 (Print)ISSN 0976 – 6359 (Online)Volume 4, Issue 3, May - June (2013), pp. 54-62© IAEME: www.iaeme.com/ijmet.aspJournal Impact Factor (2013): 5.7731 (Calculated by GISI)www.jifactor.comIJMET© I A E M E
  2. 2. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 3, May - June (2013) © IAEME55temperature by applying the similar method and later using a power series expansion.Aziz and Na [1] have applied the method of extended perturbation series to solve laminarnatural convection from an isothermal, thin vertical cylinder. Laminar natural convectionalong the outer surface a vertical cylinder is compared with a vertical flat platenumerically by Fujii and Uehara [5].Large eddy simulations of natural convection along a vertical isothermal surfacehave been carried out by Yan and Nilsson [15] using a parallel CFD code. Three-dimensional convection of air in a vertical cylinder isothermally heated and cooled from aside wall was numerically computed both in magnetic and gravity fields by Filar et al. [4].Natural convection in vertical cylinder at variable temperature have been studiednumerically by Jose et al. [7], Kalabin et al. [8], Kwang Hyo Chung et al. [9], Naturalconvection from the outer surface of a vertical cylinder to liquids – has been studiedexperimentally by Fujii et al. [6].. Sad Jar all and Campo [12] have studied the naturalconvection heat transfer in vertical cylinders at constant heat flux experimentally.In the present investigation, the analysis was carried out to study the natural convectionover a vertical circular cylinder in laminar steady state at uniform wall temperatureenclosed in a large rectangular duct, experimentally.2 EXPERIMENTAL SETUP AND MEASUREMENT PROCEDUREWhen a uniform wall temperature is given, the natural convection heat transferproblem consists of predicting the wall-to-ambient temperature difference. Forexperiment, three cylindrical test sections of different sizes made from stainless steel 301SS were used. For test section #1, diameter (d1) = 5 cm and length (L1) = 20 cm; for testsection #2, d2 = 6 cm and L2 = 30.5 cm; and for test section # 3, d3 = 6 cm and L3 = 45.1cm. Each cylinder was placed vertically on a wooden stand inside a large wooden four-side box about 60 cm x 60 cm x 60 cm. The top ends of the vertical cylinders wereplugged with wooden pieces to avoid internal circulation of air.The required heat is generated by fixing heating coils inside the inner surface ofthe cylinder. An AC power supply is the available source to heat the vertical cylinders topre-set temperature values. The power supply is varied with the help of autotransformer.The voltage and current are measured with voltmeter (0-300 V) and ammeter (0-2A).Four RTD thermo couples of range 10°C---200°C with 0.1°C resolution, accuracy ±1°Cper the given range are fixed on the outer surface of the cylinder and connected to thetemperature indicator to measure the temperature. The surface temperature of a cylinderis the average temperature of the four thermo couples. The temperature differencebetween these thermo couples is ± 5°C. Fluid properties are evaluated at the filmtemperature, T= (Ti+To)/2.The experiments have been conducted for all the three test sections at uniformtemperatures. For all voltages, the delivering surface temperatures stayed within therange of 38-78°C. Heat conduction losses through the electric cables and wooden pieceswere not taken into consideration. The schematic diagram of experimental set-up isshown in Fig 1.1.
  3. 3. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 3, May - June (2013) © IAEME56Fig. 1.1: Physical ModelIn the present investigation, the analysis was carried out to study the naturalconvection over a vertical cylinder in laminar steady state condition at uniform walltemperature. The Grashof number, Rayleigh number and Nusselt number were determined bythe following expressions.23γβ TLgGr∆= -- (1)ϑαβ TLgRa∆=3-- (2)T4Wooden boxT1T2T3HHHHWooden StandWooden capCircularCylinderT1 - T4: ThermocouplesH: Heating CoilsAirAir
  4. 4. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 3, May - June (2013) © IAEME57kLhNu = -- (3)=thNu9416925.0Pr492.0167.068.0++RaFor Ra<109--(4)4 RESULTS AND DISCUSSIONSFrom the experimental results of three set sections, the relationship betweenexperimental Nusselt number (Nu), theotical Nusselt number (Nuth), Rayleigh number (Ra)and Prandtl number (Pr) were established and shown in Fig 1.2, Fig1.3.Fig1.4 respectively.From the Fig. 1.2, it is observed that the Nusselt number increases with increasing Rayleighnumber. The trend is linear, and the relationship is given by the following equations:26.0241.1 RaNu = for d1 --(5)141.0125.8 RaNu = for d2 --(6)35.0242.0 RaNu = for d3 --(7)The correlation coefficient for d1 is 0.97; for d2 is 0.89 and for d3 is 0.94, indicating afairly good fit.From Fig.1.3, it is observed that the Nusselt number increases with increasing Rayleighnumber. The trend is linear, and the relationship is given by the following equations:25.0554.0 RaNu = for d1 --(8)22.0891.0 RaNu = for d2 --(9)25.0519.0 RaNu = for d3 --(10)The correlation coefficient for d1 is 0.99; for d2 is 0.97 and for d3 is 0.99, indicating avery good fit. The relationship between product of Rayleigh number & Prandtl number(Ra.Pr) and theoretical Nusselt number is shown in Fig. 1.4. It is observed that the theoreticalNusselt number increases with increasing the product of Rayleigh number and Prandtlnumber. The trend is linear and the relationship is given by the following equation withcorrelation coefficient 0.98.Nuth = 0.678 (Ra.Pr)0.25--(11)
  5. 5. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 3, May - June (2013) © IAEME58Ra vs Nu0501001502000 50000000 100000000RaNued1d3d2Fig. 1.2: Ra vs NuRa vs Nuth01020304050600 50000000 100000000RaNuthd1d2d3Fig. 1.3: Ra vs NuthRa.Pr vs Nuth0102030400 5000000 10000000 15000000 20000000Ra.PrNuthFig. 1.4: Ra.Pr vs. NuthNu
  6. 6. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 3, May - June (2013) © IAEME595 VALIDATIONThe validity of the proposed regression model for predicting Nusselt number in termsof Rayleigh number and Prandtl number is best assessed by comparing the predicted valueswith values obtained by the other numerical models. For this purpose reported regressionmodels of different Authors were compared with the proposed regression model.Comparison of the present results with Bejan & LeFevreThe validity of the proposed regression models for predicting Nusselt number in termsof Rayleigh number and Prandtl number is best assessed by comparing the predicted valueswith values obtained by the other numerical models. For this purpose reported regressionmodels of Bejan and LeFevre for the case of free convection heat transfer in vertical cylinderat uniform wall temperature is given below:According to Bejan , Nu = 0.689 (RaPr)0.25for Ra < 109- (12)proposed regression model, Nu = 0.678 (Ra. Pr)0.25for Ra < 109-(13)According to Le FevreDPHPPPRNurrrra)6364(35)315272(4)2120(5734 41++++= - (14)Table.1. Comparison of the present results with BejanRaNu 2 x 1052 x 1062 x 1072 x 1082 x 109Bejan Nu 13.33 23.70 42.15 74.95 133.28Present Nu 11.65 20.24 35.18 61.14 106.24Deviation 1.68 3.46 6.97 13.81 27.04Table. 2. Comparison of the present results with Le Fevre [62]RaNu 2 x 1052 x 1062 x 1072 x 1082 x 109Le Fevre 11.56 20.55 36.54 64.98 115.56Present Nu 11.65 20.24 35.18 61.14 106.24Deviation 0.009 0.31 1.36 3.84 9.32
  7. 7. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 3, May - June (2013) © IAEME60The predicted values of Nusselt number at Pr = 0.7 from Bejan expression (11), andthe proposed regression model are shown in table 1. The predicted values of Nusselt numberby using proposed regression model are lower than the results of Bejan. The difference beingin the range of 12.6% to 20%, which indicate the good agreement between these two models.The predicted values of Nusselt number at Pr = 0.7 from expression (14) andproposed regression model are given in Table 2. The predicted values Nusselt numbers byboth expressions are close to each other. The difference being 0.8% to 8%, which indicatedthat these two models are in good agreement each other. The graphical representations ofthese three models are shown in Fig. 1.5.Fig. 1.5: Ra vs Nu6 CONCLUSIONSIn the present work, an experimental study of natural convection heat transfer invertical circular cylinders immersed in air at uniform wall temperature has been presented.The analysis was carried out along the length and diameter of the cylinders. The outcome ofthe study is summarized with practical correlation equations linking to the Nusselt number tothe Rayleigh number and Prandtl number. The proposed regression models were validatedwith the regression models given by the Bejan [11], and LeFevre et al. [62]. The proposedregression models are in good agreement with the above mentioned authors. Further, theanalysis can be extended to the cases of different aspect ratios, with different materials andwith different boundary conditions.REFERENCES1. Aziz. A and Na T.Y(1982). Improved Perturbation Solution for laminar naturalconvection on a vertical cylinder; J. of Heat and Mass Transfer, Vol. 16, No. 2,pp. 83-87 .Ra vs Nu01002003004002000 2000 20000200002E+09RaNuBejanpresentLeFevreFor Pr =0.7
  8. 8. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 3, May - June (2013) © IAEME612. Bejan, A(1984)., Convection heat transfer, 2ndedition, John Wiley and sons, Inc.,3. Bejan, A(2003)., Heat Transfer, John Wiley and Sons, Inc.4. Filar, P. and Fornalik E(2005)., Three-dimensional numerical computation formagnetic convection of air inside a cylinder heated and cooled isothermally from aside wall, Int. J. Heat and Mass Transfer, Vol. 48, No.9, pp. 1858- 1867.5. Fuji, T. and Uehara, H(1970). Laminar Natural Convective Heat transfer from theouter surface of vertical cylinder, Int. J. Heat and Mass Transfer, Vol. 13,pp. 607-615.6. Fuji, T., Takeuchi. M, Fuji, M., Suzaki, K. and H. Uehara(1970) ‘Experiments onnatural convection heat transfer from the outer surface of a vertical cylinder’, Int. J.Heat and Mass Transfer, Vol. 13, pp. 753-770 ,7. Jose, L. Munoz-Cobo, Jose M. Corberan, Sergiochiva(2003), ‘Explicit formulas Forlaminar natural Convection Heat Transfer along vertical cylinders with power – lawwall temperature distribution’, J. of Heat and Mass Transfer, Vol. 39, pp. 215-222.8. Kalabin, E.V., Kanashina, M.V. and P.T. Zubkov(20050), ‘Natural Convection HeatTransfer in a Square Cavity with time-varying side-wall temperature’,J. Numerical Heat Transfer, Part A, Vol. 47, pp. 621-631.9. Kwang Hyochung, Jae Min Hyun and Hiroyuki Ozoe(2000), ‘Buoyant Convection ina vertical cylinder with azimuthally-varying sidewall temperature’, Int. J. of Heatand Mass Transfer, Vol. 43, pp. 2289-2301.10. LeFevre E.J. and A.J. Ede(1956), Laminar free convection from the outer surface ofvertical circular cylinder, Proc. Ninth. Int. Congr. Appl. Mech., Brussels, Vol.4,pp. 175-183.11. Nag, P.K(2008). Heat and Mass Transfer, Second Edition, Tata McGraw-HillPublishing Company Limited, New Delhi12. Sachdeva, R.C(2005)., Fundamentals of Engineering Heat and Mass Transfer, 2ndEdition, New Age International Publishers.13. Sad Jarah and Antonio Campo(2005),Experimental study of natural convection fromelectrically heated vertical cylinders immersed in air’, J. of Experimental HeatTransfer, Vol. 18, pp. 127-134.14. Sparrow, E.M.and J.L. Gregg(1956 ),Laminar Free Convection Heat transfer fromthe outer surface of a vertical circular cylinder, Trans. ASME, Vol. 78, pp. 1823-1829.15. Yan, Z.H. and E.E.A. Nilson( 2005 ) ‘Large eddy simulation of natural convectionalong a verticalisothermal surface’.J.ofHeatMassTransfer,Vol.46, pp. 1004- 1013.16. Ashok Tukaram Pise and Umesh Vandeorao Awasarmol, “Investigation ofEnhancement of Natural Convection Heat Transfer from Engine Cylinder withPermeable Fins”, International Journal of Mechanical Engineering & Technology(IJMET), Volume 1, Issue 1, 2010, pp. 238 - 247, ISSN Print: 0976 – 6340, ISSNOnline: 0976 – 6359.17. Sabyasachi Mondal,Tapas Ray Mahapatra and Dulal Pal, “Natural Convection in aTwo-Sided Lid-Driven Inclined Porous Enclosure with Sinusoidal Thermal BoundaryCondition”, International Journal of Mechanical Engineering & Technology (IJMET),Volume 3, Issue 3, 2012, pp. 187 - 202, ISSN Print: 0976 – 6340, ISSN Online: 0976– 6359.
  9. 9. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 3, May - June (2013) © IAEME62AUTHORS’ INFORMATIONDr. D. Subramanyam has received Ph.D in 2010 and M.Tech in2005 from S.V.University, Tirupati, Andhra pradesh, India. His previouswas research focused on Heat transfer. He is working as Professor inMechanical Engineering at CREC, Tirupati, India.M. Chandrasekhar has received M.Tech in ManufacturingEngineering in 2006 from VIT University, Vellore, India. He is workingas Associate professor in Mechanical Engineering at CREC, Tirupati,Andhra pradesh, India.R. Lokanadham is research scholar in mechanical engineering atS.V.University, Tirupati, Andhra pradesh, India. He has received M.E inThermal Engineering in 1999 from Bharatiyar University, Tamilnadu,India. He is working as Associate Professor in Mechanical Engineeringat CREC, Tirupati, A.P, India.

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