6340(Print), ISSN (Online) Volume 4, Issue 3, May - June (2013) IAEME AND TECHNOLOGY (IJMET)

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1 INTERNATIONAL International Journal of Mechanical JOURNAL Engineering OF MECHANICAL and Technology (IJMET), ENGINEERING ISSN 0976 AND TECHNOLOGY (IJMET) ISSN (Print) ISSN (Online) Volume 4, Issue 3, May - June (2013), pp IAEME: Journal Impact Factor (2013): (Calculated by GISI) IJMET I A E M E EXPERIMENTAL ANALYSIS OF NATURAL CONVECTION OVER A VERTICAL CYLINDER AT UNIFORM TEMFERATURE D. Subramanyam 1 M. Chandrasekhar 2 R. Lokanadham 3 1 Professor, Department of Mechanical Engg, CREC, Tirupati, India 2 Associate Professor, Department of Mechanical Engg, CREC, Tirupati, India 3 Associate Professor, Department of Mechanical Engg, CREC, Tirupati, India ABSTRACT In the present work, an experimental study of natural convection heat transfer in vertical circular cylinders immersed in air at uniform wall temperature has been presented. The outcome of the study is summarized with practical correlation equations linking to the Nusselt number to the yleigh number and Prandtl number. The proposed regression model was good agreement with the regression models given by previous authors. Keywords: Vertical Cylinder, Natural Convection, Uniform Temperature 1 INTRODUCTION Study of natural convection from over vertical heated cylinders is important in many applications like vertical tubes of HVAC systems in resistive heating of electronic components, space shuttle launch pads, wasted nuclear rods stored in repositories, refrigerating coils and hot radiators etc. To facilitate approximate solution of the set of coupled conservation equations descriptive of natural convection from a vertical cylinder, various assumptions need to be implemented, such as uniform surface temperature or uniform surface heat flux, unidirectional heat transfer, geometrically similar boundary layer flows etc. Sparrow and Gregg [14] provided the first approximate solution for the laminar buoyant flow of air bathing a vertical cylinder heated with a prescribed surface 54

2 temperature 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 laminar natural convection from an isothermal, thin vertical cylinder. Laminar natural convection along the outer surface a vertical cylinder is compared with a vertical flat plate numerically by Fujii and Uehara [5]. Large eddy simulations of natural convection along a vertical isothermal surface have been carried out by Yan and Nilsson [15] using a parallel CFD code. Threedimensional convection of air in a vertical cylinder isothermally heated and cooled from a side 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 studied numerically by Jose et al. [7], Kalabin et al. [8], Kwang Hyo Chung et al. [9], Natural convection from the outer surface of a vertical cylinder to liquids has been studied experimentally by Fujii et al. [6].. Sad Jar all and Campo [12] have studied the natural convection heat transfer in vertical cylinders at constant heat flux experimentally. In the present investigation, the analysis was carried out to study the natural convection over a vertical circular cylinder in laminar steady state at uniform wall temperature enclosed in a large rectangular duct, experimentally. 2 EXPERIMENTAL SETUP AND MEASUREMENT PROCEDURE When a uniform wall temperature is given, the natural convection heat transfer problem consists of predicting the wall-to-ambient temperature difference. For experiment, three cylindrical test sections of different sizes made from stainless steel 301 SS were used. For test section #1, diameter (d 1 ) = 5 cm and length (L 1 ) = 20 cm; for test section #2, d 2 = 6 cm and L 2 = 30.5 cm; and for test section # 3, d 3 = 6 cm and L 3 = 45.1 cm. Each cylinder was placed vertically on a wooden stand inside a large wooden fourside box about 60 cm x 60 cm x 60 cm. The top ends of the vertical cylinders were plugged with wooden pieces to avoid internal circulation of air. The required heat is generated by fixing heating coils inside the inner surface of the cylinder. An AC power supply is the available source to heat the vertical cylinders to pre-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 C with 0.1 C resolution, accuracy ±1 C per the given range are fixed on the outer surface of the cylinder and connected to the temperature indicator to measure the temperature. The surface temperature of a cylinder is the average temperature of the four thermo couples. The temperature difference between these thermo couples is ± 5 C. Fluid properties are evaluated at the film temperature, T= (Ti+To)/2. The experiments have been conducted for all the three test sections at uniform temperatures. For all voltages, the delivering surface temperatures stayed within the range of C. Heat conduction losses through the electric cables and wooden pieces were not taken into consideration. The schematic diagram of experimental set-up is shown in Fig

3 Air Wooden box Wooden cap H H T1 H T2 T3 H T4 Circular Cylinder Air Wooden Stand T1 - T4: Thermocouples H: Heating Coils Fig. 1.1: Physical Model In the present investigation, the analysis was carried out to study the natural convection over a vertical cylinder in laminar steady state condition at uniform wall temperature. The Grashof number, yleigh number and Nusselt number were determined by the following expressions. Gr 3 g β L T = -- (1) 2 γ = 3 g β L T α ϑ -- (2) 56

4 h L Nu = -- (3) k Nu th = Pr For < (4) 4 RESULTS AND DISCUSSIONS From the experimental results of three set sections, the relationship between experimental Nusselt number (Nu), theotical Nusselt number (Nu th ), yleigh number () 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 yleigh number. The trend is linear, and the relationship is given by the following equations: 0.26 Nu = for d 1 --(5) Nu = for d 2 --(6) 0.35 Nu = for d 3 --(7) The correlation coefficient for d 1 is 0.97; for d 2 is 0.89 and for d 3 is 0.94, indicating a fairly good fit. From Fig.1.3, it is observed that the Nusselt number increases with increasing yleigh number. The trend is linear, and the relationship is given by the following equations: 0.25 Nu = for d 1 --(8) 0.22 Nu = for d 2 --(9) 0.25 Nu = for d 3 --(10) The correlation coefficient for d 1 is 0.99; for d 2 is 0.97 and for d 3 is 0.99, indicating a very good fit. The relationship between product of yleigh number & Prandtl number (.Pr) and theoretical Nusselt number is shown in Fig It is observed that the theoretical Nusselt number increases with increasing the product of yleigh number and Prandtl number. The trend is linear and the relationship is given by the following equation with correlation coefficient Nu th = (.Pr) (11) 57

5 vs Nu d1 d3 d2 Nu Nue Fig. 1.2: vs Nu Nuth vs Nuth Fig. 1.3: vs Nuth d1 d2 d3 Nuth Pr vs Nuth Pr Fig. 1.4:.Pr vs. Nuth 58

6 5 VALIDATION The validity of the proposed regression model for predicting Nusselt number in terms of yleigh number and Prandtl number is best assessed by comparing the predicted values with values obtained by the other numerical models. For this purpose reported regression models of different Authors were compared with the proposed regression model. Comparison of the present results with Bejan & LeFevre The validity of the proposed regression models for predicting Nusselt number in terms of yleigh number and Prandtl number is best assessed by comparing the predicted values with values obtained by the other numerical models. For this purpose reported regression models of Bejan and LeFevre for the case of free convection heat transfer in vertical cylinder at uniform wall temperature is given below: According to Bejan, Nu = (Pr) 0.25 for < (12) proposed regression model, Nu = (. Pr) 0.25 for < (13) According to Le Fevre Nu Pr 4 ( Pr ) H = + - (14) 3 5( Pr ) 35 ( Pr ) D Table.1. Comparison of the present results with Bejan Nu 2 x x x x x 10 9 Bejan Nu Present Nu Deviation Table. 2. Comparison of the present results with Le Fevre [62] Nu 2 x x x x x 10 9 Le Fevre Present Nu Deviation

7 The predicted values of Nusselt number at Pr = 0.7 from Bejan expression (11), and the proposed regression model are shown in table 1. The predicted values of Nusselt number by using proposed regression model are lower than the results of Bejan. The difference being in 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) and proposed regression model are given in Table 2. The predicted values Nusselt numbers by both expressions are close to each other. The difference being 0.8% to 8%, which indicated that these two models are in good agreement each other. The graphical representations of these three models are shown in Fig Nu vs Nu For Pr =0.7 Bejan present LeFevre E+09 Fig. 1.5: vs Nu 6 CONCLUSIONS In the present work, an experimental study of natural convection heat transfer in vertical 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 of the study is summarized with practical correlation equations linking to the Nusselt number to the yleigh number and Prandtl number. The proposed regression models were validated with the regression models given by the Bejan [11], and LeFevre et al. [62]. The proposed regression models are in good agreement with the above mentioned authors. Further, the analysis can be extended to the cases of different aspect ratios, with different materials and with different boundary conditions. REFERENCES 1. Aziz. A and Na T.Y(1982). Improved Perturbation Solution for laminar natural convection on a vertical cylinder; J. of Heat and Mass Transfer, Vol. 16, No. 2, pp

8 2. Bejan, A(1984)., Convection heat transfer, 2 nd edition, 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 for magnetic convection of air inside a cylinder heated and cooled isothermally from a side wall, Int. J. Heat and Mass Transfer, Vol. 48, No.9, pp Fuji, T. and Uehara, H(1970). Laminar Natural Convective Heat transfer from the outer surface of vertical cylinder, Int. J. Heat and Mass Transfer, Vol. 13, pp Fuji, T., Takeuchi. M, Fuji, M., Suzaki, K. and H. Uehara(1970) Experiments on natural convection heat transfer from the outer surface of a vertical cylinder, Int. J. Heat and Mass Transfer, Vol. 13, pp , 7. Jose, L. Munoz-Cobo, Jose M. Corberan, Sergiochiva(2003), Explicit formulas For laminar natural Convection Heat Transfer along vertical cylinders with power law wall temperature distribution, J. of Heat and Mass Transfer, Vol. 39, pp Kalabin, E.V., Kanashina, M.V. and P.T. Zubkov(20050), Natural Convection Heat Transfer in a Square Cavity with time-varying side-wall temperature, J. Numerical Heat Transfer, Part A, Vol. 47, pp Kwang Hyochung, Jae Min Hyun and Hiroyuki Ozoe(2000), Buoyant Convection in a vertical cylinder with azimuthally-varying sidewall temperature, Int. J. of Heat and Mass Transfer, Vol. 43, pp LeFevre E.J. and A.J. Ede(1956), Laminar free convection from the outer surface of vertical circular cylinder, Proc. Ninth. Int. Congr. Appl. Mech., Brussels, Vol.4, pp Nag, P.K(2008). Heat and Mass Transfer, Second Edition, Tata McGraw-Hill Publishing Company Limited, New Delhi 12. Sachdeva, R.C(2005)., Fundamentals of Engineering Heat and Mass Transfer, 2 nd Edition, New Age International Publishers. 13. Sad Jarah and Antonio Campo(2005),Experimental study of natural convection from electrically heated vertical cylinders immersed in air, J. of Experimental Heat Transfer, Vol. 18, pp Sparrow, E.M.and J.L. Gregg(1956 ),Laminar Free Convection Heat transfer from the outer surface of a vertical circular cylinder, Trans. ASME, Vol. 78, pp Yan, Z.H. and E.E.A. Nilson( 2005 ) Large eddy simulation of natural convection along a verticalisothermal surface.j.ofheatmasstransfer,vol.46, pp Ashok Tukaram Pise and Umesh Vandeorao Awasarmol, Investigation of Enhancement of Natural Convection Heat Transfer from Engine Cylinder with Permeable Fins, International Journal of Mechanical Engineering & Technology (IJMET), Volume 1, Issue 1, 2010, pp , ISSN Print: , ISSN Online: Sabyasachi Mondal,Tapas y Mahapatra and Dulal Pal, Natural Convection in a Two-Sided Lid-Driven Inclined Porous Enclosure with Sinusoidal Thermal Boundary Condition, International Journal of Mechanical Engineering & Technology (IJMET), Volume 3, Issue 3, 2012, pp , ISSN Print: , ISSN Online:

9 AUTHORS INFORMATION Dr. D. Subramanyam has received Ph.D in 2010 and M.Tech in 2005 from S.V.University, Tirupati, Andhra pradesh, India. His previous was research focused on Heat transfer. He is working as Professor in Mechanical Engineering at CREC, Tirupati, India. M. Chandrasekhar has received M.Tech in Manufacturing Engineering in 2006 from VIT University, Vellore, India. He is working as Associate professor in Mechanical Engineering at CREC, Tirupati, Andhra pradesh, India. R. Lokanadham is research scholar in mechanical engineering at S.V.University, Tirupati, Andhra pradesh, India. He has received M.E in Thermal Engineering in 1999 from Bharatiyar University, Tamilnadu, India. He is working as Associate Professor in Mechanical Engineering at CREC, Tirupati, A.P, India. 62