ESCI
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ISSN 打印: 19402503
ISSN 在线: 19402554
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国际计算热科学期刊
DOI: 10.1615/ComputThermalScien.2020028346
pages 120
THREEDIMENSIONAL NATURAL CONVECTION PHENOMENA AROUND A UNIFORMLY HEATED CUBICAL BODY LOCATED AT THE CENTER OF A SPHERICAL ENCLOSURE
Hedia Welhezi
Laboratory of Physics of Fluids, Physics Department, Faculty of Science of Tunis, University of
Tunis ElManar, 2092 ElManar 2, Tunis, Tunisia
Nader BenCheikh
Laboratory of Mechanic of Fluids, Physics Department, Faculty of Sciences of Tunis, University of Tunis ElManar, 2092 ElManar II, Tunis, Tunisia
Brahim BenBeya
Laboratory of Physics of Fluids, Physics Department, Faculty of Science of Tunis, University of
Tunis ElManar, 2092 ElManar 2, Tunis, Tunisia
ABSTRACT
This investigation addresses a systematic numerical method based on the finite volume method and a full multigrid technique to study threedimensional natural convection phenomena around a heated cube placed inside a concentric airfilled spherical enclosure. In this work, we observed the flow structures and heat transfer characteristics in the enclosure according to the variation of the Rayleigh number. The computation is performed for Rayleigh numbers ranging from 10^{2} to 10^{6}, and the Prandtl number is of Pr = 0.71. Typical sets of streamlines and isotherms are presented to analyze the intricate circulatory flow patterns set up by the buoyancy force of the fluid. The variation of the local and surfaceaveraged Nusselt numbers at the inner hot cube wall are also presented to exhibit the overall heat transfer characteristics inside the enclosure. It was found that, when the Rayleigh numbers are low, the isotherms are approximately parallel and the conduction is the dominant heat transfer mode; whereas, as the Rayleigh number increases, buoyancyinduced convection heat transfer becomes dominant and the isotherms are squeezed because of the stronger convection effects. Results also indicate that an optimal average heat transfer rate is obtained for Rayleigh number set to 10^{2} for both cases of the spherical enclosure and inner cube.
REFERENCES

Achdou, Y. and Guermond, J.L., Convergence Analysis of a Finite Element Projection LagrangeGalerkin Method for the Incompressible NavierStokes Equations, SIAMJ. Numer. Anal., vol. 37, pp. 799826,2000.

Angeli, D., Levoni, P., and Barozzi, G.S., Numerical Predictions for Stable Buoyant Regimes within a Square Cavity Containing a Heated Horizontal Cylinder, Int. J. Heat Mass Transf., vol. 51, pp. 553565,2008.

BenCheikh, N., BenBeya, B., and Lili, T., Benchmark Solution for TimeDependent Natural Convection Flows with an Accelerated FullMultigrid Method, Numer. Heat Transf, PartB, vol. 52, pp. 131151,2007.

BenCheikh, N., BenBeya, B., and Lili, T., A Multigrid Method for Solving the NavierStokes/Boussinesq Equations, Commun. Numer. Methods Eng., vol. 24, pp. 671681,2008.

Bishop, E.H., Kolflat, R.S., Mack, L.R., and Scanlan, J.A., Convective Heat Transfer between Concentric Spheres, Proc. of 1964 Heat Transfer and Fluid Mechanics Institute, Stanford University Press, pp. 6980,1964.

Bishop, E.H., Mack, L.R., and Scanlan, J.A., Heat Transfer by Natural Convection between Concentric Spheres, Int. J. Heat Mass Transf., vol. 9, pp. 649662,1966.

Cesinia, G., Paroncinia, M., Cortellab, G., and Manzanb, M., Natural Convection from a Horizontal Cylinder in a Rectangular Cavity, Int. J. Heat Mass Transf., vol. 42, pp. 18011811,1999.

Choi, C.Y., Jo, H.W., Ha, M.Y., and Yoon, H.S., Effect of Circular Cylinder Location on ThreeDimensional Natural Convection in a Cubical Enclosure, J. Mech. Sci. Technol., vol. 29, pp. 13071318,2015.

Crawford, L. and Lemlich, R., Natural Convection in Horizontal Concentric Cylindrical Annuli, Ind. Eng. Chem. Fundam., vol. 1, pp. 260264,1962.

De, A.K. and Dalal, A., A Numerical Study of Natural Convection around a Square, Horizontal, Heated Cylinder Placed in an Enclosure, Int. J. Heat Mass Transf., vol. 49, pp. 46084623,2006.

de Vahl Davis, G., Natural Convection of Air in a Square Cavity a Benchmark Numerical Solution, Int. J. Numer. Method Fluid, vol. 3, pp. 249264,1983.

Feldman, Y. and Colonius, T., On a Transitional and Turbulent Natural Convection in Spherical Shells, Int. J. Heat Mass Transf., vol. 64, pp. 514525,2013.

Frederick, R.L. and Quiroz, F., On the Transition from Conduction to Convection Regime in a Cubical Enclosure with a Partially Heated Wall, Int. J. Heat Mass Transf., vol. 44, pp. 16991709,2001.

Fusegi, T., Hyun, J.M., Kuwahara, K., and Farouk, B., A Numerical Study of ThreeDimensional Natural Convection in a Differentially Heated Cubical Enclosure, Int. J. Heat Mass Transf., vol. 34, pp. 15431557,1991.

Gangawane, K.M. and Manikandan, B., Laminar Natural Convection Characteristics in an Enclosure with Heated Hexagonal Block for NonNewtonian Power Law Fluids, Chin. J. Chem. Eng., vol. 25, pp. 555571,2017.

Ghaddar, N.K., Natural Convection Heat Transfer between a Uniformly Heated Cylindrical Element and Its Rectangular Enclosure, Int. J. Heat Mass Transf., vol. 35, pp. 23272334,1992.

Ghaddar, N.K. and Thiele, F., Natural Convection over a Rotating Cylindrical Heat Source in a Rectangular Enclosure, Numer. Heat Transf., Part A, vol. 26, pp. 701717,1994.

Gulberg, Y. and Feldman, Y., On Laminar Natural Convection inside MultiLayered Spherical Shells, Int. J. Heat Mass Transf., vol. 91, pp. 908921,2015.

Ha, M.Y. and Jung, M.J., A Numerical Study on ThreeDimensional Conjugate Heat Transfer of Natural Convection and Conduction in a Differentially Heated Cubic Enclosure with a HeatGenerating Cubic Conducting Body, Int. J. Heat Mass Transf., vol. 43, pp. 42294248,2000.

Ha, M.Y., Kim, I.K., Yoon, H.S., Yoon, K.S., Lee, J.R., Balachandar, S., and Chun, H.H., Two Dimensional and Unsteady Natural Convection in a Horizontal Enclosure with a Square Body, Numer. Heat Transf., Part A, vol. 41, pp. 183210,2002.

Hortmann, M., Peric, M., and Scheuerer, G., Finite Volume Multigrid Prediction of Laminar Natural Convection: Benchmark Solutions, Int. J. Numer. Methods Fluids, vol. 11, pp. 189207,1990.

Ingham, D.B., Heat Transfer by Natural Convection between Spheres and Cylinders, Numer. Heat Transf., vol. 4, pp. 5367,1981.

Lee, J.R., Ha, M.Y., Balachandar, S., Yoon, H.S., and Lee, S.S., Natural Convection in a Horizontal Layer of Fluid with a Periodic Array of Square Cylinders in the Interior, Phys. Fluids, vol. 16, pp. 10971117,2004.

Lee, J.M., Ha, M.Y., and Yoon, H.S., Natural Convection in a Square Enclosure with a Circular Cylinder at Different Horizontal and Diagonal Locations, Int. J. Heat Mass Transf., vol. 53, pp. 59055919,2010.

Leonard, B.P., A Stable and Accurate Convective Modeling Procedure based on Quadratic Upstream Interpolation, Comput. Methods Appl. Mech. Eng., vol. 19, pp. 5998,1979.

Leonard, B.P., Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods, Philadelphia: SIAM, 1994.

Mack, L.R. and Hardee, H.C., Natural Convection between Concentric Spheres at Low Rayleigh Numbers, Int. J. Heat Mass Transf., vol. 11, pp. 387396,1968.

Mellah, S., BenCheikh, N., BenBeya, B., and Lili, T., Effects of a Heated Strip Arrangement on Heat Transfer Rate in Cubical Enclosures, High. Temp., vol. 52, pp. 688696,2014.

Nabavizadeh, S.A., Talebi, S., and Sefid, M., Natural Convection in a Square Cavity Containing a Sinusoidal Cylinder, Int. J. Therm. Sci., vol. 51, pp. 112120,2012.

Ostrach, S., Natural Convection in Enclosures, Adv. Heat Transf., vol. 8, pp. 161227,1972.

Padilla, E.L.M., Campregher, R., and SilveiraNeto, A., Numerical Analysis of the Natural Convection in Horizontal Annuli at Low and Moderate Ra, Eng. Termica (Thermal Eng.), vol. 5, pp. 5865,2006.

Patankar, S.V., Numerical Heat Transfer and Fluid Flow, New York: McGrawHill, 1980.

Powe, R.E. and Warrington, Jr., R.O., Natural Convection Heat Transfer between Bodies and Their Spherical Enclosure, J. Heat Transf., vol. 105, pp. 440446,1983.

Roslan, R., Saleh, H., Hashim, I., and Bataineh, A.S., Natural Convection in an Enclosure Containing a Sinusoidally Heated Cylindrical Source, Int. J. Heat Mass Transf., vol. 70, pp. 119127,2014.

Roychowdhury, D.G., Das, S.K., and Sundararajan, T.S., Numerical Simulation of Natural Convective Heat Transfer and Fluid Flow around a Heated Cylinder Inside an Enclosure, Heat Mass Transf., vol. 38, pp. 565576,2002.

Scalan, J.A., Bishop, E.H., and Powe, R.E., Natural Convection Heat Transfer between Concentric Spheres, Int. J. Heat Mass Transf., vol. 13, pp. 18571872,1970.

Shyam, R., Sairamu, M., Nirmalkar, N., and Chhabra, R.P., Free Convection from a Heated Circular Cylinder in Confined PowerLaw Fluids, Int. J. Therm. Sci, vol. 74, pp. 156173,2013.

Souayeh, B., BenCheikh, N., and BenBeya, B., Numerical Simulation of ThreeDimensional Natural Convection in a Cubic Enclosure Induced by an IsothermallyHeated Circular Cylinder at Different Inclinations, Int. J. Therm. Sci., vol. 110, pp. 325339,2016.

Tasnim, S.H., Mahmud, S., and Das, P., Effect of Aspect Ratio and Eccentricity on Heat Transfer from a Cylinder in a Cavity, Int. J. Numer. Meth. Heat Fluid Flow, vol. 12, pp. 855869,2002.

Weber, N., Powe, R.E., Bishop, E.H., and Scanlan, J.A., Heat Transfer by Natural Convection between Vertically Eccentric Spheres, Trans. ASME J. Heat Transf., vol. 95, pp. 4752,1973.

Yoon, H.S., Yu, D.H., and Ha, M.Y., ThreeDimensional Natural Convection in an Enclosure with a Sphere at Different Vertical Locations, Int. J. Heat Mass Transf., vol. 53, pp. 31433155,2010.

Yoon, H.S., Jung, J.H., Lee, H.S., and Koo, B.Y., Effect of Thermal Boundary Condition of an Inner Cube on ThreeDimensional Natural Convection in a Cubical, J. Mech. Sci. Technol., vol. 29, pp. 45274543,2015.
