Buoyancy-Induced Convection in a Square Enclosure Discretely Heated at One Side and Cooled either at the Top or at the Bottom Using both Gases and Liquids as Working Fluids

Abstract:

Laminar natural convection heat and momentum transfer in fluid-filled, square enclosures partially heated at one side and cooled either at the top or at the bottom, is studied numerically. A computational code based on the SIMPLE-C algorithm is used to solve the system of the mass, momentum and energy transfer governing equations. Simulations are performed using the Rayleigh number based on the cavity width, the thermally-active fraction of the partially heated sidewall, and the Prandtl number of the working fluid, as independent variables. It is found that the top cooling is definitely more efficient than the bottom cooling. In both cooling configurations the average Nusselt number of the cavity increases as each controlling parameter is increased. On the basis of the results obtained, a set of dimensionless correlations is developed.

• Periodical: Applied Mechanics and Materials (Volumes 423-426)
• Pages: 1741-1750
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.423-426.1741
• Online since: September 2013
• Authors: Marta Cianfrini*, Roberto de Lieto Vollaro, Alessandro Quintino, Massimo Corcione
• Keywords: Bottom or Top Cooling, Correlation, Enclosed Natural Convection, Partial Side Heating

References

[1] H. H. S. Chu, S. W. Churchill, C. V. S. Patterson, The effect of heater size, location, aspect ratio, and boundary conditions on two-dimensional, laminar, natural convection in rectangular channels, J. Heat Transfer 98 (1976) 194-201.

DOI: 10.1115/1.3450518

[2] B. L. Turner, R. D. Flack, The experimental measurement of natural convective heat transfer in rectangular enclosure with concentrated heat sources, J. Heat Transfer 102 (1980) 236-241.

DOI: 10.1115/1.3244266

[3] M. Keyhani, V. Prasad, R. Cox, An experimental study of natural convection in a vertical cavità with discrete heat sources, J. Heat Transfer 110 (1988) 616-624.

DOI: 10.1115/1.3250537

[4] M. L. Chadwick, B. W. Webb, H. S. Heaton, Natural convection from two-dimensional discrete heat siurces in a rectangular enclosure, Int. J. Heat Mass Transfer 34 (1991) 1679-1693.

DOI: 10.1016/0017-9310(91)90145-5

[5] G. Refai Ahmed, M. M. Yovanovich, Influence of discrete heat source location on natural convection heat transfer in a vertical square enclosure, J. Electronic Packaging 113 (1991) 268-274.

DOI: 10.1115/1.2905406

[6] G. Refai Ahmed, M. M. Yovanovich, Numerical study of natural convection from discrete heat sources in a vertical square enclosure, J. Thermophysics 6 (1992) 121-127.

DOI: 10.2514/3.326

[7] M. S. Polentini, S. Ramadhyani, F. P. Incropera, Single-phase thermosyphon cooling of an array of discrete heat sources in a rectangular cavità, Int. J. Heat Mass Transfer 36 (1993) 3983-3996.

DOI: 10.1016/0017-9310(93)90149-z

[8] C. J. Ho, J. Y. Chang, A study of natural convection heat transfer in a vertical rectangular enclosure with two-dimensional discrete heating: effect of aspect ratio, Int. J. Heat Mass Transfer 37 (1994) 917-925.

DOI: 10.1016/0017-9310(94)90217-8

[9] T. J. Heindel, S. Ramadhyani, F. P. Incropera, Laminar natural convection in a discretely heated cavity: I-assessment of three-dimensional effects, J. Heat Transfer 117 (1995) 902-909.

DOI: 10.1115/1.2836309

[10] T. J. Heindel, S. Ramadhyani, F. P. Incropera, Laminar natural convection in a discretely heated cavity: II-comparisons of experimental and theoretical results, J. Heat Transfer 117 (1995) 910-917.

DOI: 10.1115/1.2836310

[11] S. K. W. Tou, C. P. Tso, X. Zhang, 3-D numerical analysis of natural convective liquid cooling of a 3×3 heater array in rectangular enclosures, Int. J. Heat Mass Transfer 42 (1999) 3231-3244.

DOI: 10.1016/s0017-9310(98)00379-2

[12] Y. Liu, N. Phan-Tien, An optimum spacing problem for three chips mounted on a vertical substrate in an enclosure, Num. Heat Transfer 37 (2000) 613-630.

DOI: 10.1080/104077800274118

[13] R. L. Frederick, F. Quiroz, On the transition from conduction to convection regime in a cubical enclosure with a partially heated wall, Int. J. Heat Mass Transfer 44 (2001) 1699-1709.

DOI: 10.1016/s0017-9310(00)00219-2

[14] S. K. W. Tou, X. F. Zhang, Three-dimensional numerical simulation of natural convection in an inclined liquid-filled enclosure with an array of discrete heaters, Int. J. Heat Mass Transfer 46 (2003) 127-138.

DOI: 10.1016/s0017-9310(02)00253-3

[15] L. B. Erbay, Z. Altaç, B. Sülüş, Entropy generation in a square enclosure with partial heating from a vertical lateral wall, Heat Mass Transfer 40 (2004) 909-918.

DOI: 10.1007/s00231-003-0497-x

[16] J. H. Bae, J. M. Hyun, Time-dependent buoyant convection in an enclosure with discrete heat sources, Int. J. Thermal Sciences 43 (2004) 3-11.

DOI: 10.1016/s1290-0729(03)00102-9

[17] C. P. Tso, L. F. Lin, S. K. W. Tou, X. Zhang, Flow pattern evolution in natural convection from an array of discrete heat sources in a rectangular cavity at various orientations, Int. J. Heat Mass Transfer 47 (2004) 4061-4073.

DOI: 10.1016/j.ijheatmasstransfer.2004.05.022

[18] A. K. da Silva, S. Lorente, A. Bejan, Optimal distribution of discrete heat sources on a wall with natural convection, Int. J. Heat Mass Transfer 47 (2004) 203-214.

DOI: 10.1016/j.ijheatmasstransfer.2003.07.007

[19] Y. L. He, W. W. Yang, W. Q. Tao, Three-dimensional numerical study of natural convective heat transfer of liquid in a cubic enclosure, Num. Heat Transfer 47 (2005) 917-934.

DOI: 10.1080/10407780590921917

[20] A. K. da Silva, S. Lorente, A. Bejan, Constructal multi-scale structures for maximal heat transfer density, Energy 31 (2006) 620-635.

DOI: 10.1016/j.energy.2005.04.011

[21] N. Nithyadevi, P. Kandaswamy, J. Lee, Natural convection in a rectangular cavity with partially active side walls, Int. J. Heat Mass Transfer 50 (2007) 4688-4697.

DOI: 10.1016/j.ijheatmasstransfer.2007.03.050

[22] A. Baïri, J. M. García de María, N. Laraqi, N. Alilat, Free convection generated in an enclosure by alternate heated bands. Experimental and numerical study adapted to electronics thermal control, Int. J. Heat Fluid Flow 29 (2008) 1337-1346.

DOI: 10.1016/j.ijheatfluidflow.2008.06.007

[23] M. Corcione, E. Habib, Buoyant heat transport in fluids across tilted square cavities discretely heated at one side, Int. J. Thermal Sciences 49 (2010) 797-808.

DOI: 10.1016/j.ijthermalsci.2009.11.012

[24] S. Kimura, A. Bejan, Natural convection in a differentially heated corner region, Phys. Fluids 28 (1985) 2980-2989.

DOI: 10.1063/1.865137

[25] O. Aydin, Transient natural convection in rectangular enclosures heated from one side and cooled from above, Int. Comm. Heat Mass Transfer 26 (1999) 135-144.

DOI: 10.1016/s0735-1933(98)00129-8

[26] Y. L. He, W. W. Yang, W. Q. Tao, Three-dimensional numerical study of natural convective heat transfer of liquid in a cubic enclosure, Num. Heat Transfer 47 (2005) 917-934.

DOI: 10.1080/10407780590921917

[27] J. P. Van Doormaal, G. D. Raithby, Enhancements of the simple method for predicting incompressible fluid flows, Num. Heat Transfer 11 (1984) 147-163.

DOI: 10.1080/10407798408546946

[28] S. V. Patankar, D. B. Spalding, A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows, Int. J. Heat Mass Transfer 15 (1972) 1787-1797.

DOI: 10.1016/0017-9310(72)90054-3

[29] S. V. Patankar, Numerical Heat Transfer and Fluid Flow, Hemisphere Publ. Co., Washington, DC, (1980).

[30] B. P. Leonard, A stable and accurate convective modelling procedure based on quadratic upstream interpolation, Comp. Meth. in Appl. Mech. Engng. 19 (1979) 59-78.

DOI: 10.1016/0045-7825(79)90034-3

[31] G. de Vahl Davis, Natural convection of air in a square cavity: a bench mark numerical solution, Int. J. Num. Meth. Fluids 3 (1983) 249-264.

DOI: 10.1002/fld.1650030305

[32] H. S. Mahdi, R. B. Kinney, Time-dependent natural convection in a square cavity: application of a new finite volume method, Int. J. Num. Meth. Fluids 11 (1990) 57-86.

DOI: 10.1002/fld.1650110105

[33] M. Hortmann, M. Peric, G. Scheuerer, Finite volume multigrid prediction of laminar natural convection: bench-mark solutions, Int. J. Num. Meth. Fluids 11 (1990) 189-207.

DOI: 10.1002/fld.1650110206

[34] D. C. Wan, B. S. V. Patnaik, G. W. Wei, A new benchmark quality solution for the buoyancy-driven cavity by discrete singular convolution, Num. Heat Transfer 40 (2001) 199-228.

DOI: 10.1080/104077901752379620

[35] A. Bejan, Convection Heat Transfer, 3rd ed., John Wiley & Sons, Inc., Hoboken, New Jersey (2004).

[36] F. P. Incropera, D. P. Dewitt, T. L. Bergman, A. S. Lavine, Fundamentals of Heat and Mass Transfer, 6th ed., John Wiley & Sons, Inc., Hoboken, New Jersey (2007).