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Research Papers: Natural and Mixed Convection

The Rayleigh Number Effect on the Periodic Heating of an Enclosure Filled With a Fluid and Discrete Solid Blocks

[+] Author and Article Information
S. Moussa Mirehei

Department of Mechanical and
Aerospace Engineering,
University of Florida,
Gainesville, FL 32611-6250
e-mail: smirehei@ufl.edu

José L. Lage

Fellow ASME
Department of Mechanical Engineering,
Lyle School of Engineering,
Southern Methodist University,
Dallas, TX 75275-0337
e-mail: JLL@smu.edu

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received November 7, 2017; final manuscript received March 21, 2018; published online June 11, 2018. Assoc. Editor: Antonio Barletta.

J. Heat Transfer 140(10), 102503 (Jun 11, 2018) (8 pages) Paper No: HT-17-1663; doi: 10.1115/1.4039914 History: Received November 07, 2017; Revised March 21, 2018

The steady-periodic natural convection phenomenon inside a heated enclosure filled with disconnected, discrete solid blocks, and under horizontal, time-periodic heating is investigated numerically. This configuration is akin to several practical engineering applications, such as oven baking in food processing, heat treating of metal parts in materials processing, and storage and transportation of discrete solid goods in containerization. Because of the relative large size, and limited number of solid bodies placed inside the enclosure, the solid and fluid constituents are viewed separately and the process modeled using continuum balance equations for each with suitable compatibility conditions imposed at their interfaces. The periodic heating is driven by a sinusoidal in time hot-wall temperature, while maintaining the cold wall temperature constant, with top and bottom surfaces adiabatic. Results are presented in terms of hot and cold wall-averaged Nusselt numbers, time-varying energy capacity of the enclosure, and periodic isotherms and streamlines, for Ra varying from 103 to 107, Pr equal to 1, and 36 uniformly distributed, conducting and disconnected solid square blocks. The results explain why and how the effect of varying Ra on the convection process is significantly affected by the presence of the solid blocks. An analytical equation, valid for time-periodic heating, is proposed for anticipating the block interference effect with great accuracy, substantiating the distinct features of Nusselt versus Rayleigh observed when the blocks are present inside the enclosure.

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References

Merrikh, A. A. , and Lage, J. L. , 2005, “ From Continuum to Porous-Continuum: The Visual Resolution Impact on Modeling Natural Convection in Heterogeneous Media,” Transport Phenomena in Porous Media, Vol. 3, D. B. Ingham and I. Pop, eds., Elsevier, Oxford, UK, pp. 60–96.
Merrikh, A. A. , Lage, J. L. , and Mohamad, A. A. , 2005, “ Natural Convection in Nonhomogeneous Heat-Generating Media: Comparison of Continuum and Porous-Continuum Models,” J. Porous Media, 8(2), pp. 1–15. [CrossRef]
Whitaker, S. , 1999, Theory and Applications of Transport in Porous Media: The Method of Volume Averaging, Kluwer Academic Publishers, Norwell, MA.
Nield, D. A. , and Bejan, A. , 2017, Convection in Porous Media, 5th ed., Springer, New York. [CrossRef]
House, J. M. , Beckermann, C. , and Smith, T. F. , 1990, “ Effect of a Centered Conducting Body on Natural Convection Heat Transfer in an Enclosure,” Numer. Heat Transfer, Part A, 18(2), pp. 213–225. [CrossRef]
Oh, J. Y. , Ha, M. Y. , and Kim, K. C. , 1997, “ Numerical Study of Heat Transfer and Flow of Natural Convection in an Enclosure With a Heat-Generating Conducting Body,” Numer. Heat Transfer, Part A, 31(3), pp. 289–303. [CrossRef]
Lee, J. R. , and Ha, M. Y. , 2005, “ A Numerical Study of Natural Convection in a Horizontal Enclosure With a Conducting Body,” Int. J. Heat Mass Transfer, 48(16), pp. 3308–3318. [CrossRef]
Lee, J. R. , and Ha, M. Y. , 2006, “ Numerical Simulation of Natural Convection in a Horizontal Enclosure With a Heat-Generating Conducting Body,” Int. J. Heat Mass Transfer, 49(15–16), pp. 2684–2702. [CrossRef]
Bhave, P. , Narasimhan, A. , and Rees, D. A. S. , 2006, “ Natural Convection Heat Transfer Enhancement Using Adiabatic Block: Optimal Block Size and Prandtl Number Effect,” Int. J. Heat Mass Transfer, 49(21–22), pp. 3807–3818. [CrossRef]
Kumar De, A. , and Dalal, A. , 2006, “ A Numerical Study of Natural Convection Around a Square, Horizontal, Heated Cylinder Placed in an Enclosure,” Int. J. Heat Mass Transfer, 49(23–24), pp. 4608–4623. [CrossRef]
Merrikh, A. A. , and Mohamad, A. A. , 2001, “ Blockage Effects in Natural Convection in Differentially Heated Enclosures,” J. Enhanced Heat Transfer, 8(1), pp. 55–74. [CrossRef]
Merrikh, A. A. , and Lage, J. L. , 2005, “ Natural Convection in an Enclosure With Disconnected and Conducting Solid Blocks,” Int. J. Heat Mass Transfer, 48(7), pp. 1361–1372. [CrossRef]
Massarotti, N. , Nithiarasu, P. , and Carotenuto, A. , 2003, “ Microscopic and Macroscopic Approach for Natural Convection in Enclosures Filled With Fluid Saturated Porous Medium,” Int. J. Numer. Methods Heat Fluid Flow, 13(7), pp. 862–886. [CrossRef]
Braga, E. J. , and De Lemos, M. J. S. , 2005, “ Heat Transfer in Enclosures Having a Fixed Amount of Solid Material Simulated With Heterogeneous and Homogeneous Models,” Int. J. Heat Mass Transfer, 48(23–24), pp. 4748–4765. [CrossRef]
Braga, E. J. , and De Lemos, M. J. S. , 2005, “ Laminar Natural Convection in Cavities Filled With Circular and Square Rods,” Int. Commun. Heat Mass Transfer, 32(10), pp. 1289–1297. [CrossRef]
Pourshaghaghy, A. , Hakkaki-Fard, A. , and Mahdavi-Nejad, A. , 2007, “ Direct Simulation of Natural Convection in Square Porous Enclosure,” Energy Convers. Manage., 48(5), pp. 1579–1589. [CrossRef]
Jamalud-Din, S. D. , Rees, D. A. S. , Reddy, B. V. K. , and Narasimhan, A. , 2010, “ Prediction of Natural Convection Flow Using Network Model and Numerical Simulations Inside Enclosure With Distributed Solid Blocks,” Heat Mass Transfer, 46(3), pp. 333–343. [CrossRef]
Narasimhan, A. , and Reddy, B. V. K. , 2010, “ Natural Convection Inside a Bidisperse Porous Medium Enclosure,” ASME J. Heat Transfer, 132(1), p. 012502. [CrossRef]
Junqueira, S. L. M. , De Lai, F. C. , Franco, A. T. , and Lage, J. L. , 2013, “ Numerical Investigation of Natural Convection in Heterogeneous Rectangular Enclosures,” Heat Transfer Eng. J., 34(5–6), pp. 460–469. [CrossRef]
Qiu, H. , Lage, J. L. , Junqueira, S. L. M. , and Franco, A. T. , 2013, “ Predicting the Nusselt Number of Heterogeneous (Porous) Enclosures Using a Generic Form of the Berkovsky-Polevikov Correlations,” ASME J. Heat Transfer, 135(8), p. 082601. [CrossRef]
Lage, J. L. , and Bejan, A. , 1993, “ The Resonance of Natural Convection in an Enclosure Heated Periodically From the Side,” Int. J. Heat Mass Transfer, 36(8), pp. 2027–2038. [CrossRef]
Antohe, B. V. , and Lage, J. L. , 1994, “ A Dynamic Thermal Insulator: Inducing Resonance Within a Fluid Saturated Porous Medium Enclosure Heated Periodically From the Side,” Int. J. Heat Mass Transfer, 37(5), pp. 771–782. [CrossRef]
Antohe, B. V. , and Lage, J. L. , 1996, “ Amplitude Effect on Convection Induced by Time-Periodic Horizontal Heating,” Int. J. Heat Mass Transfer, 39(6), pp. 1121–1133. [CrossRef]
Antohe, B. V. , and Lage, J. L. , 1996, “ Experimental Investigation on Pulsating Horizontal Heating of a Water-Filled Enclosure,” ASME J. Heat Transfer, 118(4), pp. 889–896. [CrossRef]
Lage, J. L. , and Antohe, B. V. , 1997, Convection Resonance and Heat Transfer Enhancement of Periodically Heated Fluid Enclosures (Transient Convective Heat Transfer), Begell House, New York, pp. 259–268.
Antohe, B. V. , and Lage, J. L. , 1997, “ The Prandtl Number Effect on the Optimum Heating Frequency of an Enclosure Filled With Fluid or With a Saturated Porous Medium,” Int. J. Heat Mass Transfer, 40(6), pp. 1313–1323. [CrossRef]
Narasimhan, A. , and Reddy, B. V. K. , 2011, “ Resonance of Natural Convection Inside a Bidisperse Porous Medium Enclosure,” ASME J. Heat Transfer, 133(4), p. 042601. [CrossRef]
Zargartalebi, H. , Ghalambaz, M. , Khanafer, K. , and Pop, I. , 2017, “ Unsteady Conjugate Natural Convection in a Porous Cavity Boarded by Two Vertical Finite Thickness Walls,” Int. Commun. Heat Mass Transfer, 81, pp. 218–228. [CrossRef]
Ren, Q. , and Chan, C. L. , 2016, “ Natural Convection With an Array of Solid Obstacles in an Enclosure by Lattice Boltzmann Method on a CUDA Computation Platform,” Int. J. Heat Mass Transfer, 93, pp. 273–285. [CrossRef]
Kazmierczak, M. , and Chinoda, Z. , 1992, “ Buoyancy-Driven Flow in an Enclosure With Time Periodic Boundary Conditions,” Int. J. Heat Mass Transfer, 35(6), pp. 1507–1518. [CrossRef]
Patankar, S. V. , 1980, Numerical Heat Transfer and Fluid Flow, Taylor and Francis, Philadelphia, PA.
Versteeg, H. K. , and Malalasekera, W. , 1995, An Introduction to Computational Fluid Dynamics, Longman Scientific and Technical, Harlow, UK.
Mirehei, S. M. , 2015, “ Simulations and Analyses of Natural Convection Inside Heterogeneous Containers Heated by Solar Radiation,” Ph.D. dissertation, Southern Methodist University, Dallas, TX.
Bejan, A. , 2004, Convection Heat Transfer, Wiley, Hoboken, NJ. [PubMed] [PubMed]

Figures

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Fig. 1

Schematic of the domain, showing the enclosure with thirty-six solid blocks

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Fig. 2

Periodic hot wall nondimensional temperature, with period E and amplitude 2 A

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Fig. 3

Hot wall Nusselt Nuh versus time (top), for steady-periodic regime, Ra = 107, and the corresponding external (forcing) θh cycle (bottom)

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Fig. 4

Time evolution of streamlines (contour shots) corresponding to the black dots marked along the Nuh curve of Fig. 3

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Fig. 5

Time evolution of isotherms (contour hots) corresponding to the black dots marked along Nuh of Fig. 3

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Fig. 6

Cold wall Nusselt Nuc versus time (top), for steady-periodic regime, Ra = 107, and the corresponding θh cycle (bottom)

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Fig. 7

Hot wall Nusselt Nuh versus time (top), for steady-periodic regime, Ra = 103–107, and the corresponding forcing θh cycle (bottom)

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Fig. 8

Clear fluid case (N = 0): hot wall Nusselt Nuh versus time (top), for steady-periodic regime, Ra = 103–107, and the corresponding forcing θh cycle (bottom)

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Fig. 9

Net heat flow across the hot and cold walls of the enclosure (top), for steady-periodic regime, and the corresponding forcing θh cycle (bottom)

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