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Research Papers: SPECIAL SECTION PAPERS

Computation of Mixed Convection and Volumetric Radiation in Vertical Channel Based on Hybrid Thermal Lattice Boltzmann Method

[+] Author and Article Information
Soufiane Derfoufi

Laboratoire de Mécanique & Energétique,
Département de Physique,
Faculté des Sciences,
Université Mohammed 1er,
Oujda 60000, Maroc
e-mail: Soufiane.derf@gmail.com

Fayçal Moufekkir, Ahmed Mezrhab

Laboratoire de Mécanique & Energétique,
Département de Physique,
Faculté des Sciences,
Université Mohammed 1er,
60000 Oujda, Maroc

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received September 8, 2014; final manuscript received February 3, 2016; published online June 1, 2016. Assoc. Editor: Dennis A. Siginer.

J. Heat Transfer 138(9), 091003 (Jun 01, 2016) (8 pages) Paper No: HT-14-1592; doi: 10.1115/1.4032948 History: Received September 08, 2014; Revised February 03, 2016

The present paper presents a numerical study of mixed convection coupled with volumetric radiation in a vertical channel. The geometry of the physical model consists of two isothermal plates. The governing equations of the problem are solved using a hybrid scheme of the lattice Boltzmann method (LBM) and finite-difference method (FDM). The main objective of this study is to evaluate the influence of the Richardson number (Ri) and the emissivity of the walls (εi) on the heat transfer, on the flow, and on the temperature distribution. Results show that Richardson number and emissivity have a significant effect on heat transfer and air flow.

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References

Jackson, J. D. , Cotton, M. A. , and Axcell, B. P. , 1989, “ Studies of Mixed Convection in Vertical Tubes,” Int. J. Heat Fluid Flow, 10(1), pp. 2–15. [CrossRef]
Jeng, Y. N. , Chen, J. L. , and Aung, W. , 1992, “ On the Reynolds-Number Independence of Mixed Convection in a Vertical Channel Subjected to Asymmetric Wall Temperatures With and Without Flow Reversal,” Int. J. Heat Fluid Flow, 13(4), pp. 329–339. [CrossRef]
Desrayaud, G. , and Lauriat, G. , 2009, “ Flow Reversal of Laminar Mixed Convection in the Entry Region of Symmetrically Heated, Vertical Plate Channels,” Int. J. Therm. Sci., 48(11), pp. 2036–2045. [CrossRef]
Bouali, H. , and Mezrhab, A. , 2006, “ Combined Radiative and Convective Heat Transfer in a Divided Channel,” Int. J. Numer. Methods Heat Fluid Flow, 16(1), pp. 84–106. [CrossRef]
Li, R. , Bousetta, M. , Chénier, E. , and Lauriat, G. , 2013, “ Effect of Surface Radiation on Natural Convective Flows and Onset of Flow Reversal in Asymmetrically Heated Vertical Channels,” Int. J. Therm. Sci., 65, pp. 9–27. [CrossRef]
Viskanta, R. , and Grosh, R. J. , 1962, “ Effect of Surface Emissivity on Heat Transfer by Simultaneous Conduction and Radiation,” Int. J. Heat Mass Transfer, 5(8), pp. 729–734. [CrossRef]
Viskanta, R. , 1964, “ Heat Transfer in a Radiating Fluid With Slug Flow in a Parallel-Plate Channel,” Appl. Sci. Res., Sect. A, 13(1), pp. 291–331. [CrossRef]
Camera-Roda, G. , Bertela, M. , and Santarelli, F. , 1985, “ Mixed Laminar Convection in a Participating Irradiated Fluid,” Numer. Heat Transfer, 8, pp. 429–447. [CrossRef]
Bazdidi-Tehrani, F. , and Nazaripoor, H. , 2011, “ Buoyancy-Assisted Flow Reversal and Combined Mixed Convection–Radiation Heat Transfer in Symmetrically Heated Vertical Parallel Plates: Influence of Two Radiative Parameters,” Sci. Iran., 18(4), pp. 974–985. [CrossRef]
Bhatnagar, P. L. , Gross, E. P. , and Krook, M. , 1954, “ A Model for Collision Processes in Gases. I. Small Amplitude Processes in Charged and Neutral One-Component Systems,” Phys. Rev., 94(3), pp. 511–525. [CrossRef]
Lallemand, P. , and Luo, L.-S. , 2003, “ Lattice Boltzmann Method for Moving Boundaries,” J. Comput. Phys., 184(2), pp. 406–421. [CrossRef]
Niu, X. D. , Shu, C. , Chew, Y. T. , and Peng, Y. , 2006, “ A Momentum Exchange-Based Immersed Boundary-Lattice Boltzmann Method for Simulating Incompressible Viscous Flows,” Phys. Lett., 354(3), pp. 173–182. [CrossRef]
Mezrhab, A. , Bouzidi, M. , and Lallemand, P. , 2004, “ Hybrid Lattice Boltzmann Finite Difference Simulation of Convective Flows,” Comput. Fluids, 33(4), pp. 623–641. [CrossRef]
d'Humiéres, D. , 1992, “ Generalized Lattice Boltzmann Equations Rarefied Gas Dynamics: Theory and Simulations,” Prog Aeronaut Astronaut, Vol. 159, B. D. Shizgal and D. P. Weaver , eds., AIAA, Reston, VA, pp. 450–458.
Asinari, P. , Mishra, S. C. , and Borchiellini, R. , 2010, “ A Lattice Boltzmann Formulation for the Analysis of Radiative Heat Transfer Problems in a Participating Medium,” Numer. Heat Transfer, Part B, 57, pp. 1–21. [CrossRef]
Di Rienzo, A. F. , Asinari, P. , Borchiellini, R. , and Mishra, S. C. , 2011, “ Improved Angular Discretization and Error Analysis of the Lattice Boltzmann Method for Solving Radiative Heat Transfer in a Participating Medium,” Int. J. Numer. Methods Heat Fluid Flow, 21, pp. 640–662. [CrossRef]
Bindra, H. , and Patil, D. V. , 2012, “ Radiative or Neutron Transport Modeling Using a Lattice Boltzmann Equation Framework,” Phys. Rev. E, 86(1), p. 016706. [CrossRef]
Bouzidi, M. , Firdaouss, M. , and Lallemand, P. , 2001, “ Momentum Transfer of a Boltzmann Lattice Fluid With Boundaries,” Phys. Fluids, 13(11), pp. 3452–3459. [CrossRef]
Zou, Q. , and He, X. , 1997, “ On Pressure and Velocity Boundary Conditions for the Lattice Boltzmann BGK Model,” Phys. Fluids, 6, pp. 1591–1598. [CrossRef]
Ginzbourg, I. , and Adler, P. M. , 1994, “ Boundary Flow Condition Analysis for the Three-Dimensional Lattice Boltzmann Model,” J. Phys. II, 4, pp. 191–214.
Modest, M. F. , 2003, Radiative Heat Transfer, 2nd ed., Academic Press, New York.
Ozisik, M. N. , 1973, Radiative Transfer and Interaction With Convection and Conduction, Wiley, New York.

Figures

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Fig. 2

Bounce-back boundary condition. xf: last fluid node, xw: physical wall, and xs: first solid node.

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Fig. 1

(a) Schematic geometry of the channel with boundary conditions, (b) LBM lattice for dynamic problem, and (c) LBM lattice for radiative problem

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Fig. 6

Variation of axial centerline velocity with channel height for various emissivity of walls (Ri=0.1, Ra=105, and τ=1)

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Fig. 7

Variation of axial centerline velocity with channel height for various emissivity of walls (Ri=1, Ra=105, and τ=1)

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Fig. 8

Variation of axial centerline velocity with channel height for various emissivity of walls (Ri=10, Ra=105, and τ=1)

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Fig. 4

Comparison of streamlines (a) and variations of radiative wall heat fluxes with channel height for various values of ε (b)

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Fig. 5

Variation of average total Nusselt number with emissivity for various Richardson numbers (Ra=105, τ=1)

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Fig. 3

Comparison of isotherms (a), streamlines (b), and variation of axial centerline velocity with channel height for two values of channel width L (c)

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Fig. 9

Variation of median temperature with channel height for various emissivity of walls (Ri=0.1, Ra=105, and τ=1)

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Fig. 10

Variation of median temperature with channel height for various emissivity of walls (Ri=1, Ra=105, and τ=1)

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Fig. 11

Variation of median temperature with channel height for various emissivity of walls (Ri=10, Ra=105, and τ=1)

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