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Research Papers: Radiative Heat Transfer

Numerical Study of Transient Convection With Volumetric Radiation Using an Hybrid Lattice Boltzmann Bhatnagar–Gross–Krook–Control Volume Finite Element Method

[+] Author and Article Information
Raoudha Chaabane

Laboratory of Thermal and
Energetic Systems Studies (LESTE),
National School of Engineering of Monastir,
University of Monastir,
Monastir 5000, Tunisia;
Preparatory Institute of Engineering Studies of
Monastir (IPEIM),
University of Monastir,
Monastir 5000, Tunisia
e-mail: Raoudhach@gmail.com

Faouzi Askri

Laboratory of Thermal and
Energetic Systems Studies (LESTE),
National School of Engineering of Monastir,
University of Monastir,
Monastir 5000, Tunisia
e-mail: faouzi.askri@enim.rnu.tn

Abdelmajid Jemni

Laboratory of Thermal and
Energetic Systems Studies (LESTE),
National School of Engineering of Monastir,
University of Monastir,
Monastir 5000, Tunisia
e-mail: abdelmajid.jemni@enim.rnu.tn

Sassi Ben Nasrallah

Laboratory of Thermal and
Energetic Systems Studies (LESTE),
National School of Engineering of Monastir,
University of Monastir,
Monastir 5000, Tunisia
e-mail: sassi.bennasrallah@enim.rnu.tn

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received June 24, 2016; final manuscript received February 28, 2017; published online May 16, 2017. Assoc. Editor: Zhuomin Zhang.

J. Heat Transfer 139(9), 092701 (May 16, 2017) (7 pages) Paper No: HT-16-1416; doi: 10.1115/1.4036154 History: Received June 24, 2016; Revised February 28, 2017

In this paper, a new hybrid numerical algorithm is developed to solve coupled convection–radiation heat transfer in a two-dimensional cavity containing an absorbing, emitting, and scattering medium. The radiative information is obtained by solving the radiative transfer equation (RTE) using the control volume finite element method (CVFEM), and the density, velocity, and temperature fields are calculated using the two double population lattice Boltzmann equation (LBE). To the knowledge of the authors, this hybrid numerical method is applied at the first time to simulate combined transient convective radiative heat transfer in 2D participating media. In order to test the efficiency of the developed method, two configurations are examined: (i) free convection with radiation in a square cavity bounded by two horizontal insulating sides and two vertical isothermal walls and (ii) Rayleigh–Benard convection with and without radiative heat transfer. The obtained results are validated against available works in literature, and the proposed method is found to be efficient, accurate, and numerically stable.

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Figures

Grahic Jump Location
Fig. 2

Steady-state nondimensional temperature for Ra=104, ω=0, β=1, ε=1, and (a) RC=0.0 and (b) RC=0.1 for y/Y = 1/2

Grahic Jump Location
Fig. 3

Steady-state vertical velocity component profile against y-direction at Ra = 5 × 105 for Pr = 0.71

Grahic Jump Location
Fig. 1

(a) Geometry of the domain for natural convection–radiation (case 1), (b) sketch of the Rayleigh–Benard convection with radiation problem (case 2). (c) angular discretization, (d) spatial discretization in (ex, ey) plan, (e) control volume ΔVij, (f) subvolume δVij, and (g) arrangement of lattices and control volumes in the domain

Grahic Jump Location
Fig. 4

Temperature contours for different Rayleigh numbers and Pr = 0.71: (a) Ref. [14] and (b) present work

Grahic Jump Location
Fig. 5

The effect of the convection–radiation parameter RC on the mediane temperature for a gray participating media (a) for (x/X = 1/2) and (b) for (y/Y = 1/2)

Grahic Jump Location
Fig. 6

(a) The dimensionless steady-state isotherms Ra=5×104, ω=0, and Pr=0.71, (b) the dimensionless steady-state streamlines Ra=5×104, ω=0, and Pr=0.71, (c) the dimensionless isotherms Ra=5×104, ω=0, Pr=0.71, and RC=0.01 at different dimensionless times with (ξ1<  ξ2<  ξ3<  ξ4=∞), and (d) the dimensionless streamlines Ra=5×104, ω=0, Pr=0.71, and RC=0.01 at different dimensionless times with (ξ1<  ξ2<  ξ3<  ξ4=∞)

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