Radiation Element Method Coupled with the Lattice Boltzmann Method Applied to the Analysis of Transient Conduction and Radiation Heat Transfer Problem with Heat Generation in a Participating Medium

This article deals with the implementation of the radiation element method (REM) with the lattice Boltzmann method (LBM) to solve a combined mode transient conduction-radiation problem. Radiative information computed using the REM is provided to the LBM solver. The planar conducting-radiating participating medium is contained between diffuse gray boundaries, and the system may contain a volumetric heat generation source. Temperature and heat flux distributions in the medium are studied for different values of parameters such as the extinction coefficient, the scattering albedo, the conduction-radiation parameter, the emissivity of the boundaries, and the heat generation rate. To check the accuracy of the results, the problem is also solved using the finite-volume method (FVM) in conjunction with the LBM. In this case, the data for radiation field are calculated using the FVM. The REM has been found to be compatible with the LBM, and in all the cases, results of the LBM-REM and the LBM-FVM have been found to provide an excellent comparison.

[1]  S. Maruyama.  Radiative heat transfer in anisotropic scattering media with specular boundary subjected to collimated irradiation , 1998 .

[2]  H. Tan,et al.  A Curve Monte Carlo Method for Radiative Heat Transfer in Absorbing and Scattering Gradient-Index Medium , 2006 .

[3]  Shiyi Chen,et al.  LATTICE BOLTZMANN METHOD FOR FLUID FLOWS , 2001 .

[4]  J. Howell.  The Monte Carlo Method in Radiative Heat Transfer , 1998 .

[5]  Subhash C. Mishra,et al.  Discrete ordinate method with a new and a simple quadrature scheme , 2006 .

[6]  Pascal Boulet,et al.  Radiative and conductive heat transfer in a nongrey semitransparent medium. Application to fire protection curtains , 2004 .

[7]  M. Modest.  Radiative heat transfer , 1993 .

[8]  Aibing Yu,et al.  Numerical study on the thawing process of biological tissue induced by laser irradiation. , 2005, Journal of biomechanical engineering.

[9]  M. Pinar Mengüç,et al.  Thermal Radiation Heat Transfer , 2020 .

[10]  Jayathi Y. Murthy,et al.  RADIATIVE HEAT TRANSFER IN AXISYMMETRIC GEOMETRIES USING AN UNSTRUCTURED FINITE-VOLUME METHOD , 1998 .

[11]  S. Maruyama,et al.  Nongray radiative heat transfer analysis in the anisotropic scattering fog layer subjected to solar irradiation , 2004 .

[12]  B. Mondal,et al.  Simulation of Natural Convection in the Presence of Volumetric Radiation Using the Lattice Boltzmann Method , 2008 .

[13]  W. Malalasekera,et al.  COMPARISON OF THE DISCRETE TRANSFER AND MONTE CARLO METHODS FOR RADIATIVE HEAT TRANSFER IN THREE-DIMENSIONAL NONHOMOGENEOUS SCATTERING MEDIA , 1997 .

[14]  Shigenao Maruyama,et al.  Radiation Heat Transfer of Arbitrary Three–Dimensional Absorbing, Emitting and Scattering Media and Specular and Diffuse Surfaces , 1997 .

[15]  S. Maruyama,et al.  Radiative Heat Transfer and Hydrostatic Stability in Nocturnal Fog , 2004 .

[16]  Subhash C. Mishra,et al.  Lattice Boltzmann Method Applied to Variable Thermal Conductivity Conduction and Radiation Problems , 2006 .

[17]  N. Pan,et al.  Modeling and prediction of the effective thermal conductivity of random open-cell porous foams , 2008 .

[18]  A. Hakkaki-Fard,et al.  Numerical Modeling of Combined Radiation and Conduction Heat Transfer in Mineral Wool Insulations , 2009 .

[19]  Subhash C. Mishra,et al.  Solving transient conduction and radiation heat transfer problems using the lattice Boltzmann method and the finite volume method , 2007, J. Comput. Phys..

[20]  Subhash C. Mishra,et al.  Lattice Boltzmann Method Applied to the Solution of Energy Equation of a Radiation and Non-Fourier Heat Conduction Problem , 2008 .

[21]  Modeling of Radiation Heat Transfer in the Drawing of an Optical Fiber With Multilayer Structure , 2007 .

[22]  Theodore F. Smith,et al.  TECHNICAL NOTE INCORPORATION OF INTERNAL SURFACE RADIANT EXCHANGE IN THE FINITE-VOLUME METHOD , 1993 .

[23]  M. Naraghi,et al.  A Volume Radiation Heat Transfer Model for Czochralski Crystal Growth Processes , 2000, Heat Transfer: Volume 3.

[24]  J. Gastellu-Etchegorry.  3D modeling of satellite spectral images, radiation budget and energy budget of urban landscapes , 2008 .

[25]  Seung Wook Baek,et al.  Nonorthogonal finite-volume solutions of radiative heat transfer in a three-dimensional enclosure , 1998 .

[26]  G. Raithby.  Discussion of the finite-volume method for radiation, and its application using 3D unstructured meshes , 1999 .

[27]  P. S. Cumber,et al.  Improvements to the discrete transfer method of calculating radiative heat transfer , 1995 .

[28]  S. Patankar,et al.  Finite volume method for radiation heat transfer , 1994 .

[29]  Kamran Daryabeigi,et al.  Heat Transfer in High-Temperature Fibrous Insulation , 2002 .

[30]  A. Yamaguchi,et al.  A numerical study of radiation heat transfer in sodium pool combustion and response surface modeling of luminous flame emissivity , 2006 .

[31]  M. Modest.  CHAPTER 16 – THE METHOD OF DISCRETE ORDINATES (SN-APPROXIMATION) , 2003 .

[32]  Subhash C. Mishra,et al.  Application of the lattice Boltzmann method for solving the energy equation of a 2-D transient conduction–radiation problem , 2005 .

[33]  Zhixiong Guo, Sunil Kumar.  RADIATION ELEMENT METHOD FOR TRANSIENT HYPERBOLIC RADIATIVE TRANSFER IN PLANE-PARALLEL INHOMOGENEOUS MEDIA , 2001 .

[34]  Zhixin Li,et al.  A lattice Boltzmann algorithm for fluid–solid conjugate heat transfer , 2007 .

[35]  W. Marsden.  I and J , 2012 .

[36]  Kang Y. Huh,et al.  ASSESSMENT OF THE FINITE-VOLUME METHOD AND THE DISCRETE ORDINATE METHOD FOR RADIATIVE HEAT TRANSFER IN A THREE-DIMENSIONAL RECTANGULAR ENCLOSURE , 1999 .

[37]  S. Mishra,et al.  Combined conduction and radiation heat transfer with variable thermal conductivity and variable refractive index , 2008 .

[38]  Subhash C. Mishra,et al.  Lattice Boltzmann method applied to the solution of the energy equations of the transient conduction and radiation problems on non-uniform lattices , 2008 .

[39]  Seigo Sakai,et al.  Improvement of computational time in radiative heat transfer of three-dimensional participating media using the radiation element method , 2002 .

[40]  A. Sharma,et al.  Review on thermal energy storage with phase change materials and applications , 2009 .

[41]  Andrés Tremante,et al.  Analysis of the Temperature Profile of Ceramic Composite Materials Exposed to Combined Conduction–Radiation Between Concentric Cylinders , 1998 .

[42]  Pritish R. Parida,et al.  Analysis of Solidification of a Semitransparent Planar Layer Using the Lattice Boltzmann Method and the Discrete Transfer Method , 2006 .

[43]  Subhash C. Mishra,et al.  Transient Conduction-Radiation Heat Transfer in Participating Media Using the Lattice Boltzmann Method and the Discrete Transfer Method , 2005 .

[44]  G. D. Raithby,et al.  A Finite-Volume Method for Predicting a Radiant Heat Transfer in Enclosures With Participating Media , 1990 .