Radiative heat transfer in absorbing–emitting–scattering gray medium inside 1-D gray Cartesian enclosure using the collapsed dimension method

Application of the lattice Boltzmann method for solving the energy equation of a 2-D transient conduction–radiation problem

“…The LBM performance in solving the energy equation is compared against that of a FVM. The collapsed dimension method (CDM) is used to compute the radiative information [17,18] required as source in the energy equation, both in combination with the LBM and with the FVM. Results for the effects of the conduction-radiation parameter N, the scattering albedo x, the extinction coefficient b, and the aspect ratio Y/X where X and Y are the dimensions of the 2-D enclosure, are studied.…”

View factor calculation in the 2-D geometries using the collapsed dimension method

“…It is to be noted that using the block-off region procedure with the approach of the CDM discussed in [6] for the participating medium radiative heat transfer, Talukdar [7] has demonstrated the use of the CDM in calculating view factors in a 2-D rectangular geometry having a central blockage. In the present work, the formulation presented is a simple one.…”

“…Thus, in the CDM, the expression for radiative heat flux q because of radiation on/from one side of a surface (a hemisphere of actual intensities transformed to a semicircle of effective intensities) is given by [6].…”

“…In radiatively participating [6,7,9] as well as transparent medium [3][4][5], in calculating the heat flux at any point, in the approximate methods like the DOM [2], the DTM [4], the FVM [5], etc., spherical space (4π solid angle) is discretized into a finite number of elemental sub-solid angles. In each sub-solid angle, intensity is considered isotropic.…”

“…The collapsed dimension method (CDM) is an efficient method for solving radiative transport problems dealing with participating medium [6][7][8]. It has been extensively used for the radiative transport problems with participating medium.…”