Combined conduction and radiation heat transfer with variable thermal conductivity and variable refractive index

Analysis of Conduction-Radiation Heat Transfer With Variable Thermal Conductivity and Variable Refractive Index: Application of the Lattice Boltzmann Method

“…For a one-dimensional planar geometry, in the LBM with a D1Q2 lattice, the discrete Boltzmann equation with Bhatanagar-Gross-Krook (BGK) approximation is given by [8]:…”

“…Because of the mathematical complexities, a limited literature is available that individually deal with the effects of variable thermal conductivity [6] and constant and/or variable refractive index [7]. The case of variable thermal conductivity and variable refractive index finds application in the thermal analysis of graded index medium [8]. The present work is, therefore, aimed at the analysis of conduction and radiation heat transfer in a participating medium, by lattice Boltzmann method.…”

Performance evaluation of four radiative transfer methods in solving multi-dimensional radiation and/or conduction heat transfer problems

“…(1) can be solved using the FDM or the FVM. In the recent past, the LBM [30][31][32][33][34][35][36][37][38] has received a great deal of attention in the analysis of fluid flow and heat transfer problems, and very recently, its application to various heat transfer problems dealing with thermal radiation has been encouraging [32][33][34][35][36][37][38]. Therefore, in the present work, the energy equation is formulated using the LBM, and with the LBM as a base for solving the energy equation, the performances of the DTM, the DOM and the FVM as a module to provide the required radiation field r Áq R information is assessed.…”

“…Among others, some of the attributes of the LBM which make it an attractive method are clear physics, simple coding, suitable for a parallel architecture, adaptable to complex geometry and ease in implementation of the boundary conditions [30,31]. Having motivated by its successful applications to a wide range of problems in fluid mechanics [30,31], very recently the LBM has been applied to solve different class of heat transfer problems involving thermal radiation [32][33][34][35][36][37][38].…”

Transient radiative heat transfer in an inhomogeneous participating medium with Fresnel’s surfaces

“…Lemonnier et al [14] deduced expressions of radiative transfer equation for a one-dimensional gradient index medium in rectangular coordinate system. In addition, Shendeleva [15] studied radiative transfer in a non-absorbing turbid medium with a varying refractive index; Krishna et al [16] used a discrete transfer method to examine the radiative transfer in a semitransparent gradient index medium at the radiative equilibrium; Mishra et al [17] investigated coupled heat transfer in an isotropic scattering medium with diffuse surfaces and a linear distribution of refractive index, adopted a discrete transfer method to solve the radiative transfer equation and a lattice Boltzmann method to solve the coupled energy equation. Huang et al [18] proposed three different Monte Carlo ray-tracing strategies to study the radiative transfer in absorbing-emitting-scattering slab with linear and sinusoidal refractive index distribution and specular surfaces and calculated thermal emission at radiative equilibrium.…”