Abstract
Convection, conduction, and thermal radiation are the three mechanisms of heat transfer in nature. The lattice Boltzmann model (LBM) has already achieved great success in dealing with convection and conduction problems. However, the mature LBM for radiative heat transfer (RHT) is still relatively lacking. Here we propose a mesoscopic LBM for RHT in graded-index media, which enables a simple and efficient solution of both transient and steady-state RHT in graded-index media by conducting collision and streaming processes. Via the Chapman-Enskog analysis, the radiative transfer equation of graded-index media is rigorously derived from the proposed LBM. The present LBM is a universal model for RHT in media with arbitrary refractive index distribution, which can naturally handle RHT in homogeneous media with constant refractive index. This model is expected to provide a simple and efficient mesoscopic tool for RHT in complex media and pave the way for establishing a unified framework of LBM for convection, conduction, and thermal radiation heat transfer.
Highlights
In the past two decades, it has attracted a wide range of attention and some numerical methods have been developed to investigate radiative heat transfer (RHT) in graded-index media [44,45,46,47,48,49,50,51,52,53], but these methods are relatively difficult to deal with conjugated convection, conduction, and thermal radiation heat transfer in a unified manner
To test the applicability of present mesoscopic lattice Boltzmann model (LBM) for RHT in graded-index media, one-dimensional and twodimensional transient and steady-state cases are studied
The angular domain discretization scheme adopts the popular piecewise constant approximation scheme, and the derivative terms of refractive index to zenith and azimuth angles are processed by the classical finite-difference scheme [48]
Summary
Since its introduction three decades ago [1,2], the lattice Boltzmann model (LBM) has developed into a recognized and popular approach for computational fluid dynamics [3,4,5], with various applications including magnetohydrodynamics [6], turbulent flow [7], multiphase flow [8], micro- and nanoscale flow [9], thermal flow [10,11], relativistic hydrodynamics [12] and so on [13,14,15,16,17]. In the past two decades, it has attracted a wide range of attention and some numerical methods have been developed to investigate RHT in graded-index media [44,45,46,47,48,49,50,51,52,53], but these methods are relatively difficult to deal with conjugated convection, conduction, and thermal radiation heat transfer in a unified manner. It is of great significance to develop a LBM for RHT in graded-index media, to achieve a simple and efficient solution to the problem, and to pave the way for establishing a unified framework of the LBM for convection, conduction, and thermal radiation heat transfer. Zhang et al [54] developed a pioneering LBM for one-dimensional transient RHT in graded-index media They constructed the lattice Boltzmann equation (LBE) by discretizing the radiative transfer equation (RTE) in time and space. We note that the present LBM can be naturally degenerated to handle RHT in homogeneous media with constant refractive index
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