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It is challenging to solve the phonon Boltzmann transport equation numerically due to the stiff collision term induced by small relaxation time. In this work, a discrete ordinate method with streaming and collision processes is developed for phonon Boltzmann transport equation. This method is explicit and does not need a linear solver. Moreover, it is uniformly stable in terms of the Knudsen number and has an asymptotic-preserving property. Thus, the time step is not restricted by the phonon relaxation time. In order to validate the present method, we investigate four numerical test cases, including cross-plane heat conduction, in-plane heat conduction, one-dimensional transient thermal grating problem and a hotspot problem. Numerical results show that the present method can capture the ballistic-diffusive transport phenomenon accurately and efficiently in a wide range of Knudsen numbers, and may provide an alternative tool for a deep research into multiscale phonon transport problem. [ABSTRACT FROM AUTHOR]

A local radial basis function meshless (LRBFM) method is developed to solve coupled radiative and conductive heat transfer problems in multidimensional participating media, in which compact support radial basis functions (RBFs) augmented on a polynomial basis are employed to construct the trial function, and the radiative transfer equation (RTE) and energy conservation equation are discretized directly at nodes by the collocation method. LRBFM belongs to a class of truly meshless methods which require no mesh or grid, and can be readily implemented in a set of uniform or irregular node distributions with no node connectivity. Performances of the LRBFM is compared to numerical results reported in the literature via a variety of coupled radiative and conductive heat transfer problems in 1D and 2D geometries. It is demonstrated that the local radial basis function meshless method provides high accuracy and great efficiency to solve coupled radiative and conductive heat transfer problems in multidimensional participating media with uniform and irregular node distribution, especially for coupled heat transfer problems in irregular geometry with Cartesian coordinates. In addition, it is extremely simple to implement. [ABSTRACT FROM PUBLISHER]

Transient radiative transfer (TRT) in a two-dimensional scattering medium with graded refractive index distribution subjected to a collimated short-pulse irradiation is solved by a modified Monte Carlo (MMC) method coupled with the time shift and superposition (TSS) principle. The boundaries are considered as Fresnel surfaces, the refractive index at the boundary mismatches with that of the surroundings, making the reflectivity at the boundary change with the incident directions. The incident pulse consists of two parts when it hits the boundary: bundles directly reflected by the outside boundary and bundles refracted into the medium. The accuracy of the present algorithm is confirmed first. Numerical results show that by using the TSS principle, the computational efficiency is greatly improved. Afterward, the TRT in the media with different graded refractive index distributions is investigated. The time-resolved reflectance and transmittance at different locations are given. Several trends on the time-resolved signals are observed and analyzed. [ABSTRACT FROM AUTHOR]

A modified Monte Carlo (MC) method has been developed for solving transient radiative transfer in a one-dimensional scattering medium with a graded refractive index. The accuracy and computational efficiency of the algorithm are validated initially. With the introduction of time shift and superposition principle into the MC model, the computational efficiency is greatly improved. We make a comparative analysis of the time-resolved incident radiation (and radiative heat flux) distributions in the media with diffuse and specular reflection boundaries. Results show that the temporal and spatial radiative signals of the medium with specular reflection boundaries greatly differ from those having diffuse reflection boundaries. [ABSTRACT FROM AUTHOR]

Interaction phenomena between laminar forced convection and thermal radiation in complex 3-D geometries with gray participating medium are studied numerically. The solution scheme is based on the least-squares finite element method (LSFEM) which, to the knowledge of the authors, is applied at the first time to 3-D radiative heat transfer in participating media. Three test cases are examined and compared with other published works to verify this LSFEM method. Comparisons show that the LSFEM method is stable and has a good accuracy. Two cases of coupled convective and radiative heat transfer are simulated at different conduction-radiation parameters and Peclet numbers. [ABSTRACT FROM AUTHOR]

Transient radiation heat transfer in a two-layer anisotropic scattering medium is investigated. Each layer of the medium can have different thermal and radiative properties. The two surfaces are assumed to be semitransparent or opaque, and the interface between the two layers is assumed to be semitransparent. Specular reflection is considered at the surfaces and the interface. A general criterion for total reflection at the surfaces and the interface is proposed to overcome the integral singularity problem above the critical angle. A fully implicit control-volume method is used to solve the transient energy equation of coupled radiation and conduction, and a ray-tracing/nodal-analyzing method is applied in the solution of the radiative transfer. Effects of emissivities of the surfaces, extinction coefficients, and optical boundary conditions on transient radiative heat transfer are examined. Results show that for the medium layer having a larger refractive index, its average temperature level may be higher, mainly due to the contribution of total reflection at the interface facing the layer, even if its absorption coefficient is relatively small compared to the medium layer having a larger absorption coefficient and a smaller refractive index. [ABSTRACT FROM AUTHOR]

Transient combined radiation-conduction inside a semitransparent scattering gray medium with a graded index is examined. By nodal analysis, the radiative source term of the energy equation is deduced through radiative transfer coefficients (RTCs), which are deduced through a multilayer model of radiative transfer, established by employing a ray-tracing method based on the zonal method. The basic idea is that a medium with a continually variable refractive index is discretized into certain number of isothermal sublayers with constant refractive index in each sublayer and the radiative transfer in a curve inside the graded index medium is regarded as that in a straight line within each sublayer. The present results accord very well with previous results. The results show that the multilayer model for radiative transfer to simulate the radiative transfer in a graded refractive index medium is reliable and correct. In addition, effects of convection boundary conditions, scattering albedo, opaque surface emission, and refractive index distribution on transient thermal behavior are also investigated for the graded index medium. [ABSTRACT FROM AUTHOR]