Ben-Wen Li

Predication of nonlinear heat transfer in a convective-radiative fin with temperature-dependent properties by the collocation spectral method

ABSTRACT The applicability of the collocation spectral method (CSM) for solving nonlinear heat transfer problems is demonstrated in a convective-radiative fin with temperature-dependent properties. In this method, the fin temperature distribution is approximated by Lagrange interpolation polynomials at spectral collocation points. The differential form of the energy equation is transformed to a matrix form of algebraic equations. The computational convergence of the CSM approximately follows an exponential decaying law; and thus, it is a very simple and effective approach for a rapid assessment of nonlinear physical problems. The effects of temperature-dependent properties such as thermal conductivity, surface emissivity, heat transfer coefficient, convection-conduction parameter, and radiation-conduction parameter on the fin temperature distribution and efficiency are discussed.

Chebyshev Collocation Spectral Method for Three-Dimensional Transient Coupled Radiative–Conductive Heat Transfer

A Chebyshev collocation spectral method (CSM) is presented to solve transient coupled radiative and conductive heat transfer in three-dimensional absorbing, emitting, and scattering medium in Cartesian coordinates. The walls of the enclosures are considered to be opaque, diffuse, and gray and have specified temperature boundary conditions. The CSM is adopted to solve both the radiative transfer equation (RTE) and energy conservation equation in spatial domain, and the discrete ordinates method (DOM) is used for angular discretization of RTE. The exponential convergence characteristic of the CSM for transient coupled radiative and conductive heat transfer is studied. The results using the CSM show very satisfactory calculations comparing with available results in the literature. Based on this method, the effects of various parameters, such as the scattering albedo, the conduction–radiation parameter, the wall emissivity, and the optical thickness, are analyzed. [DOI: 10.1115/1.4006596]

Chebyshev collocation spectral domain decomposition method for coupled conductive and radiative heat transfer in a 3D L-shaped enclosure

ABSTRACT This paper presents a Chebyshev collocation spectral domain decomposition method (CSDDM) to study the coupled conductive and radiative heat transfer in a 3D L-shaped enclosure. The partitioned 3D L-shaped enclosure is subdivided into rectangular subdomains based on the concept of domain decomposition. The radiative transfer equation is angularly discretized by the discrete ordinate method with the SRAPN quadrature scheme and then solved by the CSDDM using the same grid system as in solving the conduction. The effects of the conduction–radiation parameter, the optical thickness, the scattering albedo, and the aspect ratio on thermal behavior of the system are investigated. The results indicate that the 3D CSDDM has a good accuracy and can be considered as a good alternative approach for the solution of the coupled conduction and radiation problems in 3D partitioned domains.

Fast transform spectral method for Poisson equation and radiative transfer equation in cylindrical coordinate system

ABSTRACT Direct matrix operation is extremely memory-consuming to solve the basic equations of the radiation-hydrodynamics (R-HD) problems, e.g., Poisson equation and radiative transfer equation (RTE), especially in the cases of large grid number and multidimensions. In this work, the fast transform spectral method (FTSM), which requires much less memory than the direct matrix operation, is developed to avoid large dense matrix operation. The proposed method converges monotonically for arbitrary initial value and is verified via the multidimensional Poisson equations and one-dimensional RTE in cylindrical coordinate system. Benchmarks are also introduced to demonstrate the good accuracy of this method. The performance of the FTSM has been validated by comparing with the matrix multiplication transform spectral method (MMTSM). The results show that, the presented method has good robustness and accuracy, when the directly matrix operation of MMTSM is out of memory the FTSM still works well with high accuracy when the grid number is large enough. This means that the FTSM can be a better selection for the R-HD problems when large number grid is needed and especially for multidimensions.

OUR RECENT WORKS ON THE COLLOCATION SPECTRAL METHOD FOR THERMAL RADIATION IN PARTICIPATING MEDIA

Due to the motivation of numerical simulation on radiative magnetohydrodynamics, as the first step, in recent few years, the authors and co-workers have adopted Chebyshev collocation spectral method (CSM) for the solutions of radiation transfer equation (RTE) in different situations and obtained many achievements. The solution cases include 1D thermal radiation with strong fluctuations and complex boundary conditions, coupled radiation and conduction in concentric spherical participating medium, pure radiation in graded index media, the steady and transient combination of radiation and conduction, etc. One most valuable work is the direct 3D Schurdecomposition for the 3D matrix equations after the discretization of RTE. The process of the applications of collocation spectral method to thermal radiation is introduced beginning from 3D case. The most favourite parts of CSM for RTE are the direct solution, the very high spatial accuracy, and the good potential of incorporation into computational fluid dynamics (CFD) and magnetohydrodynamics (MHD). As to irregular multi-dimensional geometric systems, CSM can also be adopted to solve the RTE together with the body fitted coordinates (BFC). Compared with discrete ordinates method (DOM), the accuracy of CSM is more sensitive to the number of discretized directions. Some obstacles, say, the direct solution of RTE under the cases of nonhomogeneous radiative properties, the inconsistence between the spectral accuracy in space and the only second-order accuracy in angular discretization, are stated. Finally, some possible futures are mentioned. NOMENCLATURE , , A B C coefficient square matrices in Eq. (5) p c specific heat (Jkg K)