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One‐dimensional radiative heat transfer is considered in a plane‐parallel geometry for an absorbing, emitting, and linearly anisotropic scattering medium subjected to azimuthally symmetric incident radiation at the boundaries. The integral form of the transport equation is used throughout the analysis. This formulation leads to a system of weakly‐singular Fredholm integral equations of the second kind. The resulting unknown functions are then formally expanded in Chebyshev series. These series representations are truncated at a specified number of terms, leaving residual functions as a result of the approximation. The collocation and the Ritz‐Galerkin methods are formulated, and are expressed in terms of general orthogonality conditions applied to the residual functions. The major contribution of the present work lies in developing quantitative error estimates. Error bounds are obtained for the approximating functions by developing equations relating the residuals to the errors and applying functional norms to the resulting set of equations. The collocation and Ritz‐Galerkin methods are each applied in turn to determine the expansion coefficients of the approximating functions. The effectiveness of each method is interpreted by analyzing the errors which result from the approximations.

Notes that, in a full‐scale application of the Monte Carlo method for combined heat transfer analysis, problems usually arise from the large computing requirements. Here the method to overcome this difficulty is the parallel execution of the Monte Carlo method in a distributed computing environment. Addresses the problem of determination of the temperature field formed under the assumption of radiative equilibrium in an enclosure idealizing an industrial furnace. The medium contained in this enclosure absorbs, emits and scatters anisotropically thermal radiation. Discusses two topics in detail: first, the efficiency of the parallelization of the developed code, and second, the influence of the scattering behavior of the medium. The adopted parallelization method for the first topic is the decomposition of the statistical sample and its subsequent distribution among the available processors. The measured high efficiencies showed that this method is particularly suited to the target architecture of this study, which is a dedicated network of workstations supporting the message passing paradigm. For the second topic, the results showed that taking into account the isotropic scattering, as opposed to neglecting the scattering, has a pronounced impact on the temperature distribution inside the enclosure. In contrast, the consideration of the sharply forward scattering, that is characteristic of all the real combustion particles, leaves the predicted temperature field almost undistinguishable from the absorbing/emitting case.

Influence of forward scattering, including ionized‐impurity and polar optical‐phonon scattering, on electron transport phenomena in a 3‐valley n‐type GaAs model subjected to a rapid change in field is studied. It is shown that the macroscopic effective mass of electrons in a nonparabolic band structure is smaller than the energy‐dependent effective mass, which is usually assumed for modeling of GaAs devices, during the interval of velocity overshoot when strong forward scattering is involved. As a consequence, the hydrodynamic transport model, where the macroscopic effective mass is assumed energy dependent, leads to a smaller overshoot velocity.

The paper aims to test the spectral line-based weighted sum of gray gases (SLW) method in axisymmetric geometries with particles and high temperature gradients.

An SLW model is coupled with Trivic’s mean wavelength approach to estimate the radiative heat fluxes at the wall of an enclosure and to the base wall of the rocket exhaust, thereby subsequently studying the effect of concentration variation of the gases and particles in these cases. Radiative transfer equation is solved using modified discrete ordinates method. Anisotropic scattering is modeled using transport approximation.

Two cases considered show the importance of particle emission and scattering in the rocket plume base heating problems. In cases involving only gases, the concentration of H₂O tends to have more impact on the flux values than any other gas.

A full model of gases with particles in an axially varying temperature field is reported. Such cases are very common in practical applications. The present methodology gives more insight and a firm handle on the problem vis-a-vis other traditional techniques.

Radiative heat transfer in the laminar boundary layer flow of an absorbing, emitting and anisotropically scattering gray fluid over a flat plate, with the surface of the plate reflecting radiation in diffuse‐cum‐specular fashion is analyzed. The discrete ordinates method is used to model the radiative transfer. The governing dimensionless momentum and energy equations, in the form of a partial differential system, are solved by a finite difference method. The effect of various parameters like, emittance, the degree of anisotropy in scattering, scattering albedo and the nature of surface reflection on the total heat flux from the plate to the fluid are studied and results are presented.

The purpose of this paper is to numerically investigate time-harmonic elastic wave propagation with the analysis of effective wave velocities and attenuation coefficients in a three-dimensional elastic composite consisting of infinite matrix and uniformly distributed soft, low-contrast and absolutely rigid disc-shaped micro-inclusions.

Within the assumptions of longitudinal mode of a propagating wave as well as dilute concentration and parallel orientation of inclusions in an infinite elastic matrix, Foldy’s dispersion relation is applied for introducing a complex and frequency-dependent wavenumber of homogenized structure. Then, the effective wave velocities and attenuation coefficients are directly defined from the real and imaginary parts of wavenumber, respectively. Included there a far-field forward scattering amplitude by a single low-contrast inclusion given in an analytical form, while for the other types of single scatterers it is determined from the numerical solution of boundary integral equations relative to the displacement jumps across the surfaces of soft inclusion and the stress jumps across the surfaces of rigid inclusion.

On the frequency dependencies, characteristic extremes of the effective wave velocities and attenuation coefficients are revealed and analyzed for different combinations of the filling ratios of involved types of inclusions. Anisotropic dynamic behavior of composite is demonstrated by the consideration of wave propagation in perpendicular and tangential directions relatively to the plane of inclusions. Specific frequencies are revealed for the first case of wave propagation, at which inclusion rigidities do not affect the effective wave parameters.

This paper develops a micromechanical study that provides a deeper understanding of the effect of thin-walled inclusions of diversified rigidities on elastic wave propagation in a three-dimensional composite. Described wave dispersion and attenuation regularities are important for the non-destructive testing of composite materials by ultrasonics.

A super‐condensed TLM node for modelling inhomogeneous anisotropic media on an arbitrarily graded mesh without using stubs is developed. It requires less storage, computationally is more efficient and can operate on a higher time step than existing TLM nodes. Complete derivation, implementation and validation of the new node are presented in the paper.

A finite element method for the analysis of combined radiative and conductive heat transport in a finite axisymmetric configuration is presented. The appropriate integro‐differential governing equations for a grey and non‐scattering medium with grey and diffuse walls are developed and solved for several model problems. We consider axisymmetric, cylindrical geometries with top and bottom boundaries of arbitrary convex shape. The method is accurate for media of any optical thickness and is capable of handling a wide array of axisymmetric geometries and boundary conditions. Several techniques are presented to reduce computational overhead, such as employing a Swartz‐Wendroff approximation and cut‐off criteria for evaluating radiation integrals. The method is successfully tested against several cases from the literature and is applied to some additional example problems to demonstrate its versatility. Solution of a free‐boundary, combined‐mode heat transfer problem representing the solidification of a semitransparent material, the Bridgman growth of an yttrium aluminium garnet (YAG) crystal, demonstrates the utility of this method for analysis of a complex materials processing system. The method is suitable for application to other research areas, such as the study of glass processing and the design of combustion furnace systems.

The build characteristics of two liquid crystal (LC) reactive monomers were studied using a table‐top stereolithography apparatus (TTSLA). LC materials contain stiff, rod‐like mesogenic segments in their molecules, which can be aligned causing an anisotropy in properties. When cured in the aligned state the anisotropic structure is “locked in” resulting in materials with anisotropic physical and mechanical properties. By varying the alignment of layers, properties such as thermal expansion coefficient can be optimized. High heat distortion (or glass transition) temperatures are possible depending on the monomer chemical structure. Working curves for the LC resins were developed under various conditions. A permanent magnet placed outside the TTSLA vat was used to uniformly align the monomer in the nematic state. Photo‐initiator type and content; alignment of the nematic phase; and operating conditions affected the working curve parameters. Glass transition temperatures of post‐cured parts ranged from 75 to 1488C depending on the resin and processing conditions. Mechanical analysis data revealed a factor of two difference between glassy moduli measured in the molecular alignment versus the transverse alignment directions. Based on these initial studies, more advanced resins with higher glass transitions are being developed at the University of Dayton.

This study aims to perform a comprehensive investigation to model the thermal characteristics of a coupled conduction-radiation heat transfer in a two-dimensional irregular enclosure including a triangular-shaped heat source.

For this purpose, a promising hybrid technique based on the concepts of blocked-off method, FVM and DOM is developed. The enclosure consists of several horizontal, vertical and oblique walls, and thermal conductivity within the enclosure varies directly with temperature and indirectly with position. To simplify the complex geometry, a promising mathematical model is introduced using blocked-off method. Emitting, absorbing and non-isotropic scattering gray are assumed as the main radiative characteristics of the steady medium.

DOM and FVM are, respectively, applied for solving radiative transfer equation (RTE) and the energy equation, which includes conduction, radiation and heat source terms. The temperature and heat flux distributions are calculated inside the enclosure. For validation, results are compared with previous data reported in the literature under the same conditions. Results and comparisons show that this approach is highly efficient and reliable for complex geometries with coupled conduction-radiation heat transfer. Finally, the effects of thermo-radiative parameters including surface emissivity, extinction coefficient, scattering albedo, asymmetry factor and conduction-radiation parameter on temperature and heat flux distributions are studied.

In this paper, a hybrid numerical method is used to analyze coupled conduction-radiation heat transfer in an irregular geometry. Varying thermal conductivity is included in this analysis. By applying the method, results obtained for temperature and heat flux distributions are presented and also validated by the data provided by several previous papers.