Fatmir Asllanaj

Heat transfer by radiation and conduction in fibrous media without axial symmetry

Coupled radiative and conductive heat transfer in a fibrous medium formed by silica fibres is investigated in this paper by not taking account of the axial symmetry for the distribution of fibres or the boundary conditions. Radiative properties of the medium are calculated by using the Mie theory. The model obtained depends only on optical parameters (indices of silica) and on morphological parameters (diameter and orientation of the fibres, density of the medium). Simulations make it possible to study the strongly anisotropic behaviour of the scattering of the radiation by a fibre and to study the influence of various parameters on the radiative properties of the medium. The results of the Mie theory make possible the simulation of the heat transfer coupled by radiation and conduction. To do this, we introduce a new numerical scheme able to simulate heat transfer in the lack of axial symmetry. With this model, we can show the effects of distribution of fibres and temperature on the thermal behaviour of the medium as well as showing the importance of the phenomenon of scattering in fibrous media.

Transient Radiation and Conduction Heat Transfer in a Gray Absorbing-Emitting Medium Applied on Two-Dimensional Complex-Shaped Domains

This article is devoted to transient radiation and conduction heat transfer in a gray absorbing-emitting medium in a two-dimensional complex-shaped domain using unstructured triangular meshes. The radiative transfer equation (RTE) is solved by using a new finite-volume method (FVM) based on a cell vertex scheme and associated to a modified exponential scheme. The PHAML (Parallel Hierarchical Adaptive MultiLevel) code is used to solve the energy balance equation using low- or high-order finite elements. Several benchmark cases including steady and transient states and applied to different geometries are used to validate the developed code. Results show very good agreement.

Coupled radiative and conductive heat transfer in a non-grey absorbing and emitting semitransparent media under collimated radiation

Abstract This paper deals with heat transfer in non-grey semitransparent two-dimensional sample. Considering an homogeneous purely absorbing medium, we calculated the temperature field and heat fluxes of a material irradiated under a specific direction. Coupled radiative and conductive heat transfer were considered. The radiative heat transfer equation (RTE) was solved using a S8 quadrature and a discrete ordinate method. Reflection and absorption coefficients of the medium were calculated with the silica optical properties. The conduction inside the medium was linked to the RTE through the energy conservation. Validation of the model and two original cases are also presented.

A Consistent Interpolation Function for the Solution of Radiative Transfer on Triangular Meshes. I—Comprehensive Formulation

This article presents a first-order skewed upwinding procedure for application to discretization numerical methods in the context of radiative transfer involving gray participating media. This scheme: (1) yields fast convergence of the algorithm; (2) inherently precludes the possibility of computing negative coefficients to the discretized algebraic equations; (3) reduces false scattering (diffusion); (4) is relatively insensitive to grid orientation; and (5) produces solutions completely free from undesirable oscillations. Theses attributes render the scheme attractive, especially in the context of combined modes of heat transfer and fluid flow problems for which computational time is a major concern. The suggested scheme has been validated by application to several basic test problems discussed in a companion article.

A Consistent Interpolation Function for the Solution of Radiative Transfer on Triangular Meshes, II—Validation

This article presents selected problems used to assess the validity and usefulness of a first-order skew, positive coefficient, upwind scheme (SPCUS) applied to radiative transfer. This particular procedure could be incorporated in several discretization methods such as finite-volume, finite-element, or control-volume finite-element methods for the prediction of radiative transfer in participating media. The suggested scheme has been validated by application to several basic two-dimensional test problems, acknowledged by the radiative heat transfer community, and its performance has proven to be good.

CONVERGENCE OF A NUMERICAL SCHEME FOR A NONLINEAR COUPLED SYSTEM OF RADIATIVE-CONDUCTIVE HEAT TRANSFER EQUATIONS

In this paper, we prove the convergence of a numerical scheme for one-dimensional coupled system of nonlinear partial and ordinary integro-differential equations. This system describes the steady-state coupled radiative-conductive heat transfer for a non-grey anisotropically absorbing, emitting and scattering medium, with axial symmetry and nonhomogeneous Dirichlet boundary conditions. The convergence proof follows from monotonicity arguments and the application of a discrete fixed-point problem, involving only to the temperature fields.