scholarly journals An improved iterative method for solving a class of coupled conductive-radiative heat-transfer problems

1995 ◽  
Vol 54 (4) ◽  
pp. 599-605 ◽  
Author(s):  
C.E. Siewert
Keyword(s):  
Heat Transfer ◽  
Iterative Method ◽  
Radiative Heat Transfer ◽  
Radiative Heat ◽  
Transfer Problems

scholarly journals An Iterative Method for Solving of Coupled Equations for Conductive-Radiative Heat Transfer in Dielectric Layers

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Vasyl Chekurin ◽  
Yurij Boychuk
Keyword(s):  
Heat Transfer ◽  
Iterative Method ◽  
Radiative Heat Transfer ◽  
Radiative Heat ◽  
Thick Layer ◽  
Ir Radiation ◽  
Coupled Equations ◽  
Radiation Fluxes ◽  
Radiation Properties ◽  
Unperturbed Problem

The mathematical model for describing combined conductive-radiative heat transfer in a dielectric layer, which emits, absorbs, and scatters IR radiation both in its volume and on the boundary, has been considered. A nonlinear stationary boundary-value problem for coupled heat and radiation transfer equations for the layer, which exchanges by energy with external medium by convection and radiation, has been formulated. In the case of optically thick layer, when its thickness is much more of photon-free path, the problem becomes a singularly perturbed one. In the inverse case of optically thin layer, the problem is regularly perturbed, and it becomes a regular (unperturbed) one, when the layer’s thickness is of order of several photon-free paths. An iterative method for solving of the unperturbed problem has been developed and its convergence has been tested numerically. With the use of the method, the temperature field and radiation fluxes have been studied. The model and method can be used for development of noncontact methods for temperature testing in dielectrics and for nondestructive determination of its radiation properties on the base of the data obtained by remote measuring of IR radiation emitted by the layer.

Application of Modified Discrete Ordinates Method With the Concept of Blocked-Off Region Method to Radiative Heat Transfer Problems in Irregular Geometries

2010 ◽  
Author(s):  
H. Amiri ◽  
S. H. Mansouri ◽  
A. Safavinejad
Keyword(s):  
Heat Transfer ◽  
Radiative Heat Transfer ◽  
Radiative Heat ◽  
Curvilinear Coordinates ◽  
Discrete Ordinates ◽  
Test Problems ◽  
Discrete Ordinates Method ◽  
Irregular Geometries ◽  
Transfer Problems ◽  
Ray Effects

The discrete ordinates method (DOM) for the solution of radiative heat transfer problems have received significant attention and development owing to their good compromise between accuracy, flexibility and moderate computational requirement. However, the DOM suffers from the ray effects related to the discretization of the angular distribution of the radiation intensity. The modified discrete ordinate method (MDOM) proved to significantly mitigate ray effects originated from discontinuities or abrupt changes of the wall temperature. This article presents blocked-off region treatment of irregular geometries using a modified discrete ordinates method in Cartesian coordinates. The Cartesian based 2D algorithm can be used to solve radiative heat transfer in irregular geometries by dividing the region into active and inactive regions. It is easier and convenient way of handling 2D irregular geometries than to write an algorithm in curvilinear coordinates. It is capable of handling participating (absorbing, emitting and isotropic or anisotropic scattering) or non participating gray media enclosed by gray diffuse walls. Both radiative and non-radiative equilibrium situations are considered. The walls of the enclosures can have either heat flux or temperature boundary conditions. Cases with curved and obstacle and radiation shield are considered. Some test problems are considered and results are validated with the available results in the literature. Results are found to be accurate for all kinds of situations.

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