A Generalized Variational Method for Calculating Radiant Interchange Between Surfaces

1965 ◽  
Vol 87 (1) ◽  
pp. 103-109 ◽  
Author(s):  
E. M. Sparrow ◽  
A. Haji-Sheikh
Keyword(s):  
Heat Transfer ◽  
Variational Method ◽  
Solution Method ◽  
Radiation Heat Transfer ◽  
Governing Equations ◽  
Radiation Heat ◽  
Reflecting Surfaces ◽  
Transfer Problems ◽  
Approximate Solution Method ◽  
Variational Expression

A variational expression is devised from which the governing equations are derivable for all problems of radiant interchange between diffusely emitting and reflecting surfaces. This correspondence between the variational expression and the equations of radiant interchange serves as the basis of an approximate solution method for radiation heat transfer problems. The solution method is discussed in general and then applied to specific physical situations. It is shown that the variational method yields results with remarkable ease, especially when compared with the formidable computational task inherent in a direct numerical assault on the governing integral equations.

Application of Variational Methods to Radiation Heat-Transfer Calculations

1960 ◽  
Vol 82 (4) ◽  
pp. 375-380 ◽  
Author(s):  
E. M. Sparrow
Keyword(s):  
Heat Transfer ◽  
Variational Method ◽  
Integral Equations ◽  
Radiation Heat Transfer ◽  
General Description ◽  
Parallel Plates ◽  
Radiation Heat ◽  
Transfer Problems ◽  
Plate System ◽  
Good Agreement

A variational method is presented for solving a class of integral equations which arise in radiation heat-transfer problems. First, to demonstrate the formulation of radiation problems in terms of integral equations, consideration is given to a system consisting of two nonblack, finite, parallel plates. After a general description of the variational method, its use is illustrated by application to the parallel-plate system. Comparisons are made which show very good agreement with exact solutions.

Meshless Local Petrov-Galerkin Method for Heat Transfer Analysis

2013 ◽  
Author(s):  
Singiresu S. Rao
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Boundary Conditions ◽  
Transfer Coefficient ◽  
Transfer Problem ◽  
Radiation Heat Transfer ◽  
Heat Transfer Problem ◽  
Radiation Heat ◽  
Mlpg Method ◽  
Transfer Problems

A meshless local Petrov-Galerkin (MLPG) method is proposed to obtain the numerical solution of nonlinear heat transfer problems. The moving least squares scheme is generalized, to construct the field variable and its derivative continuously over the entire domain. The essential boundary conditions are enforced by the direct scheme. The radiation heat transfer coefficient is defined, and the nonlinear boundary value problem is solved as a sequence of linear problems each time updating the radiation heat transfer coefficient. The matrix formulation is used to drive the equations for a 3 dimensional nonlinear coupled radiation heat transfer problem. By using the MPLG method, along with the linearization of the nonlinear radiation problem, a new numerical approach is proposed to find the solution of the coupled heat transfer problem. A numerical study of the dimensionless size parameters for the quadrature and support domains is conducted to find the most appropriate values to ensure convergence of the nodal temperatures to the correct values quickly. Numerical examples are presented to illustrate the applicability and effectiveness of the proposed methodology for the solution of heat transfer problems involving radiation with different types of boundary conditions. In each case, the results obtained using the MLPG method are compared with those given by the FEM method for validation of the results.

scholarly journals Radiation heat transfer model using Monte Carlo ray tracing method on hierarchical ortho-Cartesian meshes and non-uniform rational basis spline surfaces for description of boundaries

2014 ◽  
Vol 35 (2) ◽  
pp. 65-92 ◽  
Author(s):  
Paweł Kuczyński ◽  
Ryszard Białecki
Keyword(s):  
Heat Transfer ◽  
Ray Tracing ◽  
Radiation Heat Transfer ◽  
Transfer Model ◽  
Rational Basis ◽  
Radiation Heat ◽  
Cartesian Meshes ◽  
Spline Surfaces ◽  
Nurbs Surfaces ◽  
Transfer Problems

Abstract The paper deals with a solution of radiation heat transfer problems in enclosures filled with nonparticipating medium using ray tracing on hierarchical ortho-Cartesian meshes. The idea behind the approach is that radiative heat transfer problems can be solved on much coarser grids than their counterparts from computational fluid dynamics (CFD). The resulting code is designed as an add-on to OpenFOAM, an open-source CFD program. Ortho-Cartesian mesh involving boundary elements is created based upon CFD mesh. Parametric non-uniform rational basis spline (NURBS) surfaces are used to define boundaries of the enclosure, allowing for dealing with domains of complex shapes. Algorithm for determining random, uniformly distributed locations of rays leaving NURBS surfaces is described. The paper presents results of test cases assuming gray diffusive walls. In the current version of the model the radiation is not absorbed within gases. However, the ultimate aim of the work is to upgrade the functionality of the model, to problems in absorbing, emitting and scattering medium projecting iteratively the results of radiative analysis on CFD mesh and CFD solution on radiative mesh.

Investigation on the Impact of Angle Dependency and Polarization on Radiation Heat Transfer

2021 ◽  
Author(s):  
Mathieu Wijnen ◽  
Jos van Schijndel ◽  
Gunes Nakiboglu
Keyword(s):  
Heat Transfer ◽  
Semiconductor Industry ◽  
Radiation Heat Transfer ◽  
Analytical Approximation ◽  
Radiation Heat ◽  
Modeling Tools ◽  
Increasing Demand ◽  
Radiation Modeling ◽  
Reflecting Surfaces ◽  
The Impact

Abstract In the semiconductor industry there is an increasing demand for thermal stability to optimize the performance of lithography machines. This results in a need for computational tools that are able to accurately model radiation heat transfer, with the ability to include specular and angle dependent reflection and take the influence of the polarization into account. An analytical approximation model of a square passage is formulated, that includes angle dependent reflecting surfaces and the influence of polarization. These problems can be used as benchmarks to verify radiation modeling tools, e.g. COMSOL. The tool is validated by modeling an experiment and comparing the numerical results with the experimental data. The impact of angle dependency and polarization on the heat flux through passages is discussed.

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