scholarly journals CHAPARRAL: A library for solving large enclosure radiation heat transfer problems

1995 ◽  
Author(s):  
M.W. Glass
Keyword(s):  
Heat Transfer ◽  
Radiation Heat Transfer ◽  
Radiation Heat ◽  
Large Enclosure ◽  
Transfer Problems

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.

Meshless Local Petrov-Galerkin Method for Three-Dimensional Heat Transfer Analysis

2012 ◽  
Vol 134 (11) ◽  
Author(s):  
Jun Tian ◽  
Singiresu S. Rao
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Boundary Conditions ◽  
Transfer Coefficient ◽  
Transfer Problem ◽  
Radiation Heat Transfer ◽  
Three Dimensional ◽  
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 derivatives continuously over the entire domain. The essential boundary conditions are enforced by the direct scheme. By defining a radiation heat transfer coefficient, 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 three 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 one-, two-, and three-dimensional 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 finite element method (FEM) method for validating the results.

scholarly journals A new hybrid algorithm for solving transient combined conduction radiation heat transfer problems

2011 ◽  
Vol 15 (3) ◽  
pp. 649-662 ◽  
Author(s):  
Raoudha Chaabane ◽  
Faouzi Askri ◽  
Ben Nasrallah
Keyword(s):  
Heat Transfer ◽  
Control Volume ◽  
Radiation Heat Transfer ◽  
Numerical Approach ◽  
Physical Parameters ◽  
Radiation Heat ◽  
Hybrid Solver ◽  
Simple Implementation ◽  
Boltzmann Method ◽  
Transfer Problems

A new algorithm based on the lattice Boltzmann method (LBM) and the Control Volume Finite Element Method (CVFEM) is proposed as an hybrid solver for two dimensional transient conduction and radiation heat transfer problems in an optically emitting, absorbing and scattering medium. The LBM was used to solve the energy equation and the CVFEM was used to compute the radiative information. The advantages of the proposed methodology is to avoid problems that confronted when previous techniques are used to predict radiative heat transfer, essentially, in complex geometries and when there is scattering and/or non-black boundaries surfaces. This method combination, which is applied for the first time to solve this unsteady combined mode of heat transfer, has been found to accurately predict the effects of various thermo-physical parameters such as the scattering albedo, the conduction-radiation parameter and the extinction coefficient on temperature distribution. The results of the LBM-CVFEM combination were found to be in excellent agreement with the LBM-CDM (Collapsed Dimension Method)this proposed numerical approach include, among others, simple implementation on a computer, accurate CPU time, and capability of stable simulation.

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.

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