The spatial and angular domain decomposition method for radiation heat transfer in 2D rectangular enclosures with discontinuous boundary conditions

2019 ◽  
Vol 146 ◽  
pp. 106091 ◽  
Author(s):  
Zhangmao Hu ◽  
Xuwu Zhu ◽  
Zhixiong Guo ◽  
Hong Tian ◽  
Bewen Li
Keyword(s):  
Heat Transfer ◽  
Boundary Conditions ◽  
Domain Decomposition ◽  
Decomposition Method ◽  
Domain Decomposition Method ◽  
Radiation Heat Transfer ◽  
Angular Domain ◽  
Radiation Heat ◽  
Discontinuous Boundary

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 An algorithm for solving the boundary value problem of radiation heat transfer without boundary conditions for radiation intensity

2020 ◽  
pp. 114-122
Author(s):  
A.Yu. Chebotarev ◽  
◽  
P.R. Mesenev ◽  
Keyword(s):  
Heat Transfer ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Radiation Intensity ◽  
Radiation Transfer ◽  
Boundary Value ◽  
Radiation Heat Transfer ◽  
Three Dimensional ◽  
Conductive Heat ◽  
Radiation Heat

An optimization algorithm for solving the boundary value problem for the stationary equations of radiation-conductive heat transfer in the three-dimensional region is presented in the framework of the $ P_1 $ - approximation of the radiation transfer equation. The analysis of the optimal control problem that approximates the boundary value problem where they are not defined boundary conditions for radiation intensity. Theoretical analysis is illustrated by numerical examples.

A Domain Decomposition Method for Vibration Analysis of Conical Shells With Uniform and Stepped Thickness

2013 ◽  
Vol 135 (1) ◽  
Author(s):  
Yegao Qu ◽  
Yong Chen ◽  
Yifan Chen ◽  
Xinhua Long ◽  
Hongxing Hua ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Domain Decomposition ◽  
Decomposition Method ◽  
Domain Decomposition Method ◽  
Forced Vibrations ◽  
Uniform Thickness ◽  
Weighted Residual Method ◽  
Conical Shells ◽  
Free And Forced Vibrations ◽  
Special Cases

An efficient domain decomposition method is proposed to study the free and forced vibrations of stepped conical shells (SCSs) with arbitrary number of step variations. Conical shells with uniform thickness are treated as special cases of the SCSs. Multilevel partition hierarchy, viz., SCS, shell segment and shell domain, is adopted to accommodate the computing requirement of high-order vibration modes and responses. The interface continuity constraints on common boundaries and geometrical boundaries are incorporated into the system potential functional by means of a modified variational principle and least-squares weighted residual method. Double mixed series, i.e., the Fourier series and Chebyshev orthogonal polynomials, are adopted as admissible displacement functions for each shell domain. To test the convergence, efficiency and accuracy of the present method, free and forced vibrations of uniform thickness conical shells and SCSs are examined under various combinations of classical and nonclassical boundary conditions. The numerical results obtained from the proposed method show good agreement with previously published results and those from the finite element program ANSYS. The computational advantage of the approach can be exploited to gather useful and rapid information about the effects of geometry and boundary conditions on the vibrations of the uniform and stepped conical shells.

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