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.

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.

Experimental study of radiation heat transfer coefficient of diffusion flames

2007 ◽  
Vol 29 (2) ◽  
pp. 98-104
Author(s):  
Bui Van Ga ◽  
Le Van Tuy ◽  
Huynh Ba Vang ◽  
Le Van Lu ◽  
Nguyen Ngoc Linh
Keyword(s):  
Heat Transfer ◽  
Experimental Study ◽  
Heat Transfer Coefficient ◽  
Diesel Engine ◽  
Transfer Coefficient ◽  
Combustion Chamber ◽  
Diffusion Flames ◽  
Radiation Heat Transfer ◽  
Radiation Heat ◽  
Coefficient Of Diffusion

Basing on analysis of flame pictures given by visioscope by two-color method, the paper presents evolution of radiation heat transfer coefficient \(\varepsilon_s\) of soot in diffusion flames in air, in furnace and in combustion chamber of Diesel engine. \(\varepsilon_s\) reaches respectively its maximal value of 0.15; 0.30 and 0.45 in regions of maximal soot fraction of the three above flames.

Enhancement of Heat Transfer Performance in Nuclear Fuel Rod Using Nanofluids and Surface Roughness Technique

2015 ◽  
Author(s):  
Kang Liu ◽  
Titan C. Paul ◽  
Leo A. Carrilho ◽  
Jamil A. Khan
Keyword(s):  
Heat Transfer ◽  
Surface Roughness ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Nuclear Fuel ◽  
Three Dimensional ◽  
Pressurized Water ◽  
Bulk Fluid ◽  
Fuel Rod ◽  
Dimensional Surface

The experimental investigations were carried out of a pressurized water nuclear reactor (PWR) with enhanced surface using different concentration (0.5 and 2.0 vol%) of ZnO/DI-water based nanofluids as a coolant. The experimental setup consisted of a flow loop with a nuclear fuel rod section that was heated by electrical current. The fuel rod surfaces were termed as two-dimensional surface roughness (square transverse ribbed surface) and three-dimensional surface roughness (diamond shaped blocks). The variation in temperature of nuclear fuel rod was measured along the length of a specified section. Heat transfer coefficient was calculated by measuring heat flux and temperature differences between surface and bulk fluid. The experimental results of nanofluids were compared with the coolant as a DI-water data. The maximum heat transfer coefficient enhancement was achieved 33% at Re = 1.15 × 105 for fuel rod with three-dimensional surface roughness using 2.0 vol% nanofluids compared to DI-water.

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