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.

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 Inhomogeneous boundary-value problem of radiation heat transfer for a multicomponent medium

2020 ◽  
pp. 108-113
Author(s):  
A.Yu. Chebotarev ◽  
Keyword(s):  
Heat Transfer ◽  
Boundary Value Problem ◽  
Unique Solvability ◽  
Radiative Heat Transfer ◽  
Radiative Heat ◽  
Boundary Value ◽  
Radiation Heat Transfer ◽  
Multicomponent Medium ◽  
Radiation Heat ◽  
Conjugation Conditions

An analysis of the solvability of an inhomogeneous boundary value problem for the equations of radiative heat transfer with the Fresnel conjugation conditions is presented. The nonlocal unique solvability of the boundary value problem is proved.

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.

Simulation of Radiation Heat Transfer of Three Dimensional Participating Media by Radiative Exchange Method

2008 ◽  
Author(s):  
Mohammad Hadi Bordbar ◽  
Timo Hyppa¨nen
Keyword(s):  
Heat Transfer ◽  
Balance Equation ◽  
Radiation Heat Transfer ◽  
Three Dimensional ◽  
Radiation Balance ◽  
Scattering Media ◽  
Radiation Heat ◽  
Exchange Method ◽  
Participating Media ◽  
Radiative Exchange

This paper describes the theoretical bases of the Radiative Exchange Method, a new numerical method for simulating radiation heat transfer. By considering radiative interaction between all points of the geometry and solving the radiation balance equation in a mesh structure coarser than the structure used in computational fluid flow calculation, this method is able to simulate radiative heat transfer in arbitrary 3D space with absorbing, emitting and scattering media surrounded by emitting, absorbing and reflecting surfaces. A new concept is introduced, that of the exchange factors between the different elements that are necessary for completing the radiative balance equation set. Using this method leads to a set of algebraic equations for the radiative outgoing power from each coarse cell being produced and the result of this set of equations was then used to calculate the volumetric radiative source term in the fine cell structure. The formulation of the exchange factor for a three-dimensional state and also a mesh size analysis that was conducted to optimize the accuracy and runtime are presented. The results of this model to simulate typical 3D furnace shape geometry, is verified by comparison with those of other numerical methods.

Discrete Ordinates Method for Transient Radiation Transfer in Cylindrical Enclosures

2003 ◽  
Author(s):  
Kyunghan Kim ◽  
Zhixiong Guo
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Radiative Heat ◽  
Radiation Transfer ◽  
Radiation Heat Transfer ◽  
Discrete Ordinates ◽  
Radiation Heat ◽  
Discrete Ordinates Method ◽  
Transient Radiation ◽  
Tissue Welding

The Discrete Ordinates Method (DOM) for solving transient radiation transfer equation in cylindrical coordinates is developed for radiation heat transfer in participating turbid media in pico-scale time domain. The application problems addressed here are laser tissue welding and soldering. The novelty of this study lies with the use of ultrashort laser pulses as the irradiation source. The characteristics of transient radiation heat transfer in ultrafast laser tissue welding and soldering are studied with the DOM developed. The temporal distribution of radiative energy inside the tissue cylinder as well as the radiative heat flux on the tissue surface is obtained. Comparisons are performed between laser welding without use of solder and laser soldering with use of solder. The use of solder is found to have highly concentrated radiation energy deposition in the solder-stained region and reduce the surface radiative heat flux accordingly. Comparisons of transient radiation heat transfer between the spatially square-variance and Gaussian-variance laser inputs and between the temporally Gaussian and skewed input profiles are also conducted.

Natural Convection/Radiation Heat Transfer Simulations of an Enclosed Array of Vertical Rods

2006 ◽  
Author(s):  
N. R. Chalasani ◽  
Miles Greiner
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Heat Generation ◽  
Spent Nuclear Fuel ◽  
Radiation Heat Transfer ◽  
Three Dimensional ◽  
Radiation Heat ◽  
Simulation Techniques ◽  
Computational Fluid Dynamics Simulations ◽  
Dynamics Simulations

Experiments performed by others measured the temperature of twelve heated vertical rods within a constant temperature, internally finned cylindrical enclosure. Measurements were performed for a range of air and helium pressures and a range of rod heat generation rates. In the current work, three-dimensional computational fluid dynamics simulations of natural convection and radiation heat transfer within this domain were conducted to benchmark the simulation techniques. These calculations accurately reproduced the local and average temperatures when the heat generation rate was sufficiently low that the velocity field is steady. Future simulations will be used to design experiments that model spent nuclear fuel within non-isothermal cells of storage packages.

Radiation Heat Transfer of Arbitrary Three–Dimensional Absorbing, Emitting and Scattering Media and Specular and Diffuse Surfaces

1997 ◽  
Vol 119 (1) ◽  
pp. 129-136 ◽  
Author(s):  
S. Maruyama ◽  
T. Aihara
Keyword(s):  
Heat Transfer ◽  
Radiation Heat Transfer ◽  
Three Dimensional ◽  
Thermal Conditions ◽  
Emission Model ◽  
Scattering Media ◽  
Radiation Heat ◽  
Arbitrary Configuration ◽  
The Monte Carlo Method ◽  
Definition Of

Analysis of radiation heat transfer using the Radiation Element Method by Ray Emission Model, REM2, is described. The REM2 is a generalized numerical method for calculating radiation heat transfer between absorbing, emitting and scattering media and specular surfaces with arbitrary three–dimensional configurations. The ray emission model for various radiation elements is expressed by polyhedrons and polygons. Arbitrary thermal conditions can be specified for each radiation element, and generalized radiation transfer can be achieved for both of surface and volume elements by introducing a new definition of view factors. The accuracy of the present method is verified using simple configurations. A cubic participating medium with a spherical cavity covered with specular and diffuse surfaces is analyzed as an example of an arbitrary configuration. The temperature distribution shows good accuracy with a small number (45) of rays emitted from each element compared with the Monte Carlo method.

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