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.

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 Radiation heat transfer between human and cryocabin walls

2021 ◽  
Vol 2119 (1) ◽  
pp. 012146
Author(s):  
I A Burkov ◽  
S I Khutsieva ◽  
V A Voronov
Keyword(s):  
Heat Transfer ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Human Body ◽  
Transfer Problem ◽  
Radiation Heat Transfer ◽  
Vertical Wall ◽  
Heat Transfer Problem ◽  
Radiation Heat ◽  
The Impact

Abstract The paper considers the particular case of intensive radiation heat transfer in the system consisting of a human body and cryocabin walls of cryosauna. Calculations for three models have been made, namely, human-vertical wall, which is arranged parallel to a human, human-vertical wall, which is positioned at a certain angle, and a human-cryosauna. Analytical calculations are compared with Ansys-bassed numerical calculations. The impact of radiation heat transfer in this radiation-convective heat transfer problem is estimated. Conclusions are drawn about taking into account the radiation heat transfer and a rational method for calculating this heat transfer problem.

scholarly journals Heat Transfer Coefficient Determination during FC-72 Flow in a Minichannel Heat Sink Using the Trefftz Functions and ADINA Software

Energies ◽  
2020 ◽  
Vol 13 (24) ◽  
pp. 6647
Author(s):  
Magdalena Piasecka ◽  
Beata Maciejewska ◽  
Paweł Łabędzki
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Heat Sink ◽  
Transfer Problem ◽  
Heat Transfer Problem ◽  
Heated Wall ◽  
Inlet Temperature ◽  
Transfer Coefficients ◽  
Flowing Fluid

This work focuses on subcooled boiling heat transfer during flow in a minichannel heat sink with three or five minichannels of 1 mm depth. The heated element for FC-72 flowing along the minichannels was a thin foil of which temperature on the outer surface was measured due to the infrared thermography. The test section was oriented vertically or horizontally. A steady state heat transfer process and a laminar, incompressible flow of the fluid in a central minichannel were assumed. The heat transfer problem was described by the energy equations with an appropriate system of boundary conditions. Several mathematical methods were applied to solve the heat transfer problem with the Robin condition to determine the local heat transfer coefficients at the fluid/heated foil interface. Besides the 1D approach as a simple analytical method, a more sophisticated 2D approach was proposed with solutions by the Trefftz functions and ADINA software. Finite element method (FEM) calculations were conducted to find the temperature field in the flowing fluid and in the heated wall. The results were illustrated by graphs of local heated foil temperature and transfer coefficients as a function of the distance from the minichannel inlet. Temperature distributions in the heater and the fluid obtained from the FEM computations carried out by ADINA software were also shown. Similar values of the heat transfer coefficient were obtained in both the FEM calculations and the 1D approach. Example boiling curves indicating nucleation hysteresis are shown and discussed.

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