### Abstract

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.

Original language | English |
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Title of host publication | ASME International Mechanical Engineering Congress and Exposition, Proceedings (IMECE) |

Publisher | American Society of Mechanical Engineers (ASME) |

Volume | 8 A |

ISBN (Print) | 9780791856345 |

DOIs | |

State | Published - Jan 1 2013 |

Event | ASME 2013 International Mechanical Engineering Congress and Exposition, IMECE 2013 - San Diego, CA, United States Duration: Nov 15 2013 → Nov 21 2013 |

### Other

Other | ASME 2013 International Mechanical Engineering Congress and Exposition, IMECE 2013 |
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Country | United States |

City | San Diego, CA |

Period | 11/15/13 → 11/21/13 |

### Fingerprint

### ASJC Scopus subject areas

- Mechanical Engineering

### Cite this

*ASME International Mechanical Engineering Congress and Exposition, Proceedings (IMECE)*(Vol. 8 A). American Society of Mechanical Engineers (ASME). https://doi.org/10.1115/IMECE2013-64554

**Meshless local petrov-galerkin method for heat transfer analysis.** / Rao, Singiresu S.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*ASME International Mechanical Engineering Congress and Exposition, Proceedings (IMECE).*vol. 8 A, American Society of Mechanical Engineers (ASME), ASME 2013 International Mechanical Engineering Congress and Exposition, IMECE 2013, San Diego, CA, United States, 11/15/13. https://doi.org/10.1115/IMECE2013-64554

}

TY - GEN

T1 - Meshless local petrov-galerkin method for heat transfer analysis

AU - Rao, Singiresu S

PY - 2013/1/1

Y1 - 2013/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84903445666&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84903445666&partnerID=8YFLogxK

U2 - 10.1115/IMECE2013-64554

DO - 10.1115/IMECE2013-64554

M3 - Conference contribution

SN - 9780791856345

VL - 8 A

BT - ASME International Mechanical Engineering Congress and Exposition, Proceedings (IMECE)

PB - American Society of Mechanical Engineers (ASME)

ER -