Meshless local petrov-galerkin method for heat transfer analysis

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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 languageEnglish
Title of host publicationASME International Mechanical Engineering Congress and Exposition, Proceedings (IMECE)
PublisherAmerican Society of Mechanical Engineers (ASME)
Volume8 A
ISBN (Print)9780791856345
DOIs
StatePublished - Jan 1 2013
EventASME 2013 International Mechanical Engineering Congress and Exposition, IMECE 2013 - San Diego, CA, United States
Duration: Nov 15 2013Nov 21 2013

Other

OtherASME 2013 International Mechanical Engineering Congress and Exposition, IMECE 2013
CountryUnited States
CitySan Diego, CA
Period11/15/1311/21/13

Fingerprint

Galerkin methods
Heat transfer
Radiation
Heat transfer coefficients
Boundary conditions
Heat radiation
Linearization
Boundary value problems
Derivatives
Finite element method
Temperature

ASJC Scopus subject areas

  • Mechanical Engineering

Cite this

Rao, S. S. (2013). Meshless local petrov-galerkin method for heat transfer analysis. In 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.

ASME International Mechanical Engineering Congress and Exposition, Proceedings (IMECE). Vol. 8 A American Society of Mechanical Engineers (ASME), 2013.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Rao, SS 2013, Meshless local petrov-galerkin method for heat transfer analysis. in 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
Rao SS. Meshless local petrov-galerkin method for heat transfer analysis. In ASME International Mechanical Engineering Congress and Exposition, Proceedings (IMECE). Vol. 8 A. American Society of Mechanical Engineers (ASME). 2013 https://doi.org/10.1115/IMECE2013-64554
Rao, Singiresu S. / Meshless local petrov-galerkin method for heat transfer analysis. ASME International Mechanical Engineering Congress and Exposition, Proceedings (IMECE). Vol. 8 A American Society of Mechanical Engineers (ASME), 2013.
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