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Numerical Analysis of a Semi-Infinite Solid with Temperature Dependent Thermal Conductivity using Truly Meshfree Method


Affiliations
1 School of Engg., Gautam Buddha University, Greater Noida, Uttar Pradesh, India
2 Rajasthan Technical University, Kota, Rajasthan, India
 

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This article presents Meshless Local Petrov-Galerkin (MLPG) method to obtain the numerical solution of linear and non-linear heat conduction in a semi-infinite solid object with specific heat flux. Moving least square approximants are used to approximate the unknown function of temperature T(x) with Th(x). These approximants are constructed by using a linear basis, a weight function and a set of non-constant coefficients. Essential boundary condition is imposed by the penalty function method. A predictor-corrector scheme based on direct substitution iteration has been applied to address the non-linearity and two-level  method for temporal discretization. The accuracy of MLPG method is verified by comparing the results for the simplified versions of the present model with the exact solutions. Once the accuracy of MLPG method is established, the method is further extended to investigate the effects of temperature-dependent properties.

Keywords

Transient, Temperature Dependent, Semi-Infinite Solid, Penalty Method, Heat Flux, Meshless Local Petrov-Galerkin.
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  • Numerical Analysis of a Semi-Infinite Solid with Temperature Dependent Thermal Conductivity using Truly Meshfree Method

Abstract Views: 360  |  PDF Views: 223

Authors

Rajul Garg
School of Engg., Gautam Buddha University, Greater Noida, Uttar Pradesh, India
Harishchandra Thakur
School of Engg., Gautam Buddha University, Greater Noida, Uttar Pradesh, India
Brajesh Tripathi
Rajasthan Technical University, Kota, Rajasthan, India

Abstract


This article presents Meshless Local Petrov-Galerkin (MLPG) method to obtain the numerical solution of linear and non-linear heat conduction in a semi-infinite solid object with specific heat flux. Moving least square approximants are used to approximate the unknown function of temperature T(x) with Th(x). These approximants are constructed by using a linear basis, a weight function and a set of non-constant coefficients. Essential boundary condition is imposed by the penalty function method. A predictor-corrector scheme based on direct substitution iteration has been applied to address the non-linearity and two-level  method for temporal discretization. The accuracy of MLPG method is verified by comparing the results for the simplified versions of the present model with the exact solutions. Once the accuracy of MLPG method is established, the method is further extended to investigate the effects of temperature-dependent properties.

Keywords


Transient, Temperature Dependent, Semi-Infinite Solid, Penalty Method, Heat Flux, Meshless Local Petrov-Galerkin.

References





DOI: https://doi.org/10.4273/ijvss.10.4.16