Nonlinear Transient Heat Transfer Analysis Using Two Integration Methods with Different Distributions of Integration Points in the Domain in a Meshless Formulation

Document Type : Research Article

Authors

1 Department of mechanical engineering, Faculty of engineering, Yazd University, Yazd, Iran.

2 department of mechanical engineering, Yazd University, Yazd, Iran.

3 Department of mechanical engineering, Shiraz University, Shiraz, Iran.

Abstract

In this article, the transient heat transfer problem with both convection and radiation boundary conditions is studied. The meshless radial point interpolation method is implemented in this numerical study. Also, two integration methods, the Cartesian transformation method and the Gaussian quadrature method which uses background cells, are employed for computation of the domain integral. First, a homogenous medium with both convection and radiation boundary conditions is considered. The temperature distribution obtained by the proposed meshless method is compared with the analytical solution for a heat transfer problem and excellent agreement is observed. Then, a number of example problems in a layered composite and a functionally graded sample with both convection and radiation boundary conditions are solved and the temperature results are compared with those of ABAQUS software. Through the numerical examples it is observed that using the cartesian transformation method in comparison with the background cell method in convection boundary conditions reduces the error to half and in radiation boundary conditions reduces the error to one-quarter. This numerical method is a meshless method which does not require any background mesh. Moreover, the amount of error using the background cell method in problems with radiation boundary conditions is more than those with convection boundary conditions. This shows the advantage of using the cartesian transformation method in problems with radiation boundary condition which have a higher degree of nonlinearity, due to the temperature-dependent boundary conditions.

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References

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Amirkabir Journal of Mechanical Engineering
Volume 53, Issue 1 (Special Issue)
April 2021
Pages 553-572

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