Homogenization function method for time-fractional inverse heat conduction problem in 3D functionally graded materials

2021 ◽  
pp. 107478
Author(s):  
Lin Qiu ◽  
Minghui Zhang ◽  
Qing-Hua Qin
Keyword(s):  
Heat Conduction ◽  
Functionally Graded Materials ◽  
Function Method ◽  
Heat Conduction Problem ◽  
Inverse Heat Conduction Problem ◽  
Functionally Graded ◽  
Inverse Heat Conduction ◽  
Graded Materials

Transient Heat Conduction in Functionally Graded Materials by LT-MFS

2011 ◽  
Vol 189-193 ◽  
pp. 1664-1669 ◽  
Author(s):  
Ning Zhao ◽  
Lei Lei Cao ◽  
Hui Guo
Keyword(s):  
Heat Conduction ◽  
Functionally Graded Materials ◽  
Heat Conduction Problem ◽  
Transient Heat Conduction ◽  
Fundamental Solutions ◽  
Functionally Graded ◽  
Time Variable ◽  
Graded Materials ◽  
Time Space ◽  
Transient Heat Conduction Problem

: The LT-MFS approach is proposed to solve two-dimensional transient heat conduction problem in functionally graded materials (FGMs). First, a Laplace transform approach is used to move the time variable. Then, a fundamental solution in Laplace space for FGMs is constructed. Next, the solution in Laplace space is approximated by the linear combination of fundamental solutions. Further, Stefest’s algorithm is employed to convert the results in Laplace space back into the time–space domain. Finally, the method is tested on several benchmark examples. The results demonstrate well the efficiency and accuracy of the proposed method.

scholarly journals Analysis of 2D heat conduction in nonlinear functionally graded materials using a local semi-analytical meshless method

2021 ◽  
Vol 6 (11) ◽  
pp. 12599-12618
Author(s):  
Chao Wang ◽  
◽  
Fajie Wang ◽  
Yanpeng Gong ◽  
◽  
...  
Keyword(s):  
Heat Conduction ◽  
Functionally Graded Materials ◽  
Meshless Method ◽  
Large Scale ◽  
Heat Conduction Problem ◽  
Functionally Graded ◽  
Graded Materials ◽  
Kirchhoff Transformation ◽  
Graded Material ◽  
Equation Of Heat Conduction

<abstract> <p>This paper proposes a local semi-analytical meshless method for simulating heat conduction in nonlinear functionally graded materials. The governing equation of heat conduction problem in nonlinear functionally graded material is first transformed to an anisotropic modified Helmholtz equation by using the Kirchhoff transformation. Then, the local knot method (LKM) is employed to approximate the solution of the transformed equation. After that, the solution of the original nonlinear equation can be obtained by the inverse Kirchhoff transformation. The LKM is a recently proposed meshless approach. As a local semi-analytical meshless approach, it uses the non-singular general solution as the basis function and has the merits of simplicity, high accuracy, and easy-to-program. Compared with the traditional boundary knot method, the present scheme avoids an ill-conditioned system of equations, and is more suitable for large-scale simulations associated with complicated structures. Three benchmark numerical examples are provided to confirm the accuracy and validity of the proposed approach.</p> </abstract>

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