The Method of Fundamental Solution for a Radially Symmetric Heat Conduction Problem with Variable Coefficient

2021 ◽  
Vol 34 (3) ◽  
pp. 258-267
Author(s):  
global RuiMa
Keyword(s):  
Heat Conduction ◽  
Fundamental Solution ◽  
Variable Coefficient ◽  
Heat Conduction Problem

scholarly journals A Meshless Method Based on the Fundamental Solution and Radial Basis Function for Solving an Inverse Heat Conduction Problem

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Muhammad Arghand ◽  
Majid Amirfakhrian
Keyword(s):  
Heat Conduction ◽  
Fundamental Solution ◽  
Meshless Method ◽  
Heat Conduction Problem ◽  
Regularization Parameter ◽  
Linear Equations ◽  
Inverse Heat Conduction Problem ◽  
Inverse Heat Conduction ◽  
Radial Basis ◽  
The Stability

We propose a new meshless method to solve a backward inverse heat conduction problem. The numerical scheme, based on the fundamental solution of the heat equation and radial basis functions (RBFs), is used to obtain a numerical solution. Since the coefficients matrix is ill-conditioned, the Tikhonov regularization (TR) method is employed to solve the resulted system of linear equations. Also, the generalized cross-validation (GCV) criterion is applied to choose a regularization parameter. A test problem demonstrates the stability, accuracy, and efficiency of the proposed method.

scholarly journals An inspection to the hyperbolic heat conduction problem in processed meat

2017 ◽  
Vol 21 (1 Part A) ◽  
pp. 303-308 ◽  
Author(s):  
Kuo-Chi Liu ◽  
Han-Taw Chen ◽  
Yan-Nan Wang
Keyword(s):  
Experimental Study ◽  
Heat Conduction ◽  
Fundamental Solution ◽  
Thermal Wave ◽  
Numerical Scheme ◽  
Initial Temperature ◽  
Heat Conduction Problem ◽  
Processed Meat ◽  
Hyperbolic Heat Conduction ◽  
Conduction Model

This paper analyzes a hyperbolic heat conduction problem in processed meat with the non-homogenous initial temperature. This problem is related to an experimental study for the exploration of thermal wave behavior in biological tissue. Because the fundamental solution of the hyperbolic heat conduction model is difficult to be obtained, a modified numerical scheme is extended to solve the problem. The present results deviate from that in the literature and depict that the reliability of the experimentally measured properties presented in the literature is doubtful.

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