scholarly journals A Meshless Method for the Numerical Solution of a Two-Dimension IHCP

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
F. Parzlivand ◽  
A. M. Shahrezaee
Keyword(s):  
Meshless Method ◽  
Numerical Experiments ◽  
Heat Conduction Problem ◽  
Random Noise ◽  
Inverse Heat Conduction Problem ◽  
Basis Functions ◽  
Inverse Heat Conduction ◽  
Two Dimension ◽  
The Stability ◽  
Rms Errors

This paper uses the collocation method and radial basis functions (RBFs) to analyze the solution of a two-dimension inverse heat conduction problem (IHCP). The accuracy of the method is tested in terms of Error and RMS errors. Also, the stability of the technique is investigated by perturbing the additional specification data by increasing the amounts of random noise. The results of numerical experiments are compared with the analytical solution in illustrative examples to confirm the accuracy and efficiency of the presented scheme.

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 inverse problem in estimating the time dependent source term and initial temperature simultaneously by the polynomial regression and conjugate gradient method

Filomat ◽  
2020 ◽  
Vol 34 (10) ◽  
pp. 3507-3516
Author(s):  
Arzu Coşkun
Keyword(s):  
Source Term ◽  
Initial Temperature ◽  
Polynomial Regression ◽  
Heat Conduction Problem ◽  
Inverse Heat Conduction Problem ◽  
Necessary Condition ◽  
Inverse Heat Conduction ◽  
Control Framework ◽  
Ill Posed ◽  
The Stability

From the final and interior temperature measurements identifying the source term with initial temperature simultaneously is an inverse heat conduction problem which is a kind of ill-posed. The optimal control framework has been found to be effective in dealing with these problems. However, they require to find the gradient information. This idea has been employed in this research. We derive the gradient of Tikhonov functional and establish the stability of the minimizer from the necessary condition. The stability and effectiveness of evolutionary algorithm are presented for various test examples.

scholarly journals Influence of Input Parameters on the Solution of Inverse Heat Conduction Problem

2020 ◽  
Author(s):  
Rakhab C. Mehta
Keyword(s):  
Heat Transfer ◽  
Heat Conduction ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Heat Conduction Problem ◽  
Inverse Heat Conduction Problem ◽  
Inverse Heat Conduction ◽  
Input Parameters ◽  
Solid Rocket ◽  
The Stability

A one-dimensional transient heat conduction equation is solved using analytical and numerical methods. An iterative technique is employed which estimates unknown boundary conditions from the measured temperature time history. The focus of the present chapter is to investigate effects of input parameters such as time delay, thermocouple cavity, error in the location of thermocouple position and time- and temperature-dependent thermophysical properties. Inverse heat conduction problem IHCP is solved with and without material conduction. A two-time level implicit finite difference numerical method is used to solve nonlinear heat conduction problem. Effects of uniform, nonuniform and deforming computational grids on the estimated convective heat transfer are investigated in a nozzle of solid rocket motor. A unified heat transfer analysis is presented to obtain wall heat flux and convective heat transfer coefficient in a rocket nozzle. A two-node exact solution technique is applied to estimate aerodynamic heating in a free flight of a sounding rocket. The stability of the solution of the inverse heat conduction problem is sensitive to the spatial and temporal discretization.

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