Reconstruction of the thermal conductivity coefficient from the solution of the nonlinear inverse problem

1981 ◽  
Vol 41 (4) ◽  
pp. 1054-1058 ◽  
Author(s):  
E. A. Artyukhin
Keyword(s):  
Thermal Conductivity ◽  
Inverse Problem ◽  
Thermal Conductivity Coefficient ◽  
Nonlinear Inverse Problem

scholarly journals An Inverse Problem Solution for Thermal Conductivity Reconstruction

2021 ◽  
Vol 20 ◽  
pp. 187-195
Author(s):  
Tchavdar T. Marinov ◽  
Rossitza S. Marinova
Keyword(s):  
Thermal Conductivity ◽  
Inverse Problem ◽  
Boundary Value Problem ◽  
Thermal Conductivity Coefficient ◽  
Numerical Solutions ◽  
Boundary Value ◽  
Nonlinear Coefficient ◽  
Higher Order ◽  
Quadratic Functional ◽  
Problem Solution

This work deals with the inverse problem of reconstructing the thermal conductivity coefficient of the (2+1)D heat equation from over–posed data at the boundaries. The proposed solution uses a variational approach for identifying the coefficient. The inverse problem is reformulated as a higher–order elliptic boundary–value problem for minimization of a quadratic functional of the original equation. The resulting system consists of a well–posed fourth–order boundary–value problem for the temperature and an explicit equation for the unknown thermal conductivity coefficient. The existence and uniqueness of the resulting higher–order boundary–value problem are investigated. The unique solvability of the inverse coefficient problem is proven. The numerical algorithm is validated and applied to problems of reconstructing continuous nonlinear coefficient and discontinuous coefficients. Accurate and stable numerical solutions are obtained.

scholarly journals One Iterative Method for calculating the Thermal Conductivity of Layered soil

2012 ◽  
Vol 2 (2) ◽  
pp. 18
Author(s):  
Bolatbek Rysbaiuly ◽  
Gulshat Makhambetova
Keyword(s):  
Thermal Conductivity ◽  
Inverse Problem ◽  
Heat Conduction ◽  
Iterative Method ◽  
Dual Problem ◽  
Thermal Conductivity Coefficient ◽  
Layered Soil ◽  
Heterogeneous Environment ◽  
Priori Estimates ◽  
Equation Of Heat Conduction

Abstract The equation of heat conduction in a heterogeneous environment is being studied. An approximate method was developed for calculating the thermal conductivity of layered soil. Priori estimates were obtained to solve the direct and conjugate problems of difference. We prove the limitation of approximate values ​​of the thermal conductivity coefficient. Numerical calculations were aimed to test the convergence of iterative calculative scheme of the thermal conductivity of the soil. Keywords: dispersion environment, equation of heat conductivity, inverse problem, dual problem, priori estimates, thermo physical characteristics of the soil.

scholarly journals Reconstruction of the thermal conductivity coefficient in the space fractional heat conduction equation

2017 ◽  
Vol 21 (1 Part A) ◽  
pp. 81-88 ◽  
Author(s):  
Rafał Brociek ◽  
Damian Słota
Keyword(s):  
Thermal Conductivity ◽  
Inverse Problem ◽  
Approximate Solution ◽  
Heat Conduction ◽  
Direct Problem ◽  
Heat Conduction Equation ◽  
Thermal Conductivity Coefficient ◽  
Conduction Equation ◽  
Liouville Fractional Derivative ◽  
Fractional Heat Conduction

In this paper an inverse problem for the space fractional heat conduction equation is investigated. Firstly, we describe the approximate solution of the direct problem. Secondly, for the inverse problem part, we define the functional illustrating the error of approximate solution. To recover the thermal conductivity coefficient we need to minimize this functional. In order to minimize this functional the Real Ant Colony Optimization (RealACO) algorithm is used. In the model we apply the Riemann-Liouville fractional derivative. The paper presents also some examples to illustrate the accuracy and stability of the presented algorithm.

The effect of variable properties and rotation in a visco-thermoelastic orthotropic annular cylinder under the Moore–Gibson–Thompson heat conduction model

2021 ◽  
pp. 146442072098589
Author(s):  
Ahmed E Aboueregal ◽  
Hamid M Sedighi
Keyword(s):  
Thermal Conductivity ◽  
Thermal Stresses ◽  
Thermal Conductivity Coefficient ◽  
Variable Properties ◽  
Transformation Technique ◽  
Present Contribution ◽  
Conduction Model ◽  
Thermoelastic Model ◽  
Shock Heating ◽  
Physical Fields

The present contribution aims to address a problem of thermoviscoelasticity for the analysis of the transition temperature and thermal stresses in an infinitely circular annular cylinder. The inner surface is traction-free and subjected to thermal shock heating, while the outer surface is thermally insulated and free of traction. In this work, in contrast to the various problems in which the thermal conductivity coefficient is considered to be fixed, this parameter is assumed to be variable depending on the temperature change. The problem is studied by presenting a new generalized thermoelastic model of thermal conductivity described by the Moore–Gibson–Thompson equation. The new model can be constructed by incorporating the relaxation time thermal model with the Green–Naghdi type III model. The Laplace transformation technique is used to obtain the exact expressions for the radial displacement, temperature and the distributions of thermal stresses. The effects of angular velocity, viscous parameter, and variance in thermal properties are also displayed to explain the comparisons of the physical fields.

New method for determining the temperature dependence of the thermal conductivity coefficient of dielectrics in a pulse experiment

2010 ◽  
Vol 1 (2) ◽  
pp. 167-173 ◽  
Author(s):  
V. G. Baranov ◽  
Yu. N. Devyatko ◽  
A. V. Tenishev ◽  
A. V. Khlunov ◽  
O. V. Khomyakov
Keyword(s):  
Thermal Conductivity ◽  
Temperature Dependence ◽  
Thermal Conductivity Coefficient ◽  
New Method ◽  
Pulse Experiment
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