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.

Identification of the Thermal Conductivity Coefficient for Quasi-Stationary Two-Dimensional Heat Conduction Equations

2017 ◽  
Vol 90 (6) ◽  
pp. 1295-1301 ◽  
Author(s):  
Yu. M. Matsevityi ◽  
S. V. Alekhina ◽  
V. T. Borukhov ◽  
G. M. Zayats ◽  
A. O. Kostikov
Keyword(s):  
Thermal Conductivity ◽  
Heat Conduction ◽  
Thermal Conductivity Coefficient ◽  
Two Dimensional

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.

The Method of Computing the Thermal Conductivity of Heat-Insulation Oil Pipe Coupling

2013 ◽  
Vol 278-280 ◽  
pp. 251-255
Author(s):  
Li Jun Liu ◽  
Peng Yu ◽  
Ying Xu
Keyword(s):  
Thermal Conductivity ◽  
Inverse Problem ◽  
Heat Conduction ◽  
Temperature Distribution ◽  
Objective Function ◽  
Direct Problem ◽  
Heat Insulation ◽  
Pipe Coupling ◽  
Volume Method ◽  
Insulation Oil

Based on the inverse problem theory of heat conduction, thermal conductivity of heat-insulation oil pipe coupling is researched in the paper. The finite volume method is extended to solve the direct problem, and the 0.618 method is used to solve the inverse problem by optimizing the objective function. The results show that by using the method, taking the outer wall’s temperature as the sample indicators, the thermal conductivity and the temperature distribution of heat-insulation oil pipe coupling and the temperature distribution of heat-insulation oil pipe can be obtained easily and accurately.

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