A THREE-LEVEL FINITE-DIFFERENCE SCHEME FOR SOLVING MICRO HEAT TRANSPORT EQUATIONS WITH TEMPERATURE-DEPENDENT THERMAL PROPERTIES

2003 ◽  
Vol 43 (6) ◽  
pp. 509-523 ◽  
Author(s):  
Weizhong Dai ◽  
Raja Nassar
Keyword(s):  
Thermal Properties ◽  
Finite Difference ◽  
Difference Scheme ◽  
Heat Transport ◽  
Finite Difference Scheme ◽  
Transport Equations ◽  
Temperature Dependent

Numerical identification of temperature dependent thermal conductivity using least squares method

2019 ◽  
Vol 30 (6) ◽  
pp. 3083-3099
Author(s):  
Anna Ivanova ◽  
Stanislaw Migorski ◽  
Rafal Wyczolkowski ◽  
Dmitry Ivanov
Keyword(s):  
Thermal Conductivity ◽  
Finite Difference ◽  
Heat Equation ◽  
Difference Scheme ◽  
Least Squares ◽  
Finite Difference Scheme ◽  
Nonlinear Heat Equation ◽  
Temperature Dependent ◽  
Content Type ◽  
Temperature Dependent Thermal Conductivity

Purpose This paper aims to considered the problem of identification of temperature-dependent thermal conductivity in the nonstationary, nonlinear heat equation. To describe the heat transfer in the furnace charge occupied by a homogeneous porous material, the heat equation is formulated. The inverse problem consists in finding the heat conductivity parameter, which depends on the temperature, from the measurements of the temperature in fixed points of the material. Design/methodology/approach A numerical method based on the finite-difference scheme and the least squares approach for numerical solution of the direct and inverse problems has been recently developed. Findings The influence of different numerical scheme parameters on the accuracy of the identified conductivity coefficient is studied. The results of the experiment carried out on real measurements are presented. Their results confirm the ones obtained earlier by using other methods. Originality/value Novelty is in a new, easy way to identify thermal conductivity by known temperature measurements. This method is based on special finite-difference scheme, which gives a resolvable system of algebraic equations. The results sensitivity on changes in the method parameters was studies. The algorithms of identification in the case of a purely mathematical experiment and in the case of real measurements, their differences and the practical details are presented.

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