Determination of a time-dependent thermal diffusivity and free boundary in heat conduction

2014 ◽  
Vol 53 ◽  
pp. 154-163 ◽  
Author(s):  
M.S. Hussein ◽  
D. Lesnic
Keyword(s):  
Heat Conduction ◽  
Thermal Diffusivity ◽  
Free Boundary ◽  
Time Dependent

Optimal Removal of Experimental Points to Determine Apparent Thermal Diffusivity of Canned Products

2014 ◽  
Vol 10 (2) ◽  
pp. 223-231 ◽  
Author(s):  
Wilton P. da Silva ◽  
Cleide M. D. P. S. Silva ◽  
Marcos A. A. Lins ◽  
Waldemir S. da Costa
Keyword(s):  
Boundary Condition ◽  
Heat Conduction ◽  
Thermal Diffusivity ◽  
Analytical Solution ◽  
Heat Conduction Equation ◽  
Transient Heat Conduction ◽  
Agar Gel ◽  
Precision And Accuracy ◽  
Thermo Physical Properties

Abstract To describe the transient heat conduction from or to a product, its thermo-physical properties must be known. If the boundary condition of the heat conduction equation is of the first kind, the process is governed by the thermal diffusivity α. Normally this property is determined by fit of the analytical solution with only the first term of the series to an experimental dataset of the temperature versus time, in which the temperature is measured in a known position. In this case, the value obtained for α contains errors due to the consideration of only one term and the inclusion of the first experimental points in the fit. This article presents an algorithm based on optimal removal of experimental points to minimize errors in the determination of α. The algorithm was validated and applied to heating of Agar gel. The precision and accuracy of the obtained result were, respectively, 0.38 and 0.6%.

scholarly journals INverse problem of identifying a time-dependent coefficient and free boundary in heat conduction equation by using the meshless local Petrov-Galerkin (MLPG) method via moving least squares approximation

Filomat ◽  
2020 ◽  
Vol 34 (10) ◽  
pp. 3319-3337
Author(s):  
Akbar Karami ◽  
Saeid Abbasbandy ◽  
Elyas Shivanian
Keyword(s):  
Inverse Problem ◽  
Heat Conduction ◽  
Free Boundary ◽  
Least Squares ◽  
Boundary Problem ◽  
Heat Conduction Equation ◽  
Time Dependent ◽  
Moving Least Squares ◽  
Fixed Boundary ◽  
Mlpg Method

In this paper we investigated the inverse problem of identifying an unknown time-dependent coefficient and free boundary in heat conduction equation. By using the change of variable we reduced the free boundary problem into a fixed boundary problem. In direct solver problem we employed the meshless local Petrov-Galerkin (MLPG) method based on the moving least squares (MLS) approximation. Inverse reduced problem with fixed boundary is nonlinear and we formulated it as a nonlinear least-squares minimization of a scalar objective function. Minimization is performed by using of f mincon routine from MATLoptimization toolbox accomplished with the Interior - point algorithm. In order to deal with the time derivatives, a two-step time discretization method is used. It is shown that the proposed method is accurate and stable even under a large measurement noise through several numerical experiments.

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