Investigation of Numerical Evaluation Improvement for Three-Dimensional Infinite Cylindrical Heat Conduction Problems

2020 ◽  
Vol 142 (4) ◽  
Author(s):  
Te Pi ◽  
Kevin Cole ◽  
Qingjun Zhao ◽  
Wei Zhao
Keyword(s):  
Thermal Properties ◽  
Heat Conduction ◽  
Numerical Evaluation ◽  
Series Solution ◽  
Three Dimensional ◽  
Well Test ◽  
Computer Evaluation ◽  
Evaluation Time ◽  
Finite Body ◽  
Cylindrical Geometries

Abstract To estimate the thermal properties from transient data, a model is needed to produce numerical values with sufficient precision. Iterative regression or other estimation procedures must be applied to evaluate the model again and again. From this perspective, infinite or semi-infinite heat conduction problems are a challenge. Since the analytical solution usually contains improper integrals that need to be computed numerically, computer-evaluation speed is a serious issue. To improve the computation speed with precision maintained, an analytical method has been applied to three-dimensional (3D) cylindrical geometries. In this method, the numerical evaluation time is improved by replacing the integral-containing solution by a suitable finite body series solution. The precision of the series solution may be controlled to a high level and the required computer time may be minimized by a suitable choice of the extent of the finite body. The practical applications for 3D geometries include the line-source method for obtaining thermal properties, the estimation of thermal properties by the laser-flash method, and the estimation of aquifer properties or petroleum-field properties from well-test measurements. This paper is an extension of earlier works on one-dimensional (1D) and two-dimensional (2D) cylindrical geometries. In this paper, the computer-evaluation time for the finite geometry 3D solutions is shown to be hundreds of times faster than the infinite or semi-infinite solution with the precision maintained.

Efficient Numerical Evaluation of Exact Solutions for One-Dimensional and Two-Dimensional Infinite Cylindrical Heat Conduction Problems

2017 ◽  
Vol 139 (12) ◽  
Author(s):  
Te Pi ◽  
Kevin Cole ◽  
James Beck
Keyword(s):  
Thermal Properties ◽  
Exact Solutions ◽  
Series Solution ◽  
Large Body ◽  
Two Dimensional ◽  
Well Test ◽  
One Dimensional ◽  
Computer Evaluation ◽  
Evaluation Time ◽  
Finite Body

Estimation of thermal properties or diffusion properties from transient data requires that a model is available that is physically meaningful and suitably precise. The model must also produce numerical values rapidly enough to accommodate iterative regression, inverse methods, or other estimation procedures during which the model is evaluated again and again. Bodies of infinite extent are a particular challenge from this perspective. Even for exact analytical solutions, because the solution often has the form of an improper integral that must be evaluated numerically, lengthy computer-evaluation time is a challenge. The subject of this paper is improving the computer evaluation time for exact solutions for infinite and semi-infinite bodies in the cylindrical coordinate system. The motivating applications for the present work include the line-source method for obtaining thermal properties, the estimation of thermal properties by the laser-flash method, and the estimation of aquifer properties or petroleum-field properties from well-test measurements. In this paper, the computer evaluation time is improved by replacing the integral-containing solution by a suitable finite-body series solution. The precision of the series solution may be controlled to a high level and the required computer time may be minimized, by a suitable choice of the extent of the finite body. The key finding of this paper is that the resulting series may be accurately evaluated with a fixed number of terms at any value of time, which removes a long-standing difficulty with series solution in general. The method is demonstrated for the one-dimensional case of a large body with a cylindrical hole and is extended to two-dimensional geometries of practical interest. The computer-evaluation time for the finite-body solutions are shown to be hundreds or thousands of time faster than the infinite-body solutions, depending on the geometry.

A NONLINEAR INVERSE HEAT CONDUCTION TECHNIQUE TO ESTIMATE THERMAL PROPERTIES OF METALS

2020 ◽  
Author(s):  
Mariana de Melo Antunes ◽  
Rodrigo Gustavo Dourado da Silva ◽  
Nícolas Pinheiro Ramos ◽  
Sandro Metrevelle Marcondes de Lima e Silva
Keyword(s):  
Thermal Properties ◽  
Heat Conduction ◽  
Inverse Heat Conduction

Enhanced thermal properties for epoxy composites with a three-dimensional graphene oxide filler

2015 ◽  
Vol 16 (12) ◽  
pp. 2617-2626 ◽  
Author(s):  
Jian Gao ◽  
Jinhong Yu ◽  
Xinfeng Wu ◽  
Baolin Rao ◽  
Laifu Song ◽  
...  
Keyword(s):  
Graphene Oxide ◽  
Thermal Properties ◽  
Three Dimensional ◽  
Epoxy Composites

The effect of aliphatic chain length on thermal properties of poly(alkylene dicarboxylate)s

e-Polymers ◽  
2007 ◽  
Vol 7 (1) ◽  
Author(s):  
Corrado Berti ◽  
Annamaria Celli ◽  
Paola Marchese ◽  
Elisabetta Marianucci ◽  
Giancarlo Barbiroli ◽  
...  
Keyword(s):  
Thermal Properties ◽  
Three Dimensional ◽  
The Other ◽  
Aliphatic Chain ◽  
Melting Temperatures ◽  
Avrami Analysis ◽  
Isothermal Analysis ◽  
Dimensional Growth ◽  
Crystallizing Polymers ◽  
Crystalline Forms

AbstractSome poly(alkylene dicarboxylate)s, derived from ethanediol or 1,4- butanediol and different diacids, have been synthesized and analyzed by DSC to determine the correlations existing between the thermal properties and the length of the aliphatic chain. The polymers show crystallization and melting temperatures and enthalpies which increase as the polymethylene segments lengthen, due to the formation of more stable crystals. The samples derived from ethanediol are peculiar; they show reorganization processes during the melting and the melting temperatures are notably higher with respect to those of the other polyesters. This behavior is discussed. Isothermal analysis highlights that poly(alkylene dicarboxylate)s are fast crystallizing polymers. The Avrami analysis suggests a crystallization mechanism characterized by heterogeneous nucleation and three dimensional growth; secondary crystallizations is present only in the samples characterized by short -(CH2)- sequences, due to the reorganization of less perfect crystalline forms. A comparative study between the crystallization rates as a function of the undercooling is reported.

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