Numerical aspects of the identification of thermal characteristics using the hot-wire method

Vala, Jiří. "Numerical aspects of the identification of thermal characteristics using the hot-wire method." Programs and Algorithms of Numerical Mathematics. Prague: Institute of Mathematics AS CR, 2013. 187-194. <http://eudml.org/doc/271327>.

@inProceedings{Vala2013,
abstract = {The hot-wire method, based on the recording of the temperature development in time in a testing sample, supplied by a probe with its own thermal source, is useful to evaluate the thermal conductivity of materials under extremal loads, in particular in refractory brickworks. The formulae in the technical standards come from the analytical solution of the non-stationary equation of heat conduction in cylindric (finally only polar) coordinates for a simplified formulation of boundary conditions, neglecting everything except the first terms of the decomposition of related exponential integrals to infinite series, and least-squares based data fitting; such approach reduces the validity of results and obstructs the simultaneous evaluation of heat capacity. This paper demonstrates that substantial improvements can be obtained without any requirements to additional measurements, both i) under the assumption of a wire of zero-thickness and an infinite sample (following the valid Czech technical standard) with proper exponential integrals and ii) for a more realistic geometrical configuration and physical simplification (taking into account the thermal characteristics of the wire), based on the properties of Bessel functions. The suggested algorithms have been implemented in the MATLAB environment.},
author = {Vala, Jiří},
booktitle = {Programs and Algorithms of Numerical Mathematics},
keywords = {thermal conductivity; heat transfer; Bessel functions},
location = {Prague},
pages = {187-194},
publisher = {Institute of Mathematics AS CR},
title = {Numerical aspects of the identification of thermal characteristics using the hot-wire method},
url = {http://eudml.org/doc/271327},
year = {2013},
}

TY - CLSWK
AU - Vala, Jiří
TI - Numerical aspects of the identification of thermal characteristics using the hot-wire method
T2 - Programs and Algorithms of Numerical Mathematics
PY - 2013
CY - Prague
PB - Institute of Mathematics AS CR
SP - 187
EP - 194
AB - The hot-wire method, based on the recording of the temperature development in time in a testing sample, supplied by a probe with its own thermal source, is useful to evaluate the thermal conductivity of materials under extremal loads, in particular in refractory brickworks. The formulae in the technical standards come from the analytical solution of the non-stationary equation of heat conduction in cylindric (finally only polar) coordinates for a simplified formulation of boundary conditions, neglecting everything except the first terms of the decomposition of related exponential integrals to infinite series, and least-squares based data fitting; such approach reduces the validity of results and obstructs the simultaneous evaluation of heat capacity. This paper demonstrates that substantial improvements can be obtained without any requirements to additional measurements, both i) under the assumption of a wire of zero-thickness and an infinite sample (following the valid Czech technical standard) with proper exponential integrals and ii) for a more realistic geometrical configuration and physical simplification (taking into account the thermal characteristics of the wire), based on the properties of Bessel functions. The suggested algorithms have been implemented in the MATLAB environment.
KW - thermal conductivity; heat transfer; Bessel functions
UR - http://eudml.org/doc/271327
ER -