Estimation of Thermodynamic
and Transport Properties of Metallic
Materials
Filippo de Monte and Giampaolo D’Alessandro
Abstract A three-layer apparatus for thermal property measurements (conductivity
and capacity) of high-conductivity specimens where an electrical heater is sandwiched between two samples having same thickness and material is investigated.
In particular, the heater is so thin that can be modelled as a lumped body along
the heat diffusion direction and, hence, by using a boundary condition (BC) of the
fourth or sixth kind at the heated surface of the specimen. Specifically, a BC of the
4th kind or Carslaw type accounts for the heater heat capacity, while the one of the
6th kind considers also the imperfect contact between heater and sample. Once the
transient temperature distribution within the slab-shaped sample is known and the
related sensitivities are evaluated, an optimal experiment is designed by applying the
D-optimum criterion to estimate accurately and simultaneously conductivity (k) and
capacity (C). Then, the standard deviations of the estimates are also computed.
Keywords Thermal properties · D-optimum criterion · Sixth kind boundary
condition
1 Introduction
The “parameter estimation” technique is based on the transient measurements of
the temperature of the considered metallic specimen at one or more locations [1].
One of the rules of parameter estimation is that the measured temperatures have to
be as sensitive as possible to the properties of interest. In other words, the related
sensitivity coefficients have to be as large as possible in magnitude [1, 2]. If this rule
is verified, the temperature measurements can be considered valuable unless there
exists a large difference in magnitude among the same coefficients involved [3].
F. de Monte (B) · G. D’Alessandro
Department of Industrial and Information Engineering and Economics, University of L’Aquila,
Via G. Gronchi n.18, 67100 L’Aquila, Italy
e-mail: filippo.demonte@univaq.it
© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021
A. K. Parwani et al. (eds.), Recent Advances in Mechanical Infrastructure,
Lecture Notes in Intelligent Transportation and Infrastructure,
https://doi.org/10.1007/978-981-33-4176-0_19
235
and Transport Properties of Metallic
Materials
Filippo de Monte and Giampaolo D’Alessandro
Abstract A three-layer apparatus for thermal property measurements (conductivity
and capacity) of high-conductivity specimens where an electrical heater is sandwiched between two samples having same thickness and material is investigated.
In particular, the heater is so thin that can be modelled as a lumped body along
the heat diffusion direction and, hence, by using a boundary condition (BC) of the
fourth or sixth kind at the heated surface of the specimen. Specifically, a BC of the
4th kind or Carslaw type accounts for the heater heat capacity, while the one of the
6th kind considers also the imperfect contact between heater and sample. Once the
transient temperature distribution within the slab-shaped sample is known and the
related sensitivities are evaluated, an optimal experiment is designed by applying the
D-optimum criterion to estimate accurately and simultaneously conductivity (k) and
capacity (C). Then, the standard deviations of the estimates are also computed.
Keywords Thermal properties · D-optimum criterion · Sixth kind boundary
condition
1 Introduction
The “parameter estimation” technique is based on the transient measurements of
the temperature of the considered metallic specimen at one or more locations [1].
One of the rules of parameter estimation is that the measured temperatures have to
be as sensitive as possible to the properties of interest. In other words, the related
sensitivity coefficients have to be as large as possible in magnitude [1, 2]. If this rule
is verified, the temperature measurements can be considered valuable unless there
exists a large difference in magnitude among the same coefficients involved [3].
F. de Monte (B) · G. D’Alessandro
Department of Industrial and Information Engineering and Economics, University of L’Aquila,
Via G. Gronchi n.18, 67100 L’Aquila, Italy
e-mail: filippo.demonte@univaq.it
© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021
A. K. Parwani et al. (eds.), Recent Advances in Mechanical Infrastructure,
Lecture Notes in Intelligent Transportation and Infrastructure,
https://doi.org/10.1007/978-981-33-4176-0_19
235