Estimation Technique for a Contact Point Between two Materials in a Stationary Heat Transfer Problem

Umbricht, Guillermo Federico; Rubio, Diana; Tarzia, Domingo A.

doi:10.18280/mmep.070413

Cited by 5 publications

(4 citation statements)

References 19 publications

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“…There are some tools that help to study the influence of the data on the estimated parameters. Among them, the sensitivity [18,19] and elasticity analysis [15,17,19] are frequently used in the literature. The latter is widely used in economics and provides the percentage of error in the estimation for an error of 1% in the measured data.…”

Section: Local Dependence Of the Thermal Conductivity With Respect To...mentioning

confidence: 99%

Determination of Two Homogeneous Materials in a Bar with Solid-Solid Interface

Umbricht¹,

Tarzia²,

Rubio³

2022

MMEP

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In this work, a bar fully insulated on its lateral surface. composed by two different unknown materials is considered. For the analytical solution, it is assumed a perfectly assembly solid-solid interface, so no heat loss due to friction is present. This is an ideal scenario, so this loss and possible measurement errors are included by simulating noisy data for the estimation of the thermal conductivity of the unknown materials. A stationary heat transfer process along the bar is considered where a Dirichlet condition is imposed at the left that represents a source of constant temperature. At the other end of the bar, a Robin condition that models heat dissipation by convection, is assumed. The constant thermal conductivity coefficients of both solids are determined under two different situations: a) two noisy temperature measurements are available, one at the interface and the other at the right boundary; b) a temperature measurement at the interface and a heat flow measurement at the right edge of the bar are given. The bounds for the errors in the identification of the unknown coefficients are obtained based on the data measurements, the room temperature and temperature values at the boundary and interface. Numerical examples are given to illustrate the ideas used for the parameter identification and elasticity analysis is carried out to measure the dependence of the data on the estimated parameters.

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Section: Local Dependence Of the Thermal Conductivity With Respect To...mentioning

confidence: 99%

Determination of Two Homogeneous Materials in a Bar with Solid-Solid Interface

Umbricht¹,

Tarzia²,

Rubio³

2022

MMEP

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“…The elasticity function given by the expression (31) does not depend on the parameter , A  and it has particularities that deserve to be highlighted.…”

Section: Elasticity Function Analysismentioning

confidence: 99%

“…M m q q q  Another important observation is that the elasticity function is increasing. This fact can be easily seen by differentiating the expression (30) or (31) to obtain…”

Section: Positivity and Monotonicity Propertiesmentioning

confidence: 99%

Estimation of a Thermal Conductivity in a Stationary Heat Transfer Problem with a Solid-Solid Interface

Umbricht¹,

Rubio²,

Tarzia³

2021

IJHT

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An inverse problem for a stationary heat transfer process is studied for a totally isolated bar on its lateral surface, made up of two consecutive sections of different, isotropic and homogeneous materials, perfectly assembly, where one of the materials, that is unreachable and unknown, has to be identified. The length of the bar is assumed to be much greater that the diameter so that a 1D heat transfer process is considered. A constant temperature is assumed at the end of the unknown part of the rod while the other end is let free for convection. We propose a procedure to identify the unknown material of the bar based on a noisy flow measurement at the opposite end. Necessary and sufficient conditions are derived together with a bound for the estimation error. Moreover, elasticity analysis is performed to study the influence of the data in the conductivity estimation and numerical examples are included to illustrate the proposed ideas and show the estimation performance.

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“…Figure 1 (b) illustrates the phenomenon of constriction of the flow lines at the contact. TCR is the equivalent resistance of two parallel resistance Rs and Rf characterizing respectively the heat transfer through the "solid-solid" path and the heat transfer through the "solidfluid-solid" path [16,17]. The thermal contact resistance is given as follows:…”

Section: Determination Of the Thermal Contact Resistancementioning

confidence: 99%

Contribution to the Study of Solid-Solid Thermal Contact Resistances--A Comparative Study

Cheriet¹,

Bensaad²,

Bouhadjela³

et al. 2021

ACSM

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This study presents a mixed numerical / semi-empirical approach that primarily aimed to estimate the thermal contact resistance between two solids. The results obtained by this mixed method were compared and validated by experimental measurements of this resistance. Three semi-empirical models were used, namely the Mikic model, the Yovanovich model and the Antonetti model. The three-dimensional finite element numerical simulation was used to estimate the contact pressure between the two solids. Then this contact pressure obtained numerically was compared to the hardness of the solids in contact. The findings indicated that the numerically obtained contact pressures were close to hardness. Therefore, the hardness, which is usually used as an input variable in semi-empirical models, was replaced by the contact pressure. The thermal contact resistance obtained by this mixed method was then compared with the experimental one. The outcomes obtained from this comparison turned out to be very conclusive and can therefore be used to reinforce our approach which can actually be viewed as a reliable and low-cost method for estimating the thermal contact resistance between solids in contact.

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Estimation Technique for a Contact Point Between two Materials in a Stationary Heat Transfer Problem

Cited by 5 publications

References 19 publications

Determination of Two Homogeneous Materials in a Bar with Solid-Solid Interface

Determination of Two Homogeneous Materials in a Bar with Solid-Solid Interface

Estimation of a Thermal Conductivity in a Stationary Heat Transfer Problem with a Solid-Solid Interface

Contribution to the Study of Solid-Solid Thermal Contact Resistances--A Comparative Study

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