**TUTORIALS**

The goal of this tutorial is to apply the system identification technique in order to obtain an accurate direct model devoted to measurements inversion. A simple experiment will be used in order to give the basic ideas of the optimal experiment in system identification approach. It will be particularly emphasized on the choice of the excitation sequence. Two methods will be used: the correlation method and the parametric method. A direct model will thus be obtained and it will be analyzed in terms of reliability and accuracy.

As a conclusion, it will be pointed out the advantages of this approach with respect to the classical one based on the resolution of the heat diffusion equation.

**Keywords**: system identification, linear and non-linear inversion

**Objectives**: using data (heat flux and temperature) from a simple experiment to identify parameters in a model of heat transfer in the system in a form of a transfer function.

**Experimental/Numerical Tutorial**

A new experimental method for thermodynamic characterization of solid- liquid and shape-stabilized Phase Change Materials (PCM), through enthalpy- temperature function estimation, is described in this paper. The simplicity of the experimental setup is comparable to that of a hot plate and it allows fast and accurate characterization of large size samples. The heat transfer model corresponding to the experimental device is written as a constant parameters heat conduction model with a temperature dependent source term which contains all the information related to the phase change phenomenon. The enthalpy-temperature function is estimated by using an efficient inversion technique which only requires the measurement of the temperature at a point in the PCM. Through dimensionless and numerical tests, the capabilities and the limits of the proposed method have been investigated. A simple way to optimize the experimental conditions has been also proposed. An experimental test for characterization of a PCM composite is finally carried out to illustrate the appropriateness of those developments.

**Keywords**: PCM, enthalpy-temperature function, inverse method, experimental device

**Experimental Tutorial**

This tutorial aims to describe two very well known methods that allow the identification of thermal properties from transient heat transfer experiments. The metrology is based on sensors that play both the roles of the heater and the thermometer. Analytical models for both experimental configurations are based on the formalism of integral transforms (Laplace, Hankel, Fourier) in the framework of quadrupoles method. Identification of the parameters is reaches using two approaches.

**Keyword**: thermal properties, transient experiment, linear and non-linear least squares.

**Objectives**:

**Experimental tutorial**.

This tutorial is about temperature and heat flux measurement with thermocouples and can be seen as complementary information to lecture L2. Time constants, errors due to heat leakage through the connection wire of the thermocouples will be illustrated with experiments. Some rules will be explained to implement thermocouples in metallic sample in order to realize accurate and sensitive 1D heat flux sensors. Thin film heat flux sensors will also be discussed.

**Keywords: **thermal instrumentation, thermocouple, RTD, systematic errors, time constant

**Objective: **Presentation of the advanced know how for unbiased temperature and heat flux measurement

**Experimental tutorial**

This work concerns the development of a non-contact calorimeter for two- phase flow characterization. The biphasic flow is performed under a droplet configuration inside millimetric tubings that are inserted into the isoperibolic chip. The main idea is to combine the Infrared Thermography and microfluidic tools to propose a suitable technique for accurate measurements. Microfluidics enables the use of small reaction volumes thus limiting any risk of dangerous reactions inside droplets; the Infrared tool enables to monitor the thermal signature of these flows with high accuracy. The results show that this tool is able to estimate the thermophysical properties of non-reactive flows. Also, it is possible to characterize chemical reactions in terms of enthalpy and kinetics. Finally the latter characterization was compared to conventional techniques to demonstrate the benefits and the precision of the tool.

**Keywords**: Microfluidic, IR thermography, Inverse processing by correlation method

**Objectives**: use IR thermography to quantitatively estimate thermophysical properties of biphasic flow in microfluidic system. Based on experimental measurements the inverse processing will be performed.

**Numerical tutorial**

The three layers transient method is dedicated to the thermal properties measurement of insulating materials. The three layers experimental device (brass/sample/brass) and the principle of the measurement based on a pulsed method will be first presented. The three dimensional modelling of the system will be developed and used for a sensitivity analysis. The estimation method will be described and its application to simulated noisy measurements realized with COMSOL will be presented. During the workshop, several experiments will be carried on different materials and the experimental temperature records will be used to estimate the thermal properties of the tested samples. Some improvements to the initial model such as taking into account a parallel or series thermal resistance will be discussed.

**Keywords**: thermal conductivity, super-insulating material, measurement

**Objectives**: Measurement of the thermal conductivity of small samples of insulating and super-insulating materials

**Experimental Tutorial**

The solution of an inverse problem within the Bayesian framework is recast in the form of statistical inference from the posterior probability density. Such a density is obtained through Bayes' theorem and is proportional to the product of the likelihood function, which models the measurement errors, by the prior distribution, which models the information known before the experimental data is available. The focus of this tutorial is on Markov Chain Monte Carlo (MCMC) methods, but its application to state estimation problems with Bayesian filters is not treated here. Basic concepts, as well as practical issues regarding the implementation of MCMC methods, are presented in this tutorial. Computational examples, involving the application of the Metropolis-Hastings algorithm to the solution of inverse heat transfer problems, will be made available in the presentation to be given during the METTI school.

**Numerical tutorial**

This tutorial is especially designed to the beginners in inverse techniques in heat conduction. Internal components of magnetic confinement fusion machines are subjected to significant heat fluxes. In order to estimate the surface input heat flux on these plasma-facing components, some temperature measurements like embedded thermocouples are used. Through this experimental example, we propose to detail a heat flux estimation procedure associating deconvolution and regularization method (Tikhonov). After a brief presentation of the experimental context, the inversion procedure will be used on an experimental signal produced during the tutorial. The numerical codes used will be accessible to the participants.

**Keywords**: Heat Flux Estimation, Embedded temperature measurement, Regularization

**Objectives**:

- Make a thermal experience
- Estimate a heat flux with an embedded measurement

This workshop seeks to focus on two objectives. the first objective aims to develop an estimation and is based on two software. Comsol Multiphysics is a computer code to simulate different types of physical equations. Moreover, it offers the possibility to save the steps of numerical development to be able to then work on one or more parameters. Matlab helps develop the estimation algorithms and allows the use of the direct problem developed under COMSOL and modification of the parameter to be estimated. The second objective aims to study the measurement errors associated with the intrusive aspect of thermocouples. Several configurations of instrumentation are reviewed and then by making estimates with wrong data measurements, analyze the errors in the estimated values**.**

In this tutorial, a method based on the Ordinary Least Squares method (OLS) for optimizing the wavelength selection used for the multi-spectral temperature measurement of surfaces exhibiting non uniform temperature-depending emissivity is presented. The goal consists in minimizing the standard deviation of the estimated temperature (optimal design experiment). Two methods for wavelengths selection are presented, sequential and global with or without constraints on the spectral range. Then, the estimated temperature results obtained by a model taking into account up to a second-order polynomial global spectral transfer function of the overall system (including the emissivity) and for different number of parameters and wavelengths are compared. The model is based on the fluxes (Planck’s law and without fluxes ratio). Different selection criteria are presented. These points are treated from theoretical, numerical and experimental points of view.

**Keywords:** Multi-spectral, thermometry, pyrometry, temperature measurement, multi-band, optical measurement, emissivity, optimal wavelengths, infrared thermography.

Singular Value Decomposition (SVD) is a linear algebra process that allows decomposing any square Singular Value Decomposition (SVD) is a linear algebra process that allows to decompose any square or rectangular, real or complex, matrix into a product of three matrices, its central matrix being diagonal. Its diagonal coefficients are the singular values of the original matrix, which are all real and positive (or zero) numbers. This decomposition can be seen as a generalization of the eigenvalue decomposition that is valid only for square matrices. In this tutorial we will consider SVD either as a tool for calibrating a linear model (system identification) with a further use in inverse input problems, or for processing a large amount of space/time data that can be met when measuring temperatures using infrared thermography. In both applications, in order either to tackle the original ill-posed character of the original inverse problem (where the matrix at stake is the sensitivity matrix), or to perfom some specific kind of data reduction (where the matrix at stake is the matrix of space/time data), the original SVD decomposition has to be modified. It gives rise to two types of regularization: Truncated SVD (TSVD) or Tikhonov regularization of zero order.

These two different problems, identification/inverse input problem and data reduction will be studied using two examples in this tutorial: a deconvolution problem by decomposition the sensitivity matrix and an initial temperature field reconstitution by decomposition of the space and time observable data.

**Keywords**: Singular Value Decomposition, space/time data, regularization

**Objectives**: These two different problems, identification/inverse input problem and data reduction will be studied using two examples in this tutorial:

- The application of regularization to a deconvolution problem
- The application of TSVD to the data reduction and initial temperature field estimation in the case of a big sized temperature image sequence processing.

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