Non-contact heat transfer models identification for laser hyperthermia of semi-transparent materials

The identification of mathematical models of heat transfer traditionally involves the installation of temperature sensors inside the sample under study and registration of the response to external thermal effects. In cases where the use of contact methods for measuring temperature is impossible, it is necessary to develop new approaches to determining the unknown thermophysical and radiation-optical characteristics. Laser hyperthermia of superficial tissues is one such case. The paper proposes a method for identifying a model of one-dimensional unsteady heating of a semitransparent sample using non-contact thermometry. A feature of the physical process under consideration is the possibility of its discretization. Due to this, a two-stage iterative procedure for solving the inverse heat transfer problem was formulated. The implementation of the proposed algorithm using software made it possible to carry out a computational experiment. The results showed the effectiveness of this approach. The presented method can be used in the development of means for monitoring and regulating the laser hyperthermia procedure.

Estimation of Functional Form of Time-Dependent Heat Transfer Coefficient Using an Accurate and Robust Parameter Estimation Approach: An Inverse Analysis

This paper presents a numerical method to address function estimation problems in inverse heat transfer problems using parameter estimation approach without prior information on the functional form of the variable to be estimated. Using an inverse analysis, the functional form of a time-dependent heat transfer coefficient is estimated efficiently and accurately. The functional form of the heat transfer coefficient is assumed unknown and the inverse heat transfer problem should be treated using a function estimation approach by solving sensitivity and adjoint problems during the minimization process. Based on proposing a new sensitivity matrix, however, the functional form can be estimated in an accurate and very efficient manner using a parameter estimation approach without the need for solving the sensitivity and adjoint problems and imposing extra computational cost, mathematical complexity, and implementation efforts. In the proposed sensitivity analysis scheme, all sensitivity coefficients can be computed in only one direct problem solution at each iteration. In this inverse heat transfer problem, the body shape is irregular and meshed using a body-fitted grid generation method. The direct heat conduction problem is solved using the finite-difference method. The steepest-descent method is used as a minimization algorithm to minimize the defined objective function and the termination of the minimization process is carried out based on the discrepancy principle. A test case with three different functional forms and two different measurement errors is considered to show the accuracy and efficiency of the used inverse analysis.

A Multiple Regression Convolutional Neural Network for Estimating Multi-parameters Based on Overall Data in the Inverse Heat Transfer Problem

The inverse heat transfer problem (IHTP) is a central task for estimating parameters in heat transfer. It is ill-posedness that is characterised by instability and non-uniqueness of the solution. Recently, novel algorithms using deep learning and neural networks for application of various sparse data in the inverse heat transfer problem. In order to overcome the optimization problem of input nodes under sparse data, we try to use the overall data of the target as the basis for inversion. In this work, we used an improved convolutional neural network (CNN) to estimate multi-parameters in the inverse heat transfer problem. Computational fluid dynamics (CFD) and deep learning are fused to provide datasets for training of the proposed model. The proposed model was verified by experiments with a cubic cavity. Additionally, the improved CNN model was used to predict the different parameters of the more complex armored vehicle model. The results showed that the model has good prediction accuracy for estimating multi-parameters on different datasets. These attempts of introducing convolutional neural network to the IHTP in the present study were successful and it was significant for the study of the inverse heat transfer problem of estimating multi-parameters.

Cookies Internal Temperature Estimation Using IHCP Methodology

This work constitutes a continuation of previous work on determining the internal temperature of foods by applying inverse heat transfer problem solving techniques. In this research, a mathematical model of heat transfer applied to foods is developed whose central part heat transfer can be described in Cartesian coordinates. This model uses techniques established in the previous work. The technique is based on the adjustment of parameters involved in heat transfer, minimizing the sum of squared errors between the measured temperatures and those calculated by the mathematical model. This paper discusses how the precision of this method would be affected with respect to the measurement time of the surface temperature and the delay time of the measurement.

Estimation of Thermal Contact Conductances on Irregular Interfaces Using the Generalized Integral Transform Technique and the Reciprocity Functional Method

The reciprocity functional method, associated to the Classic Integral Transform Technique (CITT), has been successfully applied, obtaining analytical solutions for the inverse heat transfer problem that seeks to estimate the thermal contact conductance (TCC) distribution on the interface of a body composed of two materials. Yet, the theoretical development upon which this approach is based is not limited to the need of this interface to have a regular format. This work proposes to extend the method, thus obtaining an analytical development for the estimation of the TCC distribution on interfaces which are not necessarily regular. Several test problems were solved using the techniques described in this work, leading to very good results, with low CPU time usage by the computational implementation.

Accurate Thermal Diffusivity Measurements Using a Modified Ångström's Method With Bayesian Statistics

This work reports a custom instrument that employs a modified Ångström's method to measure the thermal diffusivity of foil-like materials in which heat propagates in one dimension. This method does not require a semi-infinite medium assumption as compared to the original Ångström's method, which also has been typically performed in vacuum. However, in this work, temperature measurements are performed in laboratory ambient conditions, which are more convenient for most experiments. To quantify and reduce uncertainties due to temperature fluctuations in noisy ambient conditions, a Bayesian framework and Metropolis algorithm are employed to solve the inverse heat transfer problem and to obtain a probability distribution function for thermal diffusivity. To demonstrate the effectiveness of the custom instrument, the thermal diffusivity of a copper 110 foil (25.0 mm long, 7.0 mm wide, and 76.2 μm thick) was measured in ambient conditions, and the results match well with previous studies performed in vacuum conditions on much longer samples.