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Item A mixed finite element method for nonlinear radiation–conduction equations in optically thick anisotropic media(Elsevier, 2024)We propose a new mixed finite element formulation for solving radiation–conduction heat transfer in optically thick anisotropic media. At this optical regime, the integro-differential equations for radiative transfer can be replaced by the simplified Pɴ approximations using an asymptotic analysis. The conductivity is assumed to be nonlinear depending on the temperature along with anisotropic absorption and scattering depending on both the direction and location variables. The simplified Pɴ approximations are enhanced by considering a diffusion tensor capable of describing anisotropic radiative heat transfer. In the present study, we investigate the performance of the unified and mixed formulations combining cubic P₃, quadratic P₂, and linear P₁ finite elements to approximate the temperature in the simplified P₃ model. To demonstrate the performance of the proposed methodology, three-dimensional examples of nonlinear radiation–conduction equations in optically thick anisotropic media are presented. The obtained numerical results demonstrate the accuracy and efficiency of the proposed mixed finite element formulation over the conventional unified finite element formulation to accurately solve the simplified P₃ equations in anisotropic media.Item Numerical modelling of hyperbolic phase change problems: Application to continuous casting(Elsevier, 2023)Heat diffusion processes are generally modeled based on Fourier’s law to estimate how the temperature propagates inside a body. This type of modeling leads to a parabolic partial differential equation, which predicts an infinite thermal wave speed of propagation. However, experimental evidence shows that diffusive processes occur with a finite velocity of thermal propagation in many applications. In this paper, we develop a mathematical formulation to predict the finite speed of heat propagation in multidimensional phase change problems. The model generalizes the enthalpy formulation by adding a hyperbolic term. The governing equations are simulated by the finite element method. The proposed model is first verified by comparing numerical and experimental results illustrating the difference between the infinite and finite propagation velocity for heat inside biological tissues. Then, the results of the two and three-dimensional numerical solution of the continuous steel casting process are presented. We will illustrate that the effects of the initial conditions vanish faster when using the parabolic equation, while they persist in the hyperbolic modeling approach. The results demonstrate significant differences in the initial thermal dynamics and at the solid-liquid interface position when adding the hyperbolic term. The changes are more noticeable in the regions of the steel beam where rapid heat loss and, consequently, faster phase change occur.Item A reduced model for phase-change problems with radiation using simplified PN approximations(Elsevier, 2025-04)Radiative heat transfer in phase-change media is of great interest in many thermal applications in sciences and engineering involving internal melting or solidification. In these problems at high temperature, a mathematical model used to describe the heat transfer and phase change should also include equations accounting for thermal radiation. Using the integro-differential equation for the radiative intensity in these models results in a system of coupled equations for which its numerical solution is computationally very demanding. In the present study, we develop a class of efficient reduced models for phase-change problems accounting for grey thermal radiation. The novelty in these models lies in the fact that effects of thermal radiation are well captured in phasechange materials without solving the computationally demanding radiative transfer equation. The model is derived from the enthalpy formulation and the simplified Pɴ approximations of spherical harmonics. The integro-differential equation for the full radiative transfer is replaced by a set of differential equations which are independent of the angle variable and easy to solve using conventional computational methods. To solve the coupled equations, we implement a second-order implicit scheme for the time integration and a mixed finite element method for the space discretization. A Newton-based algorithm is also adopted for solving the nonlinear systems resulting from the considered monolithic approach. The performance of the proposed reduced models is analyzed on several test examples for coupled radiative heat transfer and phase-change problems in two and three space dimensions. The results presented in this study demonstrate that the proposed models can accurately predict the temperature distributions and capture the phase-change interfaces in melting and solidification examples, all while maintaining a very low computational cost.Item Mental Stress Assessment in the Workplace: A Review(IEEE, 2024-09)Workers with demanding jobs are at risk of experiencing mental stress, leading to decreased performance, mental illness, and disrupted sleep. To detect elevated stress levels in the workplace, studies have explored stress measurement from physiological, psychological, and behavioral perspectives. This paper reviews the assessment methods and strategies for mitigating mental stress in the workplace and provides recommendations for early detection and mitigation of mental stress. Among the modalities, Electroencephalography (EEG), Electrocardiography (ECG) and Galvanic Skin Response (GSR) were found to be the most used in assessing mental stress in the workplace. Nevertheless, these modalities are sensitive to motion artifacts and are difficult to be integrated into real work environments. To further improve stress level assessment in the workplace, multimodality integration with a reduced number of sensors such as EEG, GSR and Functional near infrared spectroscopy (fNIRS) can be utilized. This would lead to developing strategies for stress management in real-time. Furthermore, combining EEG with fNIRS would improve source localization of mental stress. To mitigate stress, we recommend developing a closed loop system that incorporates brain data acquisition systems and machine learning with physical stimulations such as audio Binaural Beats Stimulation and/or Transcranial Electric Stimulation.Item Assessment of Brain Function After 240 Days Confinement Using Functional Near Infrared Spectroscopy(IEEE, 2024-11)Future space exploration missions will expose astronauts to various stressors, making the early detection of mental stress crucial for prolonged missions. Our study proposes using functional near infrared spectroscopy (fNIRS) combined with multiple machine learning models to assess the level of mental stress. Objective: The objective is to identify and quantify stress levels during 240 days confinement scenario. In this study, we utilize a diverse set of stress indicators including salivary alpha amylase (sAA) levels, reaction time (RT) to stimuli, accuracy of target detection, and power spectral density (PSD), in conjunction with functional connectivity networks (FCN). We estimate the PSD using Fast Fourier Transform (FFT) and the FCN using partial directed coherence. Results: Our findings reveal several intriguing insights. The sAA levels increased from the first 30 days in confinement to the culmination of the lengthy 240-day mission, suggesting a cumulative impact of stress. Conversely, RT and the accuracy of target detection exhibit significant fluctuations over the course of the mission. The power spectral density shows a significant increase with time-in-mission across all participants in most of the frontal area. The FCN shows a significant decrease in most of the right frontal areas. Five different machine learning classifiers are employed to differentiate between two levels of stress resulting in impressive classification accuracy rates: 96.44% with-nearest neighbor (KNN), 95.52% with linear discriminant analysis (LDA), 88.71% with Naïve Bayes (NB), 87.41 with decision trees (DT) and 96.48% with Support Vector Machine (SVM). In conclusion, this study demonstrates the effectiveness of combining functional near infrared spectroscopy (fNIRS) with multiple machine learning models to accurately assess and quantify mental stress levels during prolonged space missions, providing a promising approach for early stress detection in astronauts.
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