One-dimensional Heat Conduction Research Articles

A Review of Physics-Informed Neural Networks

This article presents Physics-Informed Neural Networks (PINNs), which integrate physical laws into neural network training to model complex systems governed by partial differential equations (PDEs). PINNs enhance data efficiency, allowing for accurate predictions with less training data, and have applications in fields such as biomedical engineering, geophysics, and material science. Despite their advantages, PINNs face challenges like learning high-frequency components and computational overhead. Proposed solutions include causality constraints and improved boundary condition handling. A numerical experiment demonstrates the effectiveness of PINNs in solving the one-dimensional heat conduction equation, showcasing enhanced model stability and accuracy. Overall, PINNs represent a significant advancement in merging machine learning with physics.

Heat Transfer Characteristics of Cryogenically Frozen Kulfi (A Dairy Dessert)

Kulfi was frozen from concentrated milk as well as from reconstituted dry mix with solids content of 60%. The convective heat transfer coefficients during freezing of kulfi by deep freeze and cryogenic methods were determined using one-dimensional transient heat conduction equation. The heat transfer coefficient for cryogenic freezing of kulfi from milk and dry mix concentrates was 210.57 W m-2K-1 and 216.84 W m-2K-1, respectively when compared to 8.33 W m-2K-1 for conventional deep-frozen kulfi. Freezing was achieved in 267 min in deep freeze method, while it reduced to just 185-190 s under cryogenic conditions. The freezing time was predicted using empirical equations, and the prediction accuracies were compared. Cryogenic freezing was nearly 87.66 times faster than deep freezing, and Pham’s model best-predicted the freezing time. Organoleptic evaluation using fuzzy-logic revealed that the order of ranking of quality attributes of kulfi was body and texture (highly important) > melting characteristics (highly important) > flavour and taste (highly important) > colour and appearance (important), and cryogenically frozen kulfi was statistically (p<0.05) superior to conventionally frozen kulfi.

Thermal processes affected by carbon dioxide near ground surface

Thermal processes affected by carbon dioxide near ground surface

Deep thermal state on the southern margin of the Zhangzhou Basin based on the electrical conductivity model

Deep thermal state on the southern margin of the Zhangzhou Basin based on the electrical conductivity model

Застосування методу двобічних наближень до розв’язання першої крайової задачі для одновимірного рівняння теплопровідності з експоненціально нелінійним коефіцієнтом теплопровідності

The problem of heat conduction in nonlinear media reduces to solving boundary value problems for nonlinear heat conduction equations, where the coefficients of the equation or the function of the power of heat sources depend on temperature according to some law. Among the numerical methods for solving problems for nonlinear equations of mathematical physics, one can distinguish finite difference methods, finite element methods, variational and projection methods, as well as iterative methods. Among the latter group, the two-sided approximation method is particularly attractive due to its ability to provide a convenient estimate for the error of the approximate solution and to prove the existence of a solution to the original problem. The theory of linear partially ordered spaces was developed by L. V. Kantorovich in the second half of the 1930s. Further development of this theory is associated with the works of M. A. Krasnosel’skii, H. Amann, V. I. Opojtsev, N. S. Kurpel, B. A. Shuvar, A. I. Kolosov etc. The aim of this article is to develop a two-sided approximation method based on the use of Green's functions for solving the first boundary value problem for a one-dimensional nonlinear heat conduction equation and to investigate its performance when solving test problems. To achieve this goal, the unknown function was replaced, and the boundary value problem was reduced to a Hammerstein integral equation, which was considered as a nonlinear operator equation in a partially ordered Banach space. Conditions for the existence of a unique positive solution to the problem and conditions for two-sided convergence of successive approximations to it were obtained. The developed method was implemented in software and tested on solving test problems. The results of the computational experiment are illustrated with graphical and tabular information

Heat Conduction Control Using Deep Q-Learning Approach with Physics-Informed Neural Networks

As modern systems become more complex, their control strategy no longer relies only on measurement data from probes; it also requires information from mathematical models for non-measurable places. On the other hand, those mathematical models can lead to unbearable computation times due to their own complexity, making the control process non-viable. To overcome this problem, it is possible to implement any kind of surrogate model that enables the computation of such estimates within an acceptable time frame, which allows for making decisions. Using a Physics-Informed Neural Network as a surrogate model, it is possible to compute the temperature distribution at each time step, replacing the need for running direct numerical simulations. This approach enables the use of a Deep Reinforcement Learning algorithm to train a control strategy. On this work, we considered a one-dimensional heat conduction problem, in which temperature distribution feeds a control system. Such control system has the objective of reacing and maintaining constant temperature value at a specific location of the 1D problem by activating a heat source; the desired location somehow cannot be directly measured so, the PINN approach allows to estimate its temperature with a minimum computational workload. With this approach, the control training becomes much faster without the need of performing numerical simulations or laboratory measurements.

Effect of artificially induced microcracks near the rock surface on granite fragmentation performance under heating treatment

Effect of artificially induced microcracks near the rock surface on granite fragmentation performance under heating treatment

Molecular dynamics study on phase change properties and their nano-mechanism of sugar alcohols: Melting and latent heat

Molecular dynamics study on phase change properties and their nano-mechanism of sugar alcohols: Melting and latent heat

Nonlinear vibrations of temperature-dependent FGM cylindrical panels subjected to instantaneous surface heating

Nonlinear vibrations of temperature-dependent FGM cylindrical panels subjected to instantaneous surface heating

A Robust Quintic Hermite Collocation Method for One-Dimensional Heat Conduction Equation

A Robust Quintic Hermite Collocation Method for One-Dimensional Heat Conduction Equation

Effects of heat wave propagation and initial stress on the thermo-elastic behavior of porous-auxetic FG circular plate with variable hybrid foundation

Engineering structures' heterogeneity and porous-auxetic features generate some prominent effects on their thermo-mechanical behavior. In addition, initial stress and heat wave propagation also play important roles in the mechanical behavior of FGM structures. Therefore, this paper investigates the effects of heat wave propagation and initial stress on the thermo-elastic behavior of porous-auxetic FG circular/annular plates with variable hybrid foundations. The one-dimensional transient hyperbolic heat conduction equation is modeled using the Cattaneo-Vernotte (C-V) theory and numerically solved using the Crank-sNicolson (C-N) finite difference scheme. Besides, a mathematical model of the other governing equations is extracted based on the classical thermoporoelasticity theory and semi-analytically solved by employing the state-space method and differential quadrature technique. Numerical examples are provided to illustrate the findings of this investigation graphically. The results reveal that the grading indices, and thermal relaxation time have a significant effect on heat wave propagation in the FG circular plate. Initial stress, porosity, and auxeticity also play an important role in its thermoelastic behavior.

Geothermal resource evaluation of the Middle Permian Qixia-Maokou Formation in the southern Sichuan Basin, China

Geothermal resource evaluation of the Middle Permian Qixia-Maokou Formation in the southern Sichuan Basin, China

Vibrations of skew cylindrical shells made of FG-GPLRCs under rapid surface heating

Vibrations of skew cylindrical shells made of FG-GPLRCs under rapid surface heating

Mathematical Modeling and Numerical Approximation of Heat Conduction in Three-Phase-Lag Solid

In this article, we propose a mathematical model for one-dimensional heat conduction in a three-layered solid considering that an interfacial condition is present for the temperature and heat flux conditions between the layers. The numerical approach is developed by constructing a finite difference scheme to solve the initial boundary–interface problem. The numerical scheme is designed by considering the accuracy of the model on the inner part of each layer, then extending to the interfaces and boundaries by incorporating the continuous interfacial conditions. The finite difference scheme is unconditionally stable, convergent, and easy to implement since it consists of the solution of two algebraic systems. We provide three numerical examples to confirm that our numerical approximation is consistent with the analytical solution and the physical phenomenon.

Comparing firn temperature profile retrieval based on the firn densification model and microwave data over the Antarctica

Abstract. The firn temperature is a crucial parameter for understanding firn densification processes of the Antarctic Ice Sheet (AIS). Simulations with firn densification models (FDM) can be conceptualized as a function that relies on forcing data, comprising temperature and surface mass balance, together with tuning parameters determined based on measured depth-density profiles from different locations. The simulated firn temperature is obtained in the firn densification models by solving the one-dimensional heat conduction equation. Microwave satellite data on brightness temperature at different frequencies can also provide remote sensing monitoring of firn temperature variations across the AIS (i.e., the L-band up to 1500 meters). The firn temperature can be estimated by the microwave emission model and the regression method, but these two methods need more observations of temperature profiles for correction and validation. Therefore, we compiled a dataset with temperature profiles and temperature observations with depth around 10 meters. In this work, two methods were used to simulate/retrieve firn temperature across the Antarctic ice sheet. One method estimated the temperature profiles by solving the one-dimensional heat conduction equation driven by reanalyses and regional climate models, which are used in the simulation of FDMs. The other one established a relationship between the multi-frequency brightness temperature data from microwave remote sensing satellites and the firn temperature.

Transient reflectance of silicon carbide during laser-induced phase separation

Laser irradiation can induce local modulations of functional material properties, such as a decreased resistivity or a variation in reflectance. Recent studies investigated the laser-induced phase separation of 4 H-SiC into carbon and silicon on top of regrown SiC to customize its electrical conductivity for the application in electronic devices. To understand the physical processes leading to the laser-induced phase separation, time-resolved pump-probe measurements represent a suitable tool. This study advances the state of the art by characterizing the transient reflectance changes in 4 H-SiC upon irradiation by spatially resolved pump-probe reflectometry. Since the laser heating alters the reflectance of the sample, the spatially resolved measurement enables to observe the heat conduction from the irradiated to the non-irradiated areas, which sustains for several milliseconds. Numerical simulations of the temperature evolution reveal a restricted one-dimensional heat conduction into depth due to the broad lateral extent of the irradiated area. The associated sustained increased temperature within the irradiated area most certainly abets the feasibility of the phase separation. These findings offer practical insights for optimizing the applied laser parameters to tailor the material properties via phase separation.

An improved algorithm for Finite Particle Method considering Lagrange-type remainder

An improved algorithm for Finite Particle Method considering Lagrange-type remainder

Thermoelastic free vibration of rotating pretwisted porous p-FGM, e-FGM, and s-FGM conical shells in nonlinear temperature distribution

The free vibration response of rotating pretwisted functionally graded (FG) conical shells in nonlinear thermal conditions is investigated using a finite element approach with the purpose of application in turbomachinery blades. With the aid of power, exponential, and sigmoid laws, the pretwisted conical shell is functionally graded in its transverse direction. The distribution of both even and uneven porosity is considered. The one-dimensional Fourier heat conduction equation is used to assess the nonlinear temperature distribution across the thickness of the FG conical shell. Lagrange’s equation is used to obtain the dynamic equation of motion of the rotating pretwisted FG conical shell. The proposed finite element model employs an eight-noded isoparametric shell element with five degrees of freedom per node. The effect of several factors, including porosity, temperature, twist angle, and rotational speed on the free vibration response of the FG porous conical shell has been investigated. The findings reveal that the porosity volume fraction has a significant influence on the natural frequency. The nonlinear temperature difference and pretwist angle both cause stiffness reduction to the FG conical shell upon increasing, whereas the presence of rotational speed inducts geometrical stiffness resulting in centrifugal stiffening.

Grain refinement mechanism in adiabatic shear band of solution treated Ti–10V–2Fe–3Al alloy under high strain rate

Grain refinement mechanism in adiabatic shear band of solution treated Ti–10V–2Fe–3Al alloy under high strain rate

Computational Analysis and Regression Laws for Nozzle Erosion Prediction in Hybrid Rockets

The erosion of the nozzle throat can represent one of the major limitations against the future widespread use of hybrid rocket engines (HREs) in the space industry. In fact, nozzle erosion in HREs can be more severe and harder to predict than in solid rockets due to the higher concentration of oxidizing species in the combustion products and to mixture ratio shifts and/or throttling. Therefore, an accurate understanding of the erosion phenomenon is of fundamental importance for the technological advancement of HREs. This work is focused on the investigation of graphite nozzle erosion in HREs burning high-density polyethylene with two different oxidizers, oxygen and nitrous oxide. First, the results of a computational fluid dynamics parametric analysis are used to derive closed-form regression laws for the rapid estimation of nozzle throat erosion and wall temperature depending on chamber pressure and mixture ratio. Then, a one-dimensional transient heat conduction solver is loosely coupled with the aforementioned regression laws, allowing to reconstruct the transient heating process within the solid. The obtained numerical results are validated against experimental data. Finally, the effect of gas-phase reactions on the heterogeneous reactions occurring at the nozzle surface is highlighted when moving from fuel-rich to oxidizer-rich conditions.