Article
Physics, Applied
D. Becerril, A. Camacho de la Rosa, R. Esquivel-Sirvent
Summary: In this study, the thermalization process between two bodies separated by a vacuum gap was investigated by combining the non-Fourier behavior of materials with near-field radiative heat transfer. It was found that in non-Fourier materials, the temperature behaves as a wave, and transient temperature effects occur at the onset of the thermalization process.
JOURNAL OF APPLIED PHYSICS
(2023)
Article
Mathematics, Applied
Mohd Farman Ali, Nisha Katoch
Summary: The main objective of this article is to solve the one-dimensional fractal heat-conduction problem in a fractal semi-infinite bar using local fractional calculus and the analytical Advanced Yang-Fourier transforms method.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Thermodynamics
Paolo Maria Mariano, Julia Polikarpus, Marco Spadini
Summary: We compare traveling-wave-type solutions between two models describing heat transfer, one including nonlinearities due to microstructural contributions and heat-flux-driven phase transition, and the other being the Maxwell-Cattaneo's scheme. Our closed-form results based on asymptotic-type analysis reveal how microstructural effects perturb the evolution of temperature traveling waves. Furthermore, our findings indicate a hidden link between initial conditions of heat flux and temperature, even in the Maxwell-Cattaneo's scheme.
INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER
(2022)
Article
Multidisciplinary Sciences
Kashif Ali Abro, Jose Francisco Gomez-Aguilar
Summary: This study presents a fractional modeling of non-Fourier heat conduction problem of a fin, fractionalizing the hyperbolic heat conduction equation for a fin through modern approaches of fractional differentiations. The exact solutions of temperature distribution are obtained using Laplace transform, showing that cooling process is faster via fractional models due to variability of different rheological parameters on temperature distribution. Additionally, it is observed that thermal wave propagates at a specific time leading to reciprocal trend in temperature distribution.
ARABIAN JOURNAL FOR SCIENCE AND ENGINEERING
(2021)
Article
Thermodynamics
Oleksii Nosko
Summary: This paper defines a Jeffreys heat conduction problem for coupled semispaces with an interfacial heat source and derives an analytical solution using the Laplace transform approach. The asymptotic and parametric analysis reveals that Jeffreys heat conduction results in continuous variation of the contact temperature, while its particular case - Cattaneo heat conduction - causes a step change of the contact temperature at the initial time. The findings also show that the initial heat partition is determined by the ratios of thermal conductivities and diffusivities, as well as thermal relaxation times under different heat conduction types. The applicability of the solution is demonstrated through a simulation example of ultrashort laser pulse welding, highlighting the qualitative and quantitative impacts of heat conduction on contact temperature and heat fluxes.
INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER
(2023)
Article
Thermodynamics
Milad Mozafarifard, Davood Toghraie, Hossein Sobhani
Summary: The study utilized the Caputo fractional subdiffusion model to analyze the fast-transient process of heat flow in a porous medium, demonstrating its effectiveness in simulating solid-fluid interactions and fast transient processes.
INTERNATIONAL COMMUNICATIONS IN HEAT AND MASS TRANSFER
(2021)
Article
Thermodynamics
Sheng Zhang, Xiaowei Zheng
Summary: This paper investigates a (2+1)-dimensional local fractional heat conduction equation with arbitrary non-linearity, constructs a Backlund transformation, and obtains exact non-differentiable solutions showing spatio-temporal fractal structures. Fractional calculus is shown to play a crucial role in handling non-differentiable problems.
Article
Engineering, Multidisciplinary
Zhuoxin Wen, Chi Hou, Meiying Zhao, Xiaopeng Wan
Summary: In this paper, the authors investigate the transient temperature response of a cracked plate under thermal shock using a non-Fourier heat transfer theory. They develop a peridynamic model that considers the non-Fourier effect, the orthotropy of thermal conductivity, and the crack thermal resistance. The model avoids spatial derivatives and is efficient for analyzing problems with discontinuities.
APPLIED MATHEMATICAL MODELLING
(2023)
Article
Mathematics, Applied
Jin-Liang Wang, Hui-Feng Li
Summary: MDD, as a new substitute for FD, better reflects memory effects and is more reasonable in modeling heat diffusion processes. It offers flexibility in choosing memory times and weighted functions for different media, making it suitable for exploring various diffusion problems.
APPLIED MATHEMATICS AND COMPUTATION
(2021)
Article
Optics
Bingxin Du, Guangying Xu, Dawen Xue, Jinbao Wang
Summary: This study investigates the heat transfer mechanisms in living biological tissue during pulse laser irradiation using different heat transfer equations, revealing that the FTWBT model has advantages in describing bio-heat transfer in laser therapy. The results discuss the heat wave propagation characteristics in biological tissues and highlight the importance of correct boundary conditions for model accuracy.
Article
Mathematics, Applied
Chun Yun Kee, Cherq Chua, Muhammad Zubair, L. K. Ang
Summary: This study improves the urban growth model by considering memory effects and proposes a new model based on fractional calculus. By testing the new model on different urban attributes, it is found that the fractional model provides better agreement with annual population growth and can estimate useful parameters for urban planning and decision-making.
Article
Mathematics, Applied
Aissa Guesmia
Summary: The objective of this paper is to investigate the decay of solutions for a laminated Timoshenko beam with interfacial slip in the whole space Double-struck capital R subject to a thermal effect. Results show that when the thermal effect acts on the rotation angle displacement or dynamic of the slip, both Timoshenko-Fourier and Timoshenko-Cattaneo systems satisfy the same polynomial stability estimates. The decay rate depends on the regularity of the initial data. A new stability condition is introduced when the thermal effect acts on the transversal displacement.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
Article
Chemistry, Physical
Yudong Mao, Shouyu Liu, Jiying Liu, Mingzhi Yu, Xinwei Li, Kaimin Yang
Summary: The ultra-fast laser heating process of nano-films exhibits a thermal wave phenomenon, with a greater amplitude in the vertical direction compared to the horizontal direction. Analytical solutions for heat conduction in nano-films under ultra-fast laser were obtained using the Cattaneo-Vernotte (CV) model and the dual-phase-lag (DPL) model. The temperature distribution based on the DPL model was found to be gentler than that of the CV model, and the two-dimensional solution had a lower temperature distribution than the one-dimensional solution at the same Knudsen number.
Article
Thermodynamics
Gianfranco Capriz, Krzysztof Wilmanski, Paolo Maria Mariano
Summary: By comparing the consequences of Maxwell-Cattaneo's view on heat flux and the approximation of defining it as a class of conductors, we demonstrate that the latter choice leads to a non-physical result. Additionally, in the presence of heat-driven phase transitions, the Maxwell-Cattaneo equation can be considered as emerging from a balance of microstructural interactions, including the Guyer-Krumhansl equation.
INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER
(2021)
Article
Mechanics
ZhangNa Xue, JianLin Liu, XiaoGeng Tian, YaJun Yu
Summary: This study analyzes the thermal fracture problem of an elastic half-space and strip with an insulated Griffith crack based on a newly proposed unified fractional heat conduction model. Different fractional definitions have different memory effects on transient responses, and the effects of fractional definitions on the responses vary with parameter values.
EUROPEAN JOURNAL OF MECHANICS A-SOLIDS
(2021)
Article
Multidisciplinary Sciences
Y. Povstenko, T. Kyrylych
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
(2020)
Article
Mechanics
Yuriy Povstenko, Martin Ostoja-Starzewski
Summary: This study examines the Cattaneo telegraph equation for temperature with a moving time-harmonic source on different domains using Laplace and Fourier transforms, obtaining expressions that demonstrate wave fronts and clarify the Doppler effect. Various specific cases, including the heat conduction equation and wave equation, are investigated, along with quasi-steady-state solutions for non-moving time-harmonic source and time-harmonic boundary conditions for temperature.
Review
Mathematics
Yuriy Povstenko
Summary: The article introduces the Wright function as a generalization of the exponential function and the Bessel functions, and presents integral relationships between the Mittag-Leffler functions and the Wright function. The applications of the Wright function and the Mainardi function in describing diffusion, heat conduction, thermal and diffusive stresses, as well as nonlocal elasticity within the framework of fractional calculus are also discussed.
Article
Physics, Multidisciplinary
Mikhail Selianinau, Yuriy Povstenko
Summary: This paper focuses on critical problems in residue arithmetic and proposes a novel approach for parallel reverse conversion. By parallel summation of small word-length residues in independent modular channels, the calculation complexity of mixed-radix digits is reduced, improving computational efficiency.
Article
Physics, Multidisciplinary
Yuriy Povstenko, Tamara Kyrylych, Bozena Wozna-Szczesniak, Renata Kawa, Andrzej Yatsko
Summary: This paper studies the time-fractional heat conduction equation in an infinite space with an external circular crack with the interior radius R in the case of axial symmetry. The stress intensity factor is calculated and presented graphically to analyze the variation of the crack surface under constant heat flux loading.
Article
Thermodynamics
Yuriy Povstenko, Martin Ostoja-Starzewski
Summary: This study investigates two characteristic versions of the time-fractional telegraph equation with a moving time-harmonic source on a real line, and successfully solves the problem using the integral transforms technique. The solution to the wave-type equation contains wave fronts and describes the Doppler effect, while the solution to the heat-type equation does not contain wave fronts.
INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER
(2022)
Article
Physics, Multidisciplinary
Yuriy Povstenko, Tamara Kyrylych
Summary: This paper studies the axisymmetric time-fractional diffusion equation with mass absorption using the Caputo derivative. It discusses different formulations of the problem for integer values of the time-derivatives and employs the integral transform technique. The numerical calculations are illustrated graphically for different parameter values.
Article
Physics, Multidisciplinary
Viktor Dashkiiev, Yuriy Povstenko
Summary: The discussion focuses on aviation flight safety issues related to an on-board information exchange system. Analysis of potential hazards during flight and ways to eliminate them through optimizing the system's parameters, work algorithm, and architecture are conducted. The importance of information exchange speed in ensuring safety during dynamic flight conditions is emphasized. Improving exchange speed and system effectiveness, as well as enhancing the probability of successfully resolving emergency situations, are proposed through modifications in system architecture and algorithm.
Article
Physics, Multidisciplinary
Mikhail Selianinau, Yuriy Povstenko
Summary: In this paper, a novel approach to power-of-two scaling based on the Chinese Remainder Theorem (CRT) and rank form of the number representation in residue number system (RNS) is proposed. The proposed enhancements simplify and speed up the power-of-two scaling process.
Article
Physics, Multidisciplinary
Tamara Kyrylych, Yuriy Povstenko
Summary: This paper discusses the use of multi-criteria analysis to analyze investment alternatives in complex organizational systems. The approach considers both quantitative and qualitative influences, statistical and individual properties, and expert evaluations. Criteria are defined to evaluate startup investment priorities, and Saaty's hierarchy method is applied to compare alternatives. An example analysis is conducted on three startups to identify their investment appeal based on specific features. The allocation of resources between projects according to global priorities allows for risk diversification.
Article
Thermodynamics
Yuriy Povstenko, Martin Ostoja-Starzewski, Tamara Kyrylych
Summary: This article investigates the telegraph equation with a moving time-harmonic source in polar coordinates (r, phi). Two scenarios are examined: a source moving on a straight line with constant velocity v and a source traveling on a circumference of a circle with a constant orbital frequency Omega. Solutions are derived using integral transforms technique. Additionally, the limiting cases of the telegraph equation, namely the Fourier heat conduction equation and the linear wave equation, are analyzed. The singularity of the wave equation solution at the point r = R + vt, phi = 0 for the straight-line motion scenario is described. The relationship between the orbital frequency Omega and the polar coordinates at the wave front is explored. Numerical simulation results are presented graphically for various nondimensional parameters.
INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER
(2023)
Article
Engineering, Multidisciplinary
Junren Ran, Hamza El-Kebir, Yuriy Povstenko, Richard Berlin, Joseph Bentsman, Martin Ostoja-Starzewski
Summary: This study simulates the heat conduction and motion of heat sources in electrosurgery using finite differencing in a two-dimensional setting. It finds that the motion of the heat source is supersonic and leads to multiscale phenomena such as shock waves, Mach wedges, and high-temperature concentrations.
INTERNATIONAL JOURNAL FOR MULTISCALE COMPUTATIONAL ENGINEERING
(2022)
Article
Mathematics, Interdisciplinary Applications
Junren Ran, Martin Ostoja-Starzewski, Yuriy Povstenko
Summary: This study investigates transient second sound phenomena caused by moving heat sources on planar random media, modeling spatial material randomness and decoupling fractal and Hurst effects. The Maxwell-Cattaneo model is solved using second-order central differencing, examining stochastic fluctuations of Mach wedges and comparing them to unperturbed Mach wedges. Simulation movies linked to this study illustrate all examined cases.
FRACTAL AND FRACTIONAL
(2021)
Article
Mechanics
Y. Povstenko
PHYSICAL MESOMECHANICS
(2020)
Proceedings Paper
Mathematics, Applied
Yuriy Povstenko, Tamara Kyrylych
ADVANCES IN NON-INTEGER ORDER CALCULUS AND ITS APPLICATIONS
(2020)
