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Calculation of the stationary flame propagation velocity by the variational principle of irreversible thermodynamics

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CASE STUDIES IN THERMAL ENGINEERING 2022年 30卷

作者： Karpov, Alexander, I Kudrin, Alexei, V Alies, Michael Y. Russian Acad Sci Udmurt Fed Res Ctr Ural Branch Izhevsk 426067 Russia

numerical algorithm for the prediction of the stationary flame propagation velocity over premixed gas mixture has been formulated by using the foundations of non-equilibrium thermodynamics. Considering the combustion as a set of irreversible processes, the steady-state regime of flame propagation is identified with the stationary state of the non-equilibrium thermodynamic system. The generalized form of functional has been stated allowing its minimization relatively to the sought stationary flame propagation velocity treated as additional variable. Based on this variational statement an integral relationship for the flame propagation velocity has been obtained. The calculations of the stationary flame propagation velocity over model premixed gas mixture performed by proposed algorithm showed a faster convergence at the initial steps of iteration process in comparison with the commonly used approach based on the mass conservation of combustion chemical traction. The combined algorithm has been formulated, which benefits from the proposed 'thermodynamic' approach at the initial steps and converges to final solution satisfying the general mass balance.

关键词： Flame propagation Stationary state numerical algorithm Variational principle Irreversible thermodynamics Entropy production

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Decomposition based least squares iterative estimation algorithm for output error moving average systems

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ENGINEERING COMPUTATIONS 2014年第4期31卷 709-725页

作者： Zhang, Wenge Jiangnan Univ Minist Educ Key Lab Adv Proc Control Light Ind Wuxi Peoples R China

Purpose - The purpose of this paper is to solve the heavy computational problem of parameter estimation algorithm. Design/methodology/approach - Presents a decomposition least squares based iterative identification algorithm. Findings - Can estimate the parameters for linear or pseudo-linear systems and have lower computational burden. Originality/value - This paper adopts a decomposition technique to solve engineering computation problems and offers a potential and efficient algorithm.

关键词： Computation method numerical algorithm

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On Lie symmetry mechanics for Navier-Stokes equations unified with non-Newtonian fluid model: A classical directory

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PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS 2019年 535卷 122469-000页

作者： Rehman, Khalil Ur Malik, M. Y. King Khalid Univ Coll Sci Dept Math Abha Saudi Arabia Air Univ Dept Math PAF Complex E-9 Islamabad 44000 Pakistan

It is noticed that the most of the researchers having affiliation with the field of fluid science formulate the physical problems by coupling the constitutive relation of the fluid models with the Navier-Stokes equations. The ultimate system of partial differential equations in this direction becomes non-linear in nature due to which investigators always faced problem to narrate the flow field properties. Therefore, in this article we propose the symmetry toolkit to obtain the one parameter group of transformations for the flow controlling differential equations rather than to move-on with the so-called transformations available in literature. To propose idea we have considered the thermally magnetized Williamson fluid flow field along with heat source/sink and chemical reaction effects. The mathematical model is constructed by coupling the constitutive relation of Williamson fluid model with the Navier-Stokes equations in terms of partial differential equations. Such equations are reduced into system of ordinary differential equations by using self-constructed scaling group of transformations via symmetry analysis. The reduced system is solved by numerical algorithm. The key observations are added by means of graphs and tables. It is observed that both Weissenberg number and Hartmann number has same impact of Williamson fluid velocity. Further, Williamson fluid concentration reflects decline magnitude towards higher values of both Schmidt number and chemical reaction parameter. It is well trusted that the structuring of one parameter group of transformations for the particular flow problem will be helpful to report complete description as compared to utilizing the so-called transformations from an existing work. (C) 2019 Elsevier B.V. All rights reserved.

关键词： Symmetry analysis Williamson fluid model Magnetized flow field Heat source/sink Chemical reaction numerical algorithm

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Application of fractional derivatives in a Darcy medium natural convection flow of MHD nanofluid

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AIN SHAMS ENGINEERING JOURNAL 2023年第9期14卷

作者： Khan, Mumtaz Rasheed, Amer Anwar, Muhammad Shoaib Shah, Syed Touqeer Hussain Lahore Univ Management Sci Sch Sci & Engn Dept Math Opposite Sect UDHA Lahore 54792 Pakistan Univ Jhang Dept Math Jhang 35200 Pakistan

Nanofluid thermophysical characteristics are critical for predicting heat transfer behavior. This attempt provides a computational assessment of boundary layer flow and heat transfer behavior of fractional Maxwell viscoelastic nanofluid and their hybrids over a permeable vertical surface. The effects of Lorents and buoyancy forces are also considered in the flow region. The flow problem is modeled with novel distributed order time fractional derivatives to achieve control of the flow and heat transfer. Mid-point quadrature approach is used to process the distributed order integrals, whereas nonlinear cou-pled time fractional derivatives are discretized through the finite difference method along withL1- algo- *** results shows that heat transfer rate enhanced 56:51% by enhancing the thermal Grashof number. Further, increase in nanoparticles volume fraction causes enhancement in thermal conductivity. More effects of the flow characteristic on velocity and temperature fields are shown graphically and ana-lyzed in detail. The involvement of novel distributed fractional order derivatives, and nanoparticles enhanced the importance of the simulated results, which can be helpful to effectively control related thermal engineering issues, like temperature management in internal combustion engines, cooling devices, and heat exchangers. (c) 2022 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Ain Shams Uni-versity. This is an open access article under the CC BY-NC-ND license (http://***/licenses/ by-nc-nd/4.0/).

关键词： Distributed order fractional derivative Nanofluid Natural Convection Darcy medium numerical algorithm

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Computing Contraction Metrics: Comparison of Different Implementations

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IFAC-PapersOnLine 2021年第9期54卷 310-316页

作者： P. Giesl S. Hafstein I. Mehrabinezhad Department of Mathematics University of Sussex Falmer BN1 9QH United Kingdom Faculty of Physical Sciences University of Iceland Dunhagi 5 IS-107 Reykjavik Iceland

We discuss the implementation of a novel demanding algorithm to compute contraction metrics for nonlinear systems. We compare MATLAB- and C++-implementations and study the effect of parallelizing the code. Further, we explore the use of different low-level math-libraries for the C++-implementation and the use of an undocumented code-path that considerably speeds up MATLAB code on AMD’s Ryzen processors.

关键词： Contraction metric Riemannian metric Lyapunov function numerical algorithm Mesh-free collocation

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A complex fractional mathematical modeling for the love story of Layla and Majnun

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CHAOS SOLITONS & FRACTALS 2021年 150卷 111091-111091页

作者： Kumar, Pushpendra Erturk, Vedat Suat Murillo-Arcila, Marina Cent Univ Punjab Sch Basic & Appl Sci Dept Math & Stat Bathinda 151001 Punjab India Ondokuz Mayis Univ Fac Arts & Sci Dept Math TR-55200 Atakum Samsun Turkey Univ Politecn Valencia Inst Univ Matemat Pura & Aplicada Valencia 46022 Spain

In this article, we provide numerical simulations to show the importance and the effects of fractional order derivatives in psychological studies. As it is well-known, complex variables are more realistic for defining structures in different cases. In this paper, we evidence that such dynamics become more realistic when we use fractional derivatives. We study a non-integer order, non-linear mathematical model for defining a love story of Layla and Majnun (a couple in a romantic relationship). We exemplify all necessary practical calculations to study this serious psychological phenomena. The existence of the unique solution for the given model is exhibited. We use a very recent and strong modified Predictor-Corrector algorithm to evaluate the model structure. Stability of the proposed method is also given. We exemplify that the given complex fractional model is more realistic and represents reality more closely. The proposed model is very basic, significant, and efficient at introducing distinct natures by only replacing one control parameter. In this study, we found that in some of the cases there are stable limit cycles, in some cases periodic behaviours and sometimes transiently chaotic solutions exist which cannot be observed for integer order models at same parameter values. The principal contribution of this article is to exhibit the importance of non-integer order derivatives for analysing complex dynamics. The use of complex variables makes this study more effective because they have both magnitude and phase to better explore the love and can describe different emotions such as coexisting love and hate. (c) 2021 Elsevier Ltd. All rights reserved.

关键词： Psychological modelling Complex variables Fractional mathematical model numerical algorithm New generalised Caputo type fractional derivative

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Fractional mathematical modeling of the Stuxnet virus along with an optimal control problem

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AIN SHAMS ENGINEERING JOURNAL 2023年第7期14卷

作者： Kumar, Pushpendra Govindaraj, V. Erturk, Vedat Suat Nisar, Kottakkaran Sooppy Inc, Mustafa Natl Inst Technol Puducherry Dept Math Karaikal 609609 India Fac Arts & Sci Ondokuz Mayis Univ Dept Math TR-55200 Samsun Turkiye Prince Sattam bin Abdulaziz Univ Coll Arts & Sci Dept Math Wadi Aldawaser 11991 Saudi Arabia Firat Univ Sci Fac Dept Math TR-23119 Elazig Turkiye China Med Univ China Med Univ Hosp Dept Med Res Taichung Taiwan

In this digital, internet-based world, it is not new to face cyber attacks from time to time. A number of heavy viruses have been made by hackers, and they have successfully given big losses to our systems. In the family of these viruses, the Stuxnet virus is a well-known name. Stuxnet is a very dangerous virus that probably targets the control systems of our industry. The main source of this virus can be an infected USB drive or flash drive. In this research paper, we study a mathematical model to define the dynamical structure or the effects of the Stuxnet virus on our computer systems. To study the given dynamics, we use a modified version of the Caputo-type fractional derivative, which can be used as an old Caputo derivative by fixing some slight changes, which is an advantage of this study. We demonstrate that the given fractional Caputo-type dynamical model has a unique solution using fixed point theory. We derive the solution of the proposed non-linear non-classical model with the application of a recent version of the Predictor-Corrector scheme. We analyze various graphs at different values of the arrival rate of new computers, damage rate, virus transmission rate, and natural removal rate. In the graphical interpretations, we verify the values of fractional orders and simulate 2-D and 3-D graphics to understand the dynamics clearly. The major novelty of this study is that we formulate the optimal control problem and its important consequences both theoretically and mathematically, which can be further extended graphically. The main contribution of this research work is to provide some novel results on the Stuxnet virus dynamics and explore the uses of fractional derivatives in computer science. The given methodology is effective, fully novel, and very easy to understand. (c) 2022 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Ain Shams University.

关键词： Fractional mathematical modelling Stuxnet virus Computer networks Industrial systems numerical algorithm Modified version of Caputo fractional derivative

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Time-scale investigation with the modified phase field crystal method

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MODELLING AND SIMULATION IN MATERIALS SCIENCE AND ENGINEERING 2022年第6期30卷 064001-064001页

作者： Burns, Duncan Provatas, Nikolas Grant, Martin McGill Univ Dept Phys Montreal PQ H3A 2T8 Canada

This paper extends the two time-scale modified phase-field crystal model to examine crystal plasticity. Two non-linear density dependent functions are constructed to effectively represent hydrostatic strain and dislocation density. The functions are then used to develop a new modified phase field crystal model, which accounts for strain and strain-rate couplings on density dynamics. The non-linear additions provide tunable parameters for controlling dislocation climb versus glide, as well as phonon softening mechanisms. A short-wavelength dampening is also introduced to account for phonon scattering and thermoelastic dissipation processes. Finally, a novel semi-implicit numeric scheme for efficient simulations of this model is presented, which also serves as a generalization of the commonly used Fourier pseudo-spectral method. The technique gives rise to unconditionally stable dynamics with simple numeric implementation requirements.

关键词： plasticity phase field crystal strain strain-rate numerical algorithm dislocations

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Heat spreading path optimization of IGBT thermal network model

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MICROELECTRONICS RELIABILITY 2019年 103卷 113511-000页

作者： Cui, Haoyang Hu, Fengye Zhang, Yu Zhou, Kun Shanghai Univ Elect Power Sch Elect & Informat Engn Shanghai Peoples R China

This paper presents a theoretical study on the thermal reliability of Insulated-gate bipolar transistor (IGBT) power modules. Although the Cauer thermal network (CTN) model is widely recognized as an essential tool to analyze the thermal performance of IGBT, the heat propagation path, however, deviates from the actual situation and causing an error calculation of junction temperature. Therefore, the thermal resistance (R-th) and thermal capacity (C-th) values are optimized by the heat spreading angle of each material layer, and the influence of baseplate heat dissipation effects is fully considered by adding the heat convection mechanism to the CTN model, which includes interaction between heat conduction and heat convection, thus achieving the integrity of the heat spreading path. Effectiveness of proposed model is validated by simulation studies of finite element analysis and Simulink, the junction temperature estimation results show that the proposed model is more accurate than the conventional CTN model especially in the good dissipation conditions. Thus, accurate thermal behavior estimation could be fairly interpreted by the optimized heat spreading path.

关键词： IGBT module Spreading angle Thermal network model Transient thermal impedance numerical algorithm

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Shallow water modeling of wave-structure interaction over irregular bottom?

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OCEAN ENGINEERING 2023年 267卷

作者： Gusev, Oleg Igorevich Khakimzyanov, Gayaz Salimovich Skiba, Vasiliy Savelievich Chubarov, Leonid Borisovich Fed Res Ctr Informat & Computat Technol Acad MA Lavrentiev Ave 6 Novosibirsk 630090 Novosibirsk Russia Novosibirsk State Univ 1 Pirogova str Novosibirsk 630090 Novosibirsk Russia

This paper describes the results from a numerical simulation of long surface waves interaction with fixed and partially immersed structure located over irregular bottom. The topic is connected with risk of critical wave impact on structures placed in the coastal waters of seas and oceans. The wave-structure interaction is simulated within the framework of a hierarchy of mathematical models, including the model of potential flows of an ideal fluid, a fully nonlinear dispersive and dispersionless shallow water models. The numerical algorithm for the dispersive model is described in detail. The obtained results show that rectangular cutout in the structure bottom reduces the amplitude of the reflected wave and increases that of the transmitted one;the basin bottom irregularity plays the most important role when located directly under the body. The protrusion behind the body may slightly decrease the wave force, and it significantly increases the force at other locations. Generally, the results obtained by the dispersive model correspond well with those of potential model, while the dispersionless model often significantly overestimates the wave force and amplitude of the reflected wave.

关键词： Long surface wave Partially immersed structure Irregular bottom Shallow water Nonlinear dispersion numerical algorithm

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