Article
Mathematics, Applied
Qi Chen, Di Wu, Zhifei Zhang
Summary: This paper studies the stability of shear flows of Prandtl type in the steady Navier-Stokes equations and employs a direct energy method combined with the compactness method to solve the problem.
SCIENCE CHINA-MATHEMATICS
(2023)
Article
Mathematics, Applied
Qi Chen, Di Wu, Zhifei Zhang
Summary: This paper proves the stability of Prandtl expansions of the shear flow type and introduces a direct resolvent estimate method, which could be applied to other relevant problems of hydrodynamic stability.
SCIENCE CHINA-MATHEMATICS
(2022)
Article
Mathematics, Applied
Fucai Li, Ronghua Pan, Zhipeng Zhang
Summary: This paper investigates the stability and instability of the steady state for the 3D homogeneous incompressible viscous flow in a bounded simply connected domain with a smooth boundary. It is shown that there exists a critical slip length, below which the steady state is unstable, and above which it is stable.
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
(2022)
Article
Mechanics
R. E. Caflisch, F. Gargano, M. Sammartino, V. Sciacca
Summary: This study examines the evolution of a 2D vortex layer at high Reynolds numbers, characterizing the formation of stagnation points, recirculation regions, stretching and folding dynamics, the growth of vorticity intensity, and the self-similar structure of the inner core dependent on Reynolds number. The presence of complex singularities in solutions of Navier-Stokes equations and their behavior with increasing Reynolds number suggest differences in the behavior of vortex layers compared to vortex sheets.
JOURNAL OF FLUID MECHANICS
(2021)
Article
Mechanics
Luhang Shen, Daolun Li, Wenshu Zha, Li Zhang, Jieqing Tan
Summary: This paper proposes an approximation-correction model to solve unsteady compressible seepage equations without using any labeled data. The model contains two neural networks, one for approximating the asymptotic solution and the other for correcting the error of the approximation. Numerical experiments show that the proposed method can solve seepage equations with high accuracy, which is a significant breakthrough for deep learning-based methods to solve PDEs.
Article
Mathematics, Applied
Hugo Beirao da Veiga, Francesca Crispo
Summary: This paper investigates the convergence of solutions to the three-dimensional evolutionary Navier-Stokes equations to solutions of the Euler equations as the viscosity tends to zero. It focuses on the convergence under Navier slip-type boundary conditions after considering the Cauchy problem. It is shown that, in the presence of flat boundaries (such as the half-space case), convergence holds uniformly in time with respect to the initial data's norm. However, strong inviscid limit results are proven to be false in general domains corresponding to a large family of smooth initial data. A result in this direction is presented in Section 6.
ADVANCES IN NONLINEAR ANALYSIS
(2023)
Article
Mechanics
A. Viudez
Summary: Exact solutions of the time-dependent three-dimensional nonlinear vorticity equation for Euler flows with spherical geometry are provided. The velocity solution is the sum of a multipolar oscillatory function and a rigid cylindrical motion with swirl. These solutions are important for understanding inertial oscillations and nonlinear effects in multipolar flows.
JOURNAL OF FLUID MECHANICS
(2022)
Article
Mechanics
Chuong V. Tran, Xinwei Yu, David G. Dritschel
Summary: Incompressible fluid flows are characterized by high correlations between velocity and pressure, as well as between vorticity and pressure. This correlation plays a significant role in maintaining regularity in Navier-Stokes flows. The study suggests that as long as global pressure minimum (or minima) and velocity maximum (or maxima) are mutually exclusive, regularity is likely to persist.
JOURNAL OF FLUID MECHANICS
(2021)
Article
Mechanics
R. K. Michael Thambynayagam
Summary: This paper discusses a few basic, intuitive properties of the Navier-Stokes equations for incompressible fluid flows. The authors propose a rephrased interpretation of the Navier-Stokes equation in a space with arbitrary dimensions. They then derive spatially periodic solutions for the velocity and pressure fields that span an unbounded domain in three and four dimensions, given a smooth solenoidal initial velocity vector field. In these solutions, all velocity components depend non-trivially on all coordinate directions.
EUROPEAN JOURNAL OF MECHANICS B-FLUIDS
(2023)
Article
Engineering, Mechanical
Junchao Chen, Manwai Yuen
Summary: This paper constructs two types of exact global solutions using elementary functions to describe the three-dimensional incompressible MHD equations without viscosity. These solutions correspond to a generalization of the well-known Arnold-Beltrami-Childress (ABC) flow and exhibit interesting local behaviors with infinite energy. Under special parameter values, these solutions can be reduced to those of the incompressible Euler equations.
NONLINEAR DYNAMICS
(2021)
Article
Mathematics, Applied
Yanqing Wang, Yulin Ye
Summary: In this paper, an energy conservation criterion is derived for weak solutions of both the incompressible and compressible Navier-Stokes equations. The criterion is based on a combination of velocity and its gradient. For the incompressible case, it extends known results on periodic domain, including the famous Lions' energy conservation criterion. For the compressible case, it improves recent results and extends criteria for energy conservation from incompressible to compressible flow.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics
Jie Xiao, Junjie Zhang
Summary: The note demonstrates that under certain conditions, the solution U will completely vanish.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2021)
Article
Mathematics, Applied
Lourenco Beirao da Veiga, Franco Dassi, Gianmarci Manzini, Lorenzo Mascotto
Summary: We propose a four-field virtual element discretization method for the time-dependent resistive magnetohydrodynamics equations in three dimensions, with a focus on the semi-discrete formulation. This method utilizes general polyhedral meshes and ensures divergence-free velocity and magnetic fields up to machine precision. We provide a comprehensive convergence analysis under appropriate regularity assumptions, which is supported by numerical tests.
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
(2023)
Article
Mathematics
Lu Wang, Shuokai Yan, Qinghua Zhang
Summary: This paper focuses on the global existence and time-decay rates of the strong solution for the Boussinesq system with full viscosity in R-n for n >= 3. The global existence and uniqueness of the strong solution (theta, u) for the Boussinesq system are established under certain initial assumptions. The paper also provides estimates for the solution.
JOURNAL OF MATHEMATICS
(2023)
Article
Mathematics, Applied
Eduard Marusic-Paloka
Summary: An exact solution was constructed to describe the stationary fluid flow through a channel with the upper wall attached to an elastic spring. The position of the upper wall is determined by the interaction between the fluid and the wall, with the displacement calculated from a quartic equation that can be solved by radicals and has been proven to be physically reasonable.
ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK
(2021)
Article
Thermodynamics
Mustafa Turkyilmazoglu
Summary: This paper extends the classical models for fluid flow, heat transfer, and impulsive acceleration by introducing fractional derivatives. The solutions are represented as steady and transient parts, and alternative solution methods are provided. The findings demonstrate the impact of fractional derivative in different time regimes, contributing to the understanding of diffusion phenomena.
INTERNATIONAL JOURNAL OF NUMERICAL METHODS FOR HEAT & FLUID FLOW
(2023)
Article
Mathematics, Interdisciplinary Applications
Mustafa Turkyilmazoglu, Mohamed Altanji
Summary: Distinct fractional models of falling object with linear and quadratic air resistive forces are investigated using Caputo fractional derivative. Analytical solutions are obtained for each model, providing a vivid understanding of the object's motion. The contribution of nonlinearity to the fractional models is carefully examined. These fractional models exhibit rich phenomena not found in traditional integer derivative models, but still converge to the traditional model. Short time perturbation and large time asymptotic formulae are derived. The solutions for some fractional models suggest either an increased speed surpassing gravity or asymptotic deceleration to a stop, in contrast to reaching a terminal speed. In the case of quadratic air resistance, power series and asymptotic series solutions are derived under Caputo fractional derivative and infinite base fractional differentiation, respectively. The analysis of ideal falling object motion emphasizes the impact of fractional models and fractional derivative definitions on physical motion, necessitating proper justification.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Thermodynamics
Mustafa Turkyilmazoglu
Summary: The purpose of this work is to study the fluid flow and heat transfer between a rotating cone above a stretching disk. By using suitable similarity transformations, it is found that the physical phenomenon can be represented by a system of similarity equations, which is consistent with the literature in the absence of wall expansion. Numerical simulations are used to study the effects of surface expansion on momentum, thermal layers, swirling angles, and heat transports.
INTERNATIONAL JOURNAL OF NUMERICAL METHODS FOR HEAT & FLUID FLOW
(2023)
Article
Physics, Applied
Muhammad Rahman, H. Waheed, M. Turkyilmazoglu, M. Salman Siddiqui
Summary: This study focuses on Darcy-Brinkman flow across a stretched sheet in a porous medium, considering dissipation and frictional heating. It examines the geometry and equations governing the steady flow of dust particle fluid with slip effect and porous dissipation. Using similarity transformation, a two-dimensional nonlinear partial differential equation is reduced to a sequence of nonlinear ordinary differential equations. Numerical techniques, such as Maple packages and the RK4 method, are employed to solve the system of nonlinear equations and derive the numerical findings.
INTERNATIONAL JOURNAL OF MODERN PHYSICS B
(2023)
Article
Physics, Applied
Muhammad Rahman, Humma Waheed, Mustafa Turkyilmazoglu, M. Salman Siddiqui
Summary: This paper explores the significance of slip situations in porous media and frictional heating on unsteady fluid flow through porous media. Numerical solutions of the differential equation for fluid flow through porous material, including slip effects, are presented. Using a similarity transformation, a nonlinear ordinary differential equation is obtained. The resulting set of nonlinear problems is numerically solved using Maple packages under velocity and thermal slip conditions. Both velocity and temperature increase with an increase in the Brinkman viscosity ratio parameter ?. The effects of the nondimensional parameters on flow velocity and temperature are examined using graphical profiles. The implications of relevant parameters on dimensionless temperature, velocity, local Nusselt number, and skin friction coefficient are shown and explained. The fluctuation of parameters for various flow quantities of interest is investigated and the results are presented in graphs and tables.
INTERNATIONAL JOURNAL OF MODERN PHYSICS B
(2023)
Article
Thermodynamics
Mustafa Turkyilmazoglu
Summary: This paper investigates the mechanism of triggering Benard convection through the absolute instability mode in the presence of a uniform magnetic field perpendicular to the channel walls. The locus of wavenumbers and critical Rayleigh numbers leading to absolute instability onset is determined through a theoretical linear stability approach. The magnetic field has a stabilizing effect on convection, but it becomes ineffective against the absolute instability mechanism beyond a critical location.
INTERNATIONAL JOURNAL OF NUMERICAL METHODS FOR HEAT & FLUID FLOW
(2023)
Article
Thermodynamics
Mustafa Turkyilmazoglu, Abuzar Abid Siddiqui
Summary: In this study, the scope is to extend previous work by incorporating the effective viscosity term within the transitional flow in the frame of Brinkman-Darcy-Benard convection. Numerical simulations were performed to investigate the onset of instability within the linear stability analysis, considering the Darcy number, Rayleigh number, and horizontal temperature parameter as essential physical parameters. The results showed that comparatively larger Rayleigh numbers were obtained within the Brinkman's model than the published Darcy model.
INTERNATIONAL JOURNAL OF THERMAL SCIENCES
(2023)
Article
Engineering, Chemical
Mustafa Turkyilmazoglu
Summary: This study investigates the onset and formation of Darcy-Bernard convection in a channel filled with fluid-saturated porous medium of finite depth. The Darcy model of porosity is used to identify a new family of solutions controlled by two parameters. These solutions cover most basic states associated with the Darcy law equations. The results reveal the relaxed impermeable wall constraints and provide insight into the triggering/delaying of Darcy-Bernard cells.
TRANSPORT IN POROUS MEDIA
(2023)
Article
Chemistry, Analytical
Mustafa Turkyilmazoglu, Faisal Z. Duraihem
Summary: The paper introduces new tubular shapes resulting from the imposition of Navier's velocity slip at the surface. A family of pipes induced by the slip mechanism is discovered, which modifies traditional pipes with elliptical cross-sections and resembles collapsible tubes. The velocity and temperature fields of the new pipes are analytically determined, and physical features such as wall shear stress and convective heat transfer are studied in detail. The new pipes are considered to have engineering and practical value in the micromachining industry.
Article
Mechanics
Mustafa Turkyilmazoglu
Summary: This paper presents full solutions of the energy and Navier-Stokes equations in the approximate form of Boussinesq. The study focuses on the advective fluid layer flowing within parallel horizontal infinite walls with hydro-thermal slip conditions and the control of momentum/thermal motion by a vertically applied magnetic field. The results show that hydro-thermal slip enhances both velocity and temperature fields, while magnetic field has a weaker suppression effect.
ARCHIVE OF APPLIED MECHANICS
(2023)
Article
Physics, Multidisciplinary
Mustafa Turkyilmazoglu
Summary: Forecasting the epidemic peak time is crucial for making decisions on isolation, social distance, and lockdown measures. This research introduces two formulas for accurately predicting the peak time of an infectious disease based on the SIR epidemic model. These formulas can be easily computed using a regular calculator and do not require advanced mathematical functions. The accuracy of the formulas is confirmed through a comparison with COVID-19 data and the formulas can also accurately capture the past peak time of an endemic illness. Additionally, simple approximations are provided for easy use without sophisticated laboratory equipment.
CHINESE JOURNAL OF PHYSICS
(2023)
Article
Mathematics, Applied
Mustafa Turkyilmazoglu
Summary: In this article, the onset of convection in porous media with through flow is studied based on Darcy formulation. The effects of uniform vertical flow on the thermal instability of convective cells are investigated using three different thermal boundary constraints. The influence of the Peclet number on the stability response of the porous layer is analyzed, and the critical Darcy-Rayleigh numbers and Benard cell wavenumbers are determined numerically. The results show that opposing and assisting through flows have different effects on the stability of convection depending on the thermal conditions of the walls.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2023)
Article
Mechanics
Mustafa Turkyilmazoglu, Faisal Z. Duraihem
Summary: Thermally-driven natural convection in a porous layer is explored theoretically in this work based on Darcy's law. The study focuses on the non-circulating basic cellular flow between two infinitely long horizontal plates and its instability onset. The results show that a circulatory flow and temperature variation along the horizontal axis govern the motion, and the instability can be determined through linear stability analysis and numerical calculations.
EUROPEAN JOURNAL OF MECHANICS B-FLUIDS
(2024)
Article
Materials Science, Multidisciplinary
Mustafa Turkyilmazoglu, Faisal Z. Duraihem
Summary: This paper provides closed form solutions for fluid flow affected by a uniform magnetic field inside a triangular cross section pipe. The governing equation for pressure gradient induced flow under the magnetic field is reduced to a Helmholtz partial differential equation with Dirichlet boundary conditions. The velocity solution is derived using exponential functions involving the magnetic strength parameter or Hartmann number. The effects of Lorentz force on velocity variations, centerline velocity, volumetric flow rate, and wall shears are analyzed graphically by increasing the magnetic field strength.
JOURNAL OF MAGNETISM AND MAGNETIC MATERIALS
(2023)
Article
Materials Science, Multidisciplinary
Muhammad Rahman, Mustafa Turkyilmazoglu, Kiran Matloob
Summary: This research investigates the thermal performance of a hybrid nanofluid consisting of aluminum oxide and copper nanoparticles on the flow of water and ethylene glycol over a permeable cylinder. Different nanoparticle shapes are considered and the effects of different parameters are analyzed. The study reveals the impact of porosity, Hartmann numbers, inertia factors, Prandtl number, stratification parameter, Eckert number, and Hartmann's number on the velocity field and fluid temperature of the hybrid nanofluid.
JOURNAL OF MAGNETISM AND MAGNETIC MATERIALS
(2023)
Article
Engineering, Mechanical
Rosaria Del Toro, Maria Laura De Bellis, Marcello Vasta, Andrea Bacigalupo
Summary: This article presents a multifield asymptotic homogenization scheme for analyzing Bloch wave propagation in non-standard thermoelastic periodic materials. The proposed method derives microscale field equations, solves recursive differential problems within the unit cell, establishes a down-scaling relation, and obtains average field equations. The effectiveness of this approach is validated by comparing dispersion curves with those from the Floquet-Bloch theory.
INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES
(2024)
Article
Engineering, Mechanical
Yue Bao, Zhengcheng Yao, Yue Zhang, Xueman Hu, Xiandong Liu, Yingchun Shan, Tian He
Summary: This paper proposes a novel triple-gradient phononic acoustic black hole (ABH) beam that strategically manipulates multiple gradients to enhance its performance. The study reveals that the ABH effect is not solely brought about by the thickness gradient, but also extends to the power-law gradients in density and modulus. The synergistic development of three different gradient effects leads to more pronounced and broader bandgaps in PCs.
INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES
(2024)
Article
Engineering, Mechanical
Matthias Ryser, Jason Steffen, Bekim Berisha, Markus Bambach
Summary: This study investigates the feasibility of replacing complex experiments with multiple simpler ones to determine the anisotropic yielding behavior of sheet metal. The results show that parameter identifiability and accuracy can be achieved by combining multiple specimen geometries and orientations, enhancing the understanding of the yield behavior.
INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES
(2024)
Article
Engineering, Mechanical
Wenjun Li, Pengfei Zhang, Siyong Yang, Shenling Cai, Kai Feng
Summary: This study presents a novel two-dimensional non-contact platform based on Near-field Acoustic Levitation (NFAL), which can realize both one-dimensional and two-dimensional transportation. Numerical and experimental results prove the feasibility and ease of this method.
INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES
(2024)
Article
Engineering, Mechanical
Shuo Liu, Lu Che, Guodong Fang, Jun Liang
Summary: This study presents a novel lamina conjugated bond-based peridynamic (BB-PD) model that overcomes the limitations of material properties and is applicable to composite laminates with different stacking sequences. The accuracy and applicability of the model are validated through simulations of elastic deformation and progressive damage behavior, providing an explanation of the damage modes and failure mechanisms of laminated composite materials subjected to uniaxial loading.
INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES
(2024)
Article
Engineering, Mechanical
Omar El-Khatib, S. Kumar, Wesley J. Cantwell, Andreas Schiffer
Summary: Sandwich-structured honeycombs (SSHCs) are hierarchical structures with enhanced mass-specific properties. A model capable of predicting the elastic properties of hexagonal SSHCs is presented, showing superior in-plane elastic and shear moduli compared to traditional honeycombs, while the out-of-plane shear moduli are reduced.
INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES
(2024)
Article
Engineering, Mechanical
Zhi-Jian Li, Hong-Liang Dai, Yuan Yao, Jing-Ling Liu
Summary: This paper proposes a process-performance prediction model for estimating the yield strength and ultimate tensile strength of metallic parts fabricated by powder bed fusion additive manufacturing. The effect of main process variables on the mechanical performance of printed metallic parts is analyzed and the results can serve as a guideline for improvement. The accuracy of the proposed model is validated by comparison with literature.
INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES
(2024)
Article
Engineering, Mechanical
Saman A. Bapir, Kawa M. A. Manmi, Rostam K. Saeed, Abdolrahman Dadvand
Summary: This study numerically investigates the behavior of an ultrasonically driven gas bubble between two parallel rigid circular walls with a cylindrical micro-indentation in one wall. The primary objective is to determine the conditions that facilitate the removal of particulate contamination from the indentation using the bubble jet. The study found that the bubble jet can effectively remove contamination from the indentation for certain ranges of indentation diameter, but becomes less effective for larger indentation diameters.
INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES
(2024)
Article
Engineering, Mechanical
E. Polyzos, E. Vereroudakis, S. Malefaki, D. Vlassopoulos, D. Van Hemelrijck, L. Pyl
Summary: This research investigates the elastic and damage characteristics of individual composite beads used in 3D printed composites. A new analytical probabilistic progressive damage model (PPDM) is introduced to capture the elastic and damage attributes of these beads. Experimental results show strong agreement with the model in terms of elastic behavior and ultimate strength and strain.
INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES
(2024)
