Xiao Xin, Y. Masthanaiah, A. Rushikesava, Nainaru Tarakaramu, Sherzod Abdullaev, M. Ijaz Khan, Imen Rashid Bouazzi
Abstract In this study, we investigate the phenomenon of mixed convection in viscous fluid flow by a vertical channel, considering the presence of magneto‐hydro‐dynamics and porosity. Mixed convection occurs when both buoyancy forces and external forces, such as pumps or fans, influence the flow behavior. Understanding and accurately predicting mixed convection is crucial for optimizing heat exchanger design and performance. To model the temperature equation, we utilize the concept of the first law of thermodynamics. Additionally, we incorporate effects such as Joule heating, heat generation, and radiative heat flux in the energy equation modeling. The resulting physical liquid equations are solved using the shooting technique with the RKF (Runge–Kutta–Fehlberg) scheme. We present graphical representations of the flow variables, discussing their behavior in detail. The introduction provides an overview of the paper's roadmap, while the conclusion highlights the main and significant results obtained from our study. We found that, the temperature is more when liquid motion in between channel for large numerical values of thermal radiation parameter and Reynolds number.
{"title":"Magnetic field and dissipation effects on mixed convection viscous fluid flow by a channel in the presence of porous medium and heat generation/absorption phenomenon","authors":"Xiao Xin, Y. Masthanaiah, A. Rushikesava, Nainaru Tarakaramu, Sherzod Abdullaev, M. Ijaz Khan, Imen Rashid Bouazzi","doi":"10.1002/zamm.202300625","DOIUrl":"https://doi.org/10.1002/zamm.202300625","url":null,"abstract":"Abstract In this study, we investigate the phenomenon of mixed convection in viscous fluid flow by a vertical channel, considering the presence of magneto‐hydro‐dynamics and porosity. Mixed convection occurs when both buoyancy forces and external forces, such as pumps or fans, influence the flow behavior. Understanding and accurately predicting mixed convection is crucial for optimizing heat exchanger design and performance. To model the temperature equation, we utilize the concept of the first law of thermodynamics. Additionally, we incorporate effects such as Joule heating, heat generation, and radiative heat flux in the energy equation modeling. The resulting physical liquid equations are solved using the shooting technique with the RKF (Runge–Kutta–Fehlberg) scheme. We present graphical representations of the flow variables, discussing their behavior in detail. The introduction provides an overview of the paper's roadmap, while the conclusion highlights the main and significant results obtained from our study. We found that, the temperature is more when liquid motion in between channel for large numerical values of thermal radiation parameter and Reynolds number.","PeriodicalId":23924,"journal":{"name":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135568065","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract The present research uncovers the mathematical exploration of the magnetohydrodynamic radiative Casson nanofluid flow produced due to stretching and coaxially rotating surfaces of two disks inside a non‐Darcy porous medium under the dominance of the diacritic Hall current and heat generation. The energy field is displayed under the dominance of radiative and dissipative heat transport by involving the consequences of distinctive nonlinear thermal radiation, viscous dissipation, and Joule heating. The present study overcomes the barrier of heat and mass transport by annexing Cattaneo‐Christov double diffusion effects. The current exploration shows the characteristics of the concentration field due to arising chemical reaction incited by activation energy. A substantive mathematical problem is modeled by assigning nonlinear partial differential equations together with convective boundary conditions. A compatible similarity transformation comprised in the current study is exerted to produce a set of nonlinear ordinary differential equations with competent boundary conditions. The resulting mathematical model is numerically solved via dispensing the SLM. The present article deals with an in‐depth exploration of diagnostic flow parameters' attributes against the flow field and efficient physical quantities with the help of distinctive graphs and tables. As per the current investigation, the energy field becomes potent due to enhancing the stretching of each of the disks. Besides, augmenting the thermophoretic diffusion and chemical reaction boosts diluting the concentration of nanoparticles. The flow along the radial direction gets controlled near the upper disk under the increasing influence of the Hall current, intensity of the magnetic field, and stretching rate of the lower disk. On the other hand, the enlarging Casson parameter, rotation parameter, and stretching parameter for the lower disk lead to controlling the flow along the radial direction adjacent to the lower disk. Apart from that, the intense effects of the stretching rate of the upper disk and rotation rein axial flow throughout the flow region.
{"title":"Radiative heat transport of cattaneo‐christov double diffusive casson nanofluid flow between two rotating disks with hall current and activation energy","authors":"Anindita Sahoo, Raj Nandkeolyar","doi":"10.1002/zamm.202200419","DOIUrl":"https://doi.org/10.1002/zamm.202200419","url":null,"abstract":"Abstract The present research uncovers the mathematical exploration of the magnetohydrodynamic radiative Casson nanofluid flow produced due to stretching and coaxially rotating surfaces of two disks inside a non‐Darcy porous medium under the dominance of the diacritic Hall current and heat generation. The energy field is displayed under the dominance of radiative and dissipative heat transport by involving the consequences of distinctive nonlinear thermal radiation, viscous dissipation, and Joule heating. The present study overcomes the barrier of heat and mass transport by annexing Cattaneo‐Christov double diffusion effects. The current exploration shows the characteristics of the concentration field due to arising chemical reaction incited by activation energy. A substantive mathematical problem is modeled by assigning nonlinear partial differential equations together with convective boundary conditions. A compatible similarity transformation comprised in the current study is exerted to produce a set of nonlinear ordinary differential equations with competent boundary conditions. The resulting mathematical model is numerically solved via dispensing the SLM. The present article deals with an in‐depth exploration of diagnostic flow parameters' attributes against the flow field and efficient physical quantities with the help of distinctive graphs and tables. As per the current investigation, the energy field becomes potent due to enhancing the stretching of each of the disks. Besides, augmenting the thermophoretic diffusion and chemical reaction boosts diluting the concentration of nanoparticles. The flow along the radial direction gets controlled near the upper disk under the increasing influence of the Hall current, intensity of the magnetic field, and stretching rate of the lower disk. On the other hand, the enlarging Casson parameter, rotation parameter, and stretching parameter for the lower disk lead to controlling the flow along the radial direction adjacent to the lower disk. Apart from that, the intense effects of the stretching rate of the upper disk and rotation rein axial flow throughout the flow region.","PeriodicalId":23924,"journal":{"name":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135883083","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract An exciting new class of heat transmission fluids, nanofluids, has been developed as an alternative to traditional fluids in manufacturing. Fuel cells, heat exchangers and pharmaceutical processes are just a few of the many uses for them. When compared to monofluids, the heat transmission properties of hybrid fluids are superior. These are findings used in an extensive diversity of fields, from solar energy to air conditioning. The objective of this paper is to examine how Lorentz force and chemical reaction parameters affect the characteristics of a couple stress hybrid nanofluid (Ethylene Glycol + Graphene + Copper) flow via an exponentially stretching surface. The heat transport phenomenon is studied using viscous dissipation, exponential heat source and thermal radiation parameters. Furthermore, irreversibility analysis is provided in this paper. Governing equations are transformed into a set of nonlinear ordinary differential equations using suitable similarity transformations. The bvp4c solver in MATLAB is used to solve the transformed system. Engineering parameters of interest, including skin friction coefficient, are described using bar diagrams. It has been noted that the magnetic field and volume fraction of graphene nanoparticles (ϕ 1 ) reduce the skin friction coefficient. At , the skin friction coefficient decreases at a rate of 4.68187. It is observed that there is an increment in the fluid temperature with the rise in the exponential heat source parameter, and the velocity profile increases with the increase in the mixed convection parameter. It is detected that, while Eckert number () was set to , Nusselt number was reduced by 6.29239. It is noticed that, while the chemical reaction () is set to , the mass transfer rate rises at a Rate of 0.349644. It has been observed that as the Brinkmann number and magnetic field parameters increase, so does the rate of entropy production. It is also detected that as the porosity parameter increases, the fluid momentum decreases. Furthermore, increasing the couple stress parameter decreases the fluid velocity.
{"title":"Dynamics of thermal radiation and Lorentz force on the hybrid nanofluid (Ethylene Glycol + Graphene + Copper) flow via an exponentially stretching sheet with chemical reaction: An irreversibility analysis","authors":"Gandrakota Kathyayani, Poojari Prakash Gowd","doi":"10.1002/zamm.202300130","DOIUrl":"https://doi.org/10.1002/zamm.202300130","url":null,"abstract":"Abstract An exciting new class of heat transmission fluids, nanofluids, has been developed as an alternative to traditional fluids in manufacturing. Fuel cells, heat exchangers and pharmaceutical processes are just a few of the many uses for them. When compared to monofluids, the heat transmission properties of hybrid fluids are superior. These are findings used in an extensive diversity of fields, from solar energy to air conditioning. The objective of this paper is to examine how Lorentz force and chemical reaction parameters affect the characteristics of a couple stress hybrid nanofluid (Ethylene Glycol + Graphene + Copper) flow via an exponentially stretching surface. The heat transport phenomenon is studied using viscous dissipation, exponential heat source and thermal radiation parameters. Furthermore, irreversibility analysis is provided in this paper. Governing equations are transformed into a set of nonlinear ordinary differential equations using suitable similarity transformations. The bvp4c solver in MATLAB is used to solve the transformed system. Engineering parameters of interest, including skin friction coefficient, are described using bar diagrams. It has been noted that the magnetic field and volume fraction of graphene nanoparticles (ϕ 1 ) reduce the skin friction coefficient. At , the skin friction coefficient decreases at a rate of 4.68187. It is observed that there is an increment in the fluid temperature with the rise in the exponential heat source parameter, and the velocity profile increases with the increase in the mixed convection parameter. It is detected that, while Eckert number () was set to , Nusselt number was reduced by 6.29239. It is noticed that, while the chemical reaction () is set to , the mass transfer rate rises at a Rate of 0.349644. It has been observed that as the Brinkmann number and magnetic field parameters increase, so does the rate of entropy production. It is also detected that as the porosity parameter increases, the fluid momentum decreases. Furthermore, increasing the couple stress parameter decreases the fluid velocity.","PeriodicalId":23924,"journal":{"name":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135888660","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract A review of publications on stability of mechanical equilibrium of multicomponent mixtures in gases and liquids under non‐isothermal and isothermal conditions is given. Studies where diffusion in binary and multicomponent mixtures led to the occurrence of instability of mechanical equilibrium of the system have been analyzed. The main attention is paid to the description of approaches predicting the areas where there are increasing convective disturbances, as well as the determination of the spectrum of thermophysical parameters where the contribution of convection to heat and mass transfer is negligible. At the same time, the problems determining the role of diffusion, thermodiffusion, and double diffusion mechanisms in the separation of mixture components at the boundary of convective instability were given priority in the description. The results of investigations related to the study of the evolution of flows arising due to instability at the initial stage of mixing were also discussed.
{"title":"Diffusion mechanisms of convective instability in liquid and gas mixtures","authors":"Vladimir Kossov, Holm Altenbach","doi":"10.1002/zamm.202300801","DOIUrl":"https://doi.org/10.1002/zamm.202300801","url":null,"abstract":"Abstract A review of publications on stability of mechanical equilibrium of multicomponent mixtures in gases and liquids under non‐isothermal and isothermal conditions is given. Studies where diffusion in binary and multicomponent mixtures led to the occurrence of instability of mechanical equilibrium of the system have been analyzed. The main attention is paid to the description of approaches predicting the areas where there are increasing convective disturbances, as well as the determination of the spectrum of thermophysical parameters where the contribution of convection to heat and mass transfer is negligible. At the same time, the problems determining the role of diffusion, thermodiffusion, and double diffusion mechanisms in the separation of mixture components at the boundary of convective instability were given priority in the description. The results of investigations related to the study of the evolution of flows arising due to instability at the initial stage of mixing were also discussed.","PeriodicalId":23924,"journal":{"name":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136033656","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract This article discusses the scattering in a trifurcated guided wave featuring the combination of hard and flexible exterior surfaces. Through the formulation of the relevant boundary value problem and modes matching of orthogonal and non‐orthogonal functions, a comprehensive solution is obtained through infinite linear algebraic equations. The structural complexity of these structures introduces challenges related to non‐linearities in dispersive relations, and uncommon orthogonal characteristics of eigenfunctions. Therefore, by reorganizing the differential system into an algebraic one, a solution is obtained by truncating the system numerically. Further, analytical and numerical tests validate the solution, including graphical representations of relative powers versus frequency. The results reveal that transmission dominates reflection for frequencies above 900Hz in the symmetrical setting, with nearly equal power propagating through regions 2, 3, and 4. In the non‐symmetrical setting, power primarily transmits through region 4 for frequencies above 600Hz whereas most of the power being reflected at cut‐on frequencies when region 3 as rigid‐soft instead of rigid‐rigid. The obtained solution also confirms the properties of eigenfunctions, and the power distribution among different regions validates the accuracy of the solution. This work holds significance as it provides a standard procedure for modeling and solving a broad range of multifurcated problems with multiple dynamic boundary properties. The findings aid the understanding and development of waveguide systems, offering vision to practical applications in various fields involving complex wave propagation.
{"title":"Modeling and analysis of scattering in trifurcated guided waves with hard and flexible outer surfaces: A mathematical study","authors":"Hani Alahmadi","doi":"10.1002/zamm.202300470","DOIUrl":"https://doi.org/10.1002/zamm.202300470","url":null,"abstract":"Abstract This article discusses the scattering in a trifurcated guided wave featuring the combination of hard and flexible exterior surfaces. Through the formulation of the relevant boundary value problem and modes matching of orthogonal and non‐orthogonal functions, a comprehensive solution is obtained through infinite linear algebraic equations. The structural complexity of these structures introduces challenges related to non‐linearities in dispersive relations, and uncommon orthogonal characteristics of eigenfunctions. Therefore, by reorganizing the differential system into an algebraic one, a solution is obtained by truncating the system numerically. Further, analytical and numerical tests validate the solution, including graphical representations of relative powers versus frequency. The results reveal that transmission dominates reflection for frequencies above 900Hz in the symmetrical setting, with nearly equal power propagating through regions 2, 3, and 4. In the non‐symmetrical setting, power primarily transmits through region 4 for frequencies above 600Hz whereas most of the power being reflected at cut‐on frequencies when region 3 as rigid‐soft instead of rigid‐rigid. The obtained solution also confirms the properties of eigenfunctions, and the power distribution among different regions validates the accuracy of the solution. This work holds significance as it provides a standard procedure for modeling and solving a broad range of multifurcated problems with multiple dynamic boundary properties. The findings aid the understanding and development of waveguide systems, offering vision to practical applications in various fields involving complex wave propagation.","PeriodicalId":23924,"journal":{"name":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136033663","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Finite difference modelling of turbulent heat and mass flow visualization finds numerous applications in atmospheric flows/oceanic currents, wind turbines, thermal transfer in nuclear reactors, drag in oil pipelines, cooling of industrial machineries, and to investigate the complexity, dynamic and chaotic nature of the physical system. A turbulent phenomenon is effectively implemented in engineering, physics, earth sciences, bio‐engineering and medicine. Hence, motivated by the advantages of turbulence in various engineering fields, in the current article, a finite difference analysis is performed to demonstrate the k‐ε turbulence model‐based heat and mass lines visualization in boundary layer regime under turbulent buoyancy‐driven convective conditions along a cylinder. Turbulent flow characteristics are accurately explored by deploying the classical Newtonian flow model. Further, to accomplish a more sophisticated finite difference simulation, the effects of extra kinetic energy and its dissipation rate equations are considered. The produced Navier‐Stokes equations for time‐dependent turbulent heat and mass transmission are rendered to non‐dimensional by deploying suitable dimensionless numbers. The advanced coupled nonlinear turbulent unsteady buoyancy‐motivated vertical convection problem is then solved with a well‐sophisticated finite difference scheme such as Crank‐Nicolson technique using computational software. Authentication of current results with former solutions over a range of buoyancy number, Schmidt, and Prandtl parameters are presented. An extensive tabular and graphical discussion along with contours, heat and masslines visualization is included to enumerate the hydro‐dynamic, thermal and mass diffusion behaviour for the impact of emerged regulating numbers in the Prandtl regime. It is confirmed that, the accelerating turbulent buoyancy‐ratio number, maximizes the velocity, kinetic energy and dissipation rate at . Further, the numerical values of laminar thermal and mass diffusion rates are monotonically enhanced when compared to the turbulent values. Also, to verify the current findings, the authors compared the LRN k‐ε model turbulent results with the existing solutions and found good agreement. Further, the uniqueness and novelty of the current investigation is the exploration of heat and masslines in unsteady buoyancy‐driven convection regime under the influence of k‐ε turbulence model which extends the former studies and offers a more precise appraisal of the thermal and mass diffusion lines via the Crank‐Nicolson analysis.
{"title":"Turbulent heat and mass lines in finite difference regime","authors":"Suresha S P, G. Janardhana Reddy, Hussain Basha","doi":"10.1002/zamm.202300093","DOIUrl":"https://doi.org/10.1002/zamm.202300093","url":null,"abstract":"Abstract Finite difference modelling of turbulent heat and mass flow visualization finds numerous applications in atmospheric flows/oceanic currents, wind turbines, thermal transfer in nuclear reactors, drag in oil pipelines, cooling of industrial machineries, and to investigate the complexity, dynamic and chaotic nature of the physical system. A turbulent phenomenon is effectively implemented in engineering, physics, earth sciences, bio‐engineering and medicine. Hence, motivated by the advantages of turbulence in various engineering fields, in the current article, a finite difference analysis is performed to demonstrate the k‐ε turbulence model‐based heat and mass lines visualization in boundary layer regime under turbulent buoyancy‐driven convective conditions along a cylinder. Turbulent flow characteristics are accurately explored by deploying the classical Newtonian flow model. Further, to accomplish a more sophisticated finite difference simulation, the effects of extra kinetic energy and its dissipation rate equations are considered. The produced Navier‐Stokes equations for time‐dependent turbulent heat and mass transmission are rendered to non‐dimensional by deploying suitable dimensionless numbers. The advanced coupled nonlinear turbulent unsteady buoyancy‐motivated vertical convection problem is then solved with a well‐sophisticated finite difference scheme such as Crank‐Nicolson technique using computational software. Authentication of current results with former solutions over a range of buoyancy number, Schmidt, and Prandtl parameters are presented. An extensive tabular and graphical discussion along with contours, heat and masslines visualization is included to enumerate the hydro‐dynamic, thermal and mass diffusion behaviour for the impact of emerged regulating numbers in the Prandtl regime. It is confirmed that, the accelerating turbulent buoyancy‐ratio number, maximizes the velocity, kinetic energy and dissipation rate at . Further, the numerical values of laminar thermal and mass diffusion rates are monotonically enhanced when compared to the turbulent values. Also, to verify the current findings, the authors compared the LRN k‐ε model turbulent results with the existing solutions and found good agreement. Further, the uniqueness and novelty of the current investigation is the exploration of heat and masslines in unsteady buoyancy‐driven convection regime under the influence of k‐ε turbulence model which extends the former studies and offers a more precise appraisal of the thermal and mass diffusion lines via the Crank‐Nicolson analysis.","PeriodicalId":23924,"journal":{"name":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135766165","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract The present article presents the interaction of anti‐plane shear waves by two collinear cracks in one dimensional (1D) hexagonal piezoelectric quasicrystals (PQCs). With the aid of Fourier transform, the mixed boundary value problem (MBVP) is transformed into three pairs of dual integral equations, which are solved analytically by Hilbert transform. The explicit expressions for dynamic stress intensity factors (DSIFs) of phonon and phason fields, crack opening displacement (COD) and electric displacement (ED) are derived in closed form and some special cases are studied. Numerical values of DSIFs of phonon and phason fields, COD and ED are plotted to show the effect of crack length and electric boundary condition. Moreover, the DSIFs of phonon field and COD are represented graphically for single crack.
{"title":"Interaction of anti‐plane shear waves with two collinear cracks in 1D hexagonal piezoelectric quasicrystals","authors":"Sourav Kumar Panja, Subhas Chandra Mandal","doi":"10.1002/zamm.202300393","DOIUrl":"https://doi.org/10.1002/zamm.202300393","url":null,"abstract":"Abstract The present article presents the interaction of anti‐plane shear waves by two collinear cracks in one dimensional (1D) hexagonal piezoelectric quasicrystals (PQCs). With the aid of Fourier transform, the mixed boundary value problem (MBVP) is transformed into three pairs of dual integral equations, which are solved analytically by Hilbert transform. The explicit expressions for dynamic stress intensity factors (DSIFs) of phonon and phason fields, crack opening displacement (COD) and electric displacement (ED) are derived in closed form and some special cases are studied. Numerical values of DSIFs of phonon and phason fields, COD and ED are plotted to show the effect of crack length and electric boundary condition. Moreover, the DSIFs of phonon field and COD are represented graphically for single crack.","PeriodicalId":23924,"journal":{"name":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135918642","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract We use isotropic hypoelastic models based on corotational stress rates to simulate deformations of elastic bodies with initial stresses. Four material models based on different corotational stress rates are used: the Zaremba–Jaumann, Green–Naghdi, logarithmic, and Hill models. The main result of the study are new objective algorithms for integrating stresses that provide sufficiently accurate values of stresses for large time steps. In addition, a new approach to symmetrizing tangent stiffness matrices that has a clear mechanical interpretation was used in computations. All four material models were implemented in a homemade FE system for nonlinear analysis of deforming bodies. The developed algorithms were verified and validated by solving both uniform deformation problems that have exact solutions and applied problem of plate bending with non‐equilibrated initial stresses. The performance of the developed software was assessed by comparing numerical solutions obtained using this software with similar solutions obtained using the commercial MSC.Marc nonlinear FE system. Comparative analysis of the obtained solutions shows that our software is comparable in performance with one of the leading commercial software packages for solving problems of isotropic hypoelasticity with initial stresses.
{"title":"Simulating body deformations with initial stresses using Hooke‐like isotropic hypoelasticity models based on corotational stress rates","authors":"Sergey N. Korobeynikov, A. Yu. Larichkin","doi":"10.1002/zamm.202300568","DOIUrl":"https://doi.org/10.1002/zamm.202300568","url":null,"abstract":"Abstract We use isotropic hypoelastic models based on corotational stress rates to simulate deformations of elastic bodies with initial stresses. Four material models based on different corotational stress rates are used: the Zaremba–Jaumann, Green–Naghdi, logarithmic, and Hill models. The main result of the study are new objective algorithms for integrating stresses that provide sufficiently accurate values of stresses for large time steps. In addition, a new approach to symmetrizing tangent stiffness matrices that has a clear mechanical interpretation was used in computations. All four material models were implemented in a homemade FE system for nonlinear analysis of deforming bodies. The developed algorithms were verified and validated by solving both uniform deformation problems that have exact solutions and applied problem of plate bending with non‐equilibrated initial stresses. The performance of the developed software was assessed by comparing numerical solutions obtained using this software with similar solutions obtained using the commercial MSC.Marc nonlinear FE system. Comparative analysis of the obtained solutions shows that our software is comparable in performance with one of the leading commercial software packages for solving problems of isotropic hypoelasticity with initial stresses.","PeriodicalId":23924,"journal":{"name":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135146188","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract This paper presents a model for a thin active structure interacting with a viscous fluid, as well as a discretization and numerical simulations of the arising fluid‐structure interaction problem. The developed model allows to reproduce the behavior of cilia or flagella immersed in a viscous flow. In the context of linear or nonlinear elasticity, the model is based upon the definition of a suitable internal Piola‐Kirchoff tensor mimicking the action of the internal dyneins that induce the motility of the structure. In the subsequent fluid‐structure interaction problem, two difficulties arise and are discussed: on the one hand the internal activity of the structure leads to more restrictive well‐posedness conditions and, on the other hand, the coupling conditions between the fluid and the structure require a specific numerical treatment. A weak formulation of the time‐discretized problem is derived in functional spaces that include the coupling conditions, but for numerical purposes, an equivalent formulation using Lagrange multipliers is introduced in order to get rid of the constraints in the functional spaces. This new formulation allows for the use of standard (fluid and structure) solvers, up to an iterative procedure. Numerical simulations are presented, including the beating of one or two cilia in 2d, discussing the competition between the magnitude of the internal activity and the viscosity of the surrounding fluid.
{"title":"A continuum active structure model for the interaction of cilia with a viscous fluid","authors":"Astrid Decoene, Sébastien Martin, Fabien Vergnet","doi":"10.1002/zamm.202100534","DOIUrl":"https://doi.org/10.1002/zamm.202100534","url":null,"abstract":"Abstract This paper presents a model for a thin active structure interacting with a viscous fluid, as well as a discretization and numerical simulations of the arising fluid‐structure interaction problem. The developed model allows to reproduce the behavior of cilia or flagella immersed in a viscous flow. In the context of linear or nonlinear elasticity, the model is based upon the definition of a suitable internal Piola‐Kirchoff tensor mimicking the action of the internal dyneins that induce the motility of the structure. In the subsequent fluid‐structure interaction problem, two difficulties arise and are discussed: on the one hand the internal activity of the structure leads to more restrictive well‐posedness conditions and, on the other hand, the coupling conditions between the fluid and the structure require a specific numerical treatment. A weak formulation of the time‐discretized problem is derived in functional spaces that include the coupling conditions, but for numerical purposes, an equivalent formulation using Lagrange multipliers is introduced in order to get rid of the constraints in the functional spaces. This new formulation allows for the use of standard (fluid and structure) solvers, up to an iterative procedure. Numerical simulations are presented, including the beating of one or two cilia in 2d, discussing the competition between the magnitude of the internal activity and the viscosity of the surrounding fluid.","PeriodicalId":23924,"journal":{"name":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134946890","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract We analyze the effect of wall slip on the fully developed reverse mixed convection of Jeffery nanofluids between two inclined parallel plates with uniform wall heat flux conditions. The theory of tri‐hybrid water‐based nanoparticles with unique shapes, namely, cylindrical (copper), spherical (titanium oxide), and platelet (aluminum oxide) for heat transfer enhancement is utilized since it has better heat performance applicable in a dynamic of fuels and coolant in automobiles as compared with regular Newtonian fluid and nanofluid. The equations describing the above transport phenomena are nondimensional through appropriate scale transformations. Analytical solutions for velocity, temperature, and pressure distributions are obtained. Four different flow regimes including no reversal, bottom reversal, top reversal, and on both walls reversal are found for different combinations of buoyancy and pressure. Particularly, we notice that the wall slip significantly affects flow reversal. Furthermore, we notice that Magyari 's conclusion that the results of the homogeneous nanofluid flow model can be recovered from the corresponding Newtonian fluid model has great limitations. Besides, the effect of several physical factors on velocity and temperature distributions and important physical quantities, including skin friction coefficient and Nusselt number, are analyzed and graphically discussed.
{"title":"Fully developed opposing mixed convection of a Jeffery tri‐hybrid nanofluid between two parallel inclined plates subjected to wall‐slip condition","authors":"Aneela Bibi, Hang Xu","doi":"10.1002/zamm.202300177","DOIUrl":"https://doi.org/10.1002/zamm.202300177","url":null,"abstract":"Abstract We analyze the effect of wall slip on the fully developed reverse mixed convection of Jeffery nanofluids between two inclined parallel plates with uniform wall heat flux conditions. The theory of tri‐hybrid water‐based nanoparticles with unique shapes, namely, cylindrical (copper), spherical (titanium oxide), and platelet (aluminum oxide) for heat transfer enhancement is utilized since it has better heat performance applicable in a dynamic of fuels and coolant in automobiles as compared with regular Newtonian fluid and nanofluid. The equations describing the above transport phenomena are nondimensional through appropriate scale transformations. Analytical solutions for velocity, temperature, and pressure distributions are obtained. Four different flow regimes including no reversal, bottom reversal, top reversal, and on both walls reversal are found for different combinations of buoyancy and pressure. Particularly, we notice that the wall slip significantly affects flow reversal. Furthermore, we notice that Magyari 's conclusion that the results of the homogeneous nanofluid flow model can be recovered from the corresponding Newtonian fluid model has great limitations. Besides, the effect of several physical factors on velocity and temperature distributions and important physical quantities, including skin friction coefficient and Nusselt number, are analyzed and graphically discussed.","PeriodicalId":23924,"journal":{"name":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135482338","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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