J. Singh, Hanumantha, Suneetha Kolasani, S. Hussain
The key attention of this paper is to explore the heat and mass transport in oscillatory hydromagnetic Titanium alloy water nanofluid flow within two vertical alternatively non‐conducting and conducting walls enclosing Darcy‐Brinkman porous medium. Motional induction is considered because it is sufficiently strong in comparison to Ohmic dissipation. Hall phenomenon is considered because the electromotive force induced due to revolving of fluid particle about the magnetic field lines is significant. Suitable physical laws (constitutive and field equations) are used to derive the equations leading the flow model. An analytical approach is followed to extract the solutions of the flow model. The quantities of physical interest such as wall shear stress (WSS), rate of heat transport rate (RHT) and rate of mass transport rate (RMT) at the walls are obtained from the extracted solutions. The physical insight into flow manners is discovered from the graphs and tables generated from the numerical computation of the solutions. It is important to note from the study that the volume concentration of nanofluid and magnetic diffusion produce resistivity in the flow and tends to slow down the fluid flow. Magnetic diffusion weakens the strength of the primarily motional induced magnetic field.
{"title":"Exploration of heat and mass transport in oscillatory hydromagnetic nanofluid flow within two verticals alternatively conducting surfaces","authors":"J. Singh, Hanumantha, Suneetha Kolasani, S. Hussain","doi":"10.1002/zamm.202300216","DOIUrl":"https://doi.org/10.1002/zamm.202300216","url":null,"abstract":"The key attention of this paper is to explore the heat and mass transport in oscillatory hydromagnetic Titanium alloy water nanofluid flow within two vertical alternatively non‐conducting and conducting walls enclosing Darcy‐Brinkman porous medium. Motional induction is considered because it is sufficiently strong in comparison to Ohmic dissipation. Hall phenomenon is considered because the electromotive force induced due to revolving of fluid particle about the magnetic field lines is significant. Suitable physical laws (constitutive and field equations) are used to derive the equations leading the flow model. An analytical approach is followed to extract the solutions of the flow model. The quantities of physical interest such as wall shear stress (WSS), rate of heat transport rate (RHT) and rate of mass transport rate (RMT) at the walls are obtained from the extracted solutions. The physical insight into flow manners is discovered from the graphs and tables generated from the numerical computation of the solutions. It is important to note from the study that the volume concentration of nanofluid and magnetic diffusion produce resistivity in the flow and tends to slow down the fluid flow. Magnetic diffusion weakens the strength of the primarily motional induced magnetic field.","PeriodicalId":23924,"journal":{"name":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","volume":"47 1","pages":""},"PeriodicalIF":2.3,"publicationDate":"2023-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74192772","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}
In this paper, we study the existence and uniqueness of solutions to the initial‐boundary‐value problem for time‐dependent flows of heat‐conducting incompressible fluids through the two‐dimensional channel. The boundary conditions are of two types: the so‐called “do nothing” boundary condition on the outflow and the so‐called Navier boundary conditions on the solid walls of the channel. A priori estimates play a crucial role in existential analysis, however, the considered mixed boundary conditions do not enable us to derive an energy‐type estimate of the solution. Our aim is to prove the existence and uniqueness of a solution on a sufficiently short time interval for arbitrarily large data.
{"title":"On buoyancy‐driven viscous incompressible flows with various types of boundary conditions","authors":"M. Beneš, P. Kučera, Petra Vacková","doi":"10.1002/zamm.202200529","DOIUrl":"https://doi.org/10.1002/zamm.202200529","url":null,"abstract":"In this paper, we study the existence and uniqueness of solutions to the initial‐boundary‐value problem for time‐dependent flows of heat‐conducting incompressible fluids through the two‐dimensional channel. The boundary conditions are of two types: the so‐called “do nothing” boundary condition on the outflow and the so‐called Navier boundary conditions on the solid walls of the channel. A priori estimates play a crucial role in existential analysis, however, the considered mixed boundary conditions do not enable us to derive an energy‐type estimate of the solution. Our aim is to prove the existence and uniqueness of a solution on a sufficiently short time interval for arbitrarily large data.","PeriodicalId":23924,"journal":{"name":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","volume":"25 1","pages":""},"PeriodicalIF":2.3,"publicationDate":"2023-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81621742","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}
In this paper, we present the distributed dislocation technique (DDT) based numerical algorithms to study the generalized strip saturated (GSS) models for two equal collinear cracks in 2‐D finite and infinite piezoelectric media. Numerical studies for particular cases such as linear, quadratic and cubic strip saturated models are simulated by considering their equivalent forms based on the principle of superposition. Two equal collinear cracks problem and its particular case of coalesced zones are considered in 2‐D semipermeable piezoelectric media under arbitrary poling direction and in‐plane electromechanical loadings. The results of saturated zone lengths (inner and outer) and local stress intensity factors (at inner and outer tips) are evaluated numerically for infinite and finite domain problems. The results of infinite domain obtained using DDT are compared with the reference analytical solutions. A good agreement of the results shows the efficacy of the proposed algorithms based on DDT for solving GSS two equal collinear cracks problems in 2‐D finite/infinite piezoelectric media.
{"title":"Simplified numerical algorithms for generalized strip saturated two equal collinear cracks in piezoelectric media using distributed dislocation technique","authors":"K. Sharma, Sandeep Singh, T. Bui","doi":"10.1002/zamm.202300004","DOIUrl":"https://doi.org/10.1002/zamm.202300004","url":null,"abstract":"In this paper, we present the distributed dislocation technique (DDT) based numerical algorithms to study the generalized strip saturated (GSS) models for two equal collinear cracks in 2‐D finite and infinite piezoelectric media. Numerical studies for particular cases such as linear, quadratic and cubic strip saturated models are simulated by considering their equivalent forms based on the principle of superposition. Two equal collinear cracks problem and its particular case of coalesced zones are considered in 2‐D semipermeable piezoelectric media under arbitrary poling direction and in‐plane electromechanical loadings. The results of saturated zone lengths (inner and outer) and local stress intensity factors (at inner and outer tips) are evaluated numerically for infinite and finite domain problems. The results of infinite domain obtained using DDT are compared with the reference analytical solutions. A good agreement of the results shows the efficacy of the proposed algorithms based on DDT for solving GSS two equal collinear cracks problems in 2‐D finite/infinite piezoelectric media.","PeriodicalId":23924,"journal":{"name":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","volume":"12 1","pages":""},"PeriodicalIF":2.3,"publicationDate":"2023-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79073544","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}
The properties of Rayleigh wave velocity are analyzed by considering the rotation and electric bias. The algebraic equation is derived for determining the piezoelectric Rayleigh wave velocity analytically and numerically for Lithium Niobate. The main results reveal that the rotation as well as electric bias has exerted an appreciable influence on the wave velocity. Particularly, the Coriolis force under the rotatory condition can decrease wave velocity considerably, and such attributes are significant for the acoustic electronics.
{"title":"Effects of rotation and electric bias in the semi‐infinite piezoelectric medium on Rayleigh wave velocity","authors":"Xiaoguang Yuan, Zefeng Gao, Chaoyu Hao, Q. Jiang","doi":"10.1002/zamm.202200440","DOIUrl":"https://doi.org/10.1002/zamm.202200440","url":null,"abstract":"The properties of Rayleigh wave velocity are analyzed by considering the rotation and electric bias. The algebraic equation is derived for determining the piezoelectric Rayleigh wave velocity analytically and numerically for Lithium Niobate. The main results reveal that the rotation as well as electric bias has exerted an appreciable influence on the wave velocity. Particularly, the Coriolis force under the rotatory condition can decrease wave velocity considerably, and such attributes are significant for the acoustic electronics.","PeriodicalId":23924,"journal":{"name":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","volume":"119 1","pages":""},"PeriodicalIF":2.3,"publicationDate":"2023-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75783950","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}
In the present study, the free vibration of functionally graded graphene platelet‐reinforced (FG‐GPLs) and functionally graded carbon nanotube‐reinforced (FG‐CNTs) hybrid laminated nanocomposite truncated conical shells and panels are analyzed. Multi‐layers truncated conical shell and panel of pure FG‐CNTs, pure FG‐GPLs and hybrid CNTs‐GPLs reinforcement were evaluated. In light of its high accuracy in the calculation of thin and thick shells, a third‐order shear deformation theory is adopted. The governing equations and boundary conditions is derived using Hamilton's principle and is solved numerically using the systematic differential quadrature method (DQM) which uses Kronecker delta function. The effective mechanical properties of the CNT‐reinforced nanocomposite layers are estimated using the rule of mixtures, whereas those of the GPL‐reinforced nanocomposite layers is calculated using the Halpin‐Tsai micromechanical model. Convergence and accuracy evaluation of the presented study are confirmed and a number of parameters, including the CNTS volume fraction, GPLs mass fraction, distribution patterns (i.e., Uniform distribution (UD), Functionally graded O‐distribution (FG‐O), Functionally graded X‐distribution (FG‐X), Functionally graded V‐distribution (FG‐V) and FG‐A), different boundary conditions and the vertex angle of the cone, are investigated. The results obtained in this article for the combination of two different materials, GPLs and CNTs, showed that in controlling the natural frequency of the system, without changing the percentage of fiber and only by changing the arrangement, very wonderful results can be achieved.
{"title":"Free vibration analysis of FG‐GPL and FG‐CNT hybrid laminated nano composite truncated conical shells using systematic differential quadrature method","authors":"H. Ghasemi, Y. Mohammadi, F. Ebrahimi","doi":"10.1002/zamm.202300280","DOIUrl":"https://doi.org/10.1002/zamm.202300280","url":null,"abstract":"In the present study, the free vibration of functionally graded graphene platelet‐reinforced (FG‐GPLs) and functionally graded carbon nanotube‐reinforced (FG‐CNTs) hybrid laminated nanocomposite truncated conical shells and panels are analyzed. Multi‐layers truncated conical shell and panel of pure FG‐CNTs, pure FG‐GPLs and hybrid CNTs‐GPLs reinforcement were evaluated. In light of its high accuracy in the calculation of thin and thick shells, a third‐order shear deformation theory is adopted. The governing equations and boundary conditions is derived using Hamilton's principle and is solved numerically using the systematic differential quadrature method (DQM) which uses Kronecker delta function. The effective mechanical properties of the CNT‐reinforced nanocomposite layers are estimated using the rule of mixtures, whereas those of the GPL‐reinforced nanocomposite layers is calculated using the Halpin‐Tsai micromechanical model. Convergence and accuracy evaluation of the presented study are confirmed and a number of parameters, including the CNTS volume fraction, GPLs mass fraction, distribution patterns (i.e., Uniform distribution (UD), Functionally graded O‐distribution (FG‐O), Functionally graded X‐distribution (FG‐X), Functionally graded V‐distribution (FG‐V) and FG‐A), different boundary conditions and the vertex angle of the cone, are investigated. The results obtained in this article for the combination of two different materials, GPLs and CNTs, showed that in controlling the natural frequency of the system, without changing the percentage of fiber and only by changing the arrangement, very wonderful results can be achieved.","PeriodicalId":23924,"journal":{"name":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","volume":"127 1","pages":""},"PeriodicalIF":2.3,"publicationDate":"2023-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76585520","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}
The Local Linear Timoshenko (LLT) model for the planar motion of a rod that undergoes flexure, shear and extension, was recently derived in Van Rensburg et al. (2021). In this paper we present an algorithm developed for this model. The algorithm is based on the mixed finite element method, and projections into finite dimensional subspaces are used for dealing with nonlinear forces and moments. The algorithm is used for an investigation into elastic waves propagated in the LLT rod. Interesting properties of the LLT rod include the increased propagation speed of elastic waves when compared to the linear Timoshenko beam, and the appearance of buckled states or equilibrium solutions for compressed LLT beams. It is also shown that the LLT rod is applicable to large displacements and rotations for a wide range of slender elastic objects; from beams to highly slender flexible rods.
{"title":"Large displacements and rotations of a local linear elastic rod","authors":"S. du Toit, M. Labuschagne, Alna van der Merwe","doi":"10.1002/zamm.202200586","DOIUrl":"https://doi.org/10.1002/zamm.202200586","url":null,"abstract":"The Local Linear Timoshenko (LLT) model for the planar motion of a rod that undergoes flexure, shear and extension, was recently derived in Van Rensburg et al. (2021). In this paper we present an algorithm developed for this model. The algorithm is based on the mixed finite element method, and projections into finite dimensional subspaces are used for dealing with nonlinear forces and moments. The algorithm is used for an investigation into elastic waves propagated in the LLT rod. Interesting properties of the LLT rod include the increased propagation speed of elastic waves when compared to the linear Timoshenko beam, and the appearance of buckled states or equilibrium solutions for compressed LLT beams. It is also shown that the LLT rod is applicable to large displacements and rotations for a wide range of slender elastic objects; from beams to highly slender flexible rods.","PeriodicalId":23924,"journal":{"name":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","volume":"28 1","pages":""},"PeriodicalIF":2.3,"publicationDate":"2023-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72966827","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}
{"title":"Preface for the ZAMM special issue “Energy‐Based Mathematical Methods for Reactive Multiphase Flows”","authors":"M. Liero, M. Thomas, D. Peschka","doi":"10.1002/zamm.202302011","DOIUrl":"https://doi.org/10.1002/zamm.202302011","url":null,"abstract":",","PeriodicalId":23924,"journal":{"name":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","volume":"21 10","pages":""},"PeriodicalIF":2.3,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72562416","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}
We consider the local discontinuous Galerkin (LDG) method for a third order singularly perturbed problem with different kinds of boundary layer. On graded Duran‐Shishkin and Duran type meshes, we prove optimal order error estimate in the energy‐norm which is valid uniformly up to a logarithmic factor. Numerical experiments are given to confirm our theoretical findings.
{"title":"Local discontinuous Galerkin method on graded meshes for a third‐order singularly perturbed problem","authors":"Li Yan, Yao Cheng","doi":"10.1002/zamm.202300238","DOIUrl":"https://doi.org/10.1002/zamm.202300238","url":null,"abstract":"We consider the local discontinuous Galerkin (LDG) method for a third order singularly perturbed problem with different kinds of boundary layer. On graded Duran‐Shishkin and Duran type meshes, we prove optimal order error estimate in the energy‐norm which is valid uniformly up to a logarithmic factor. Numerical experiments are given to confirm our theoretical findings.","PeriodicalId":23924,"journal":{"name":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","volume":"167 1","pages":""},"PeriodicalIF":2.3,"publicationDate":"2023-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76455008","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}
In this article, we propose the weak Galerkin (WG) finite element schemes for H(div;Ω)${bf H}(mbox{div}; {Omega })$ ‐elliptic problems with and without stabilizers. Optimal orders of convergence are established for the WG approximations in both discrete energy norm and L2 norm. Removing stabilizers from WG finite element methods will simplify the formulations, reduce programming complexity, and may also speed up the computation time. More precisely, for sufficiently smooth solutions, we have proved the supercloseness of order two for the stabilizer free weak Galerkin finite element solution. Several numerical tests are presented to demonstrate the effectiveness of our method.
{"title":"Weak Galerkin finite element methods with and without stabilizers for H(div;Ω)${bf H}(mbox{div}; Omega )$‐elliptic problems","authors":"Raman Kumar, B. Deka","doi":"10.1002/zamm.202200207","DOIUrl":"https://doi.org/10.1002/zamm.202200207","url":null,"abstract":"In this article, we propose the weak Galerkin (WG) finite element schemes for H(div;Ω)${bf H}(mbox{div}; {Omega })$ ‐elliptic problems with and without stabilizers. Optimal orders of convergence are established for the WG approximations in both discrete energy norm and L2 norm. Removing stabilizers from WG finite element methods will simplify the formulations, reduce programming complexity, and may also speed up the computation time. More precisely, for sufficiently smooth solutions, we have proved the supercloseness of order two for the stabilizer free weak Galerkin finite element solution. Several numerical tests are presented to demonstrate the effectiveness of our method.","PeriodicalId":23924,"journal":{"name":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","volume":"27 1","pages":""},"PeriodicalIF":2.3,"publicationDate":"2023-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74913407","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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