This entire study aims to investigate the impacts of linear thermal radiation and MHD Casson ternary hybrid nanofluid flows over a vertical porous plate for comparison of nanofluid, hybrid, and tri‐hybrid nanofluids with Newtonian and non‐Newtonian fluids. We used a ternary hybrid nanofluid, Blood contains three types of oxides and metals: spherical ferric oxide (Fe3O4), platelet‐shaped zinc (Zn), and cylindrically‐shaped gold (Au) nanoparticles. The coupled nonlinear dual partial differential equations (PDEs) are turned into PDEs using nondimensional quantities. The Finite Difference Method (FDM) and the Perturbation Method are then used to solve the PDEs. The impacts of different parameters on temperature, velocity, Nusselt number, and Skin friction profiles have been discussed. The increase in viscosity occurs because an increase in Gr also causes an increase in the velocity field for nanofluid, hybrid, and tri‐hybrid nanofluids. A tri‐hybrid nanofluids performs better among the three, such as nanofluid, hybrids and tri‐hybrid nanofluids. As the volume fractions (Fe3O4) increase, the temperature increase for both Newtonian and non‐Newtonian fluids. The increase in temperature is due to the thermal conductivity of nanoparticles, which is enhanced by growth estimates of the nanoparticle volume fraction. The high temperature of the fluid is observed for large estimates of nanoparticle volume fraction. An increase gold (Au) also increases the temperature for shapes (cylinder, platelet, and spherical). A spherical shape performs better among the three, such as cylinder, platelet, and spherical. In this model, biomedical applications such as antiviral and therapeutic, treatment of the COVID‐19 virus, cancer treatment, and anticancer medication delivery systems.
{"title":"MHD Casson ternary hybrid nanofluid flow through a vertical porous plate with thermal radiation: A finite difference approach","authors":"K. Sakkaravarthi, I. Sakthi, P. Bala Anki Reddy","doi":"10.1002/zamm.202300571","DOIUrl":"https://doi.org/10.1002/zamm.202300571","url":null,"abstract":"This entire study aims to investigate the impacts of linear thermal radiation and MHD Casson ternary hybrid nanofluid flows over a vertical porous plate for comparison of nanofluid, hybrid, and tri‐hybrid nanofluids with Newtonian and non‐Newtonian fluids. We used a ternary hybrid nanofluid, Blood contains three types of oxides and metals: spherical ferric oxide (<jats:italic>Fe3O4</jats:italic>), platelet‐shaped zinc (<jats:italic>Zn</jats:italic>), and cylindrically‐shaped gold (<jats:italic>Au</jats:italic>) nanoparticles. The coupled nonlinear dual partial differential equations (PDEs) are turned into PDEs using nondimensional quantities. The Finite Difference Method (FDM) and the Perturbation Method are then used to solve the PDEs. The impacts of different parameters on temperature, velocity, Nusselt number, and Skin friction profiles have been discussed. The increase in viscosity occurs because an increase in <jats:italic>Gr</jats:italic> also causes an increase in the velocity field for nanofluid, hybrid, and tri‐hybrid nanofluids. A tri‐hybrid nanofluids performs better among the three, such as nanofluid, hybrids and tri‐hybrid nanofluids. As the volume fractions (<jats:italic>Fe3O4</jats:italic>) increase, the temperature increase for both Newtonian and non‐Newtonian fluids. The increase in temperature is due to the thermal conductivity of nanoparticles, which is enhanced by growth estimates of the nanoparticle volume fraction. The high temperature of the fluid is observed for large estimates of nanoparticle volume fraction. An increase gold (<jats:italic>Au</jats:italic>) also increases the temperature for shapes (cylinder, platelet, and spherical). A spherical shape performs better among the three, such as cylinder, platelet, and spherical. In this model, biomedical applications such as antiviral and therapeutic, treatment of the COVID‐19 virus, cancer treatment, and anticancer medication delivery systems.","PeriodicalId":501230,"journal":{"name":"ZAMM - Journal of Applied Mathematics and Mechanics","volume":"61 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141153027","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Amin Amiri Delouei, Amin Emamian, Saeed Ghorbani, Fuli He
The objective of this research paper is to propose an exact solution for resolving the transient conduction in a 2D sphere. The coefficients of governing equation are varied according to the material properties. The thermo‐physical properties are regarded as functions that follow a power‐law relationship concerning the radial direction. Both radial and angular thermal conductivity coefficients change with radius. Thermal boundary conditions are considered in a general state, which can cover different thermal conditions, including Dirichlet, Neumann, and Convection surface conditions. Laplace transform and Meromorphic function methods are used in the solution approach to the current unsteady problem. Two unsteady case studies with complex boundary conditions have been considered to show the credibility of the current solution. The results of both case studies have been successfully validated. The results confirm the high capability of the present solution in solving unsteady thermal problems of functionally graded materials in spherical coordinates.
{"title":"Spherical partial differential equation with non‐constant coefficients for modeling of nonlinear unsteady heat conduction in functionally graded materials","authors":"Amin Amiri Delouei, Amin Emamian, Saeed Ghorbani, Fuli He","doi":"10.1002/zamm.202300725","DOIUrl":"https://doi.org/10.1002/zamm.202300725","url":null,"abstract":"The objective of this research paper is to propose an exact solution for resolving the transient conduction in a 2D sphere. The coefficients of governing equation are varied according to the material properties. The thermo‐physical properties are regarded as functions that follow a power‐law relationship concerning the radial direction. Both radial and angular thermal conductivity coefficients change with radius. Thermal boundary conditions are considered in a general state, which can cover different thermal conditions, including Dirichlet, Neumann, and Convection surface conditions. Laplace transform and Meromorphic function methods are used in the solution approach to the current unsteady problem. Two unsteady case studies with complex boundary conditions have been considered to show the credibility of the current solution. The results of both case studies have been successfully validated. The results confirm the high capability of the present solution in solving unsteady thermal problems of functionally graded materials in spherical coordinates.","PeriodicalId":501230,"journal":{"name":"ZAMM - Journal of Applied Mathematics and Mechanics","volume":"18 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141153059","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this work, an attention is paid to the prediction of torsional vibration frequencies of functionally graded porous nanotubes based on the Lam strain gradient elasticity theory. The nanotubes are formed of functionally graded porous nanomaterials that vary in the radial direction. This study also aims to obtain the analytical solution of the strain gradient model presented by Lam for torsional vibration response, in a simple manner, for different rigid or restrained boundary conditions. The torsion angle of a functionally graded nanotube is defined by an infinite Fourier series. Then, the Stokes’ transformation is applied to force the boundary conditions to the desired state. An eigenvalue problem is established with the help of the two systems of equations obtained. This eigenvalue problem, which includes deformable springs at both ends of the nanotube, appears as a general analytical solution that can find torsional vibration frequencies. It is shown that the vibrational responses can be significantly influenced by the through‐radius gradings of material, material length scale parameters and deformable springs of the functionally graded nanotubes and consequently can be predicted by giving proper values to torsional spring parameters.
{"title":"An investigation on the torsional vibration of a FG strain gradient nanotube","authors":"Büşra Uzun, Mustafa Özgür Yaylı, Ömer Civalek","doi":"10.1002/zamm.202301093","DOIUrl":"https://doi.org/10.1002/zamm.202301093","url":null,"abstract":"In this work, an attention is paid to the prediction of torsional vibration frequencies of functionally graded porous nanotubes based on the Lam strain gradient elasticity theory. The nanotubes are formed of functionally graded porous nanomaterials that vary in the radial direction. This study also aims to obtain the analytical solution of the strain gradient model presented by Lam for torsional vibration response, in a simple manner, for different rigid or restrained boundary conditions. The torsion angle of a functionally graded nanotube is defined by an infinite Fourier series. Then, the Stokes’ transformation is applied to force the boundary conditions to the desired state. An eigenvalue problem is established with the help of the two systems of equations obtained. This eigenvalue problem, which includes deformable springs at both ends of the nanotube, appears as a general analytical solution that can find torsional vibration frequencies. It is shown that the vibrational responses can be significantly influenced by the through‐radius gradings of material, material length scale parameters and deformable springs of the functionally graded nanotubes and consequently can be predicted by giving proper values to torsional spring parameters.","PeriodicalId":501230,"journal":{"name":"ZAMM - Journal of Applied Mathematics and Mechanics","volume":"169 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140835173","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Mohammed Alaoui, EL‐Hassan Essoufi, Abdelhafid Ouaanabi, Mustapha Bouallala
In this work, we study, from a variational point of view, a dynamic contact problem between a thermo‐piezoelectric body and a thermally conductive foundation. The normal compliance contact condition and Coulomb's friction law are employed to model the contact. We provide existence and uniqueness results of a weak solution to the model using adequate auxiliary problems, an abstract result on nonlinear first‐order evolution inequalities and Banach fixed point argument. Finally, the continuous dependence of the solution on the surface traction force and the surface electrical charge is studied.
{"title":"On the dynamic Coulomb's frictional contact problem for thermo‐piezoelectric materials","authors":"Mohammed Alaoui, EL‐Hassan Essoufi, Abdelhafid Ouaanabi, Mustapha Bouallala","doi":"10.1002/zamm.202300891","DOIUrl":"https://doi.org/10.1002/zamm.202300891","url":null,"abstract":"In this work, we study, from a variational point of view, a dynamic contact problem between a thermo‐piezoelectric body and a thermally conductive foundation. The normal compliance contact condition and Coulomb's friction law are employed to model the contact. We provide existence and uniqueness results of a weak solution to the model using adequate auxiliary problems, an abstract result on nonlinear first‐order evolution inequalities and Banach fixed point argument. Finally, the continuous dependence of the solution on the surface traction force and the surface electrical charge is studied.","PeriodicalId":501230,"journal":{"name":"ZAMM - Journal of Applied Mathematics and Mechanics","volume":"151 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140835249","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We construct mathematical hierarchical models in Eulerian coordinates for an ideal and a Newtonian viscous fluid flow in the prismatic shell‐like domains. The peculiarities of well‐posedness of boundary conditions for angular domains are discussed.
{"title":"Construction and investigation of differential hierarchical models for the Newtonian fluids","authors":"George Jaiani","doi":"10.1002/zamm.202300251","DOIUrl":"https://doi.org/10.1002/zamm.202300251","url":null,"abstract":"We construct mathematical hierarchical models in Eulerian coordinates for an ideal and a Newtonian viscous fluid flow in the prismatic shell‐like domains. The peculiarities of well‐posedness of boundary conditions for angular domains are discussed.","PeriodicalId":501230,"journal":{"name":"ZAMM - Journal of Applied Mathematics and Mechanics","volume":"60 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140835396","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We consider a rate‐independent system with nonconvex energy under discontinuous external loading. The underlying space is finite‐dimensional and the loads are functions in . We investigate the stability of various solution concepts w.r.t. a sequence of loads converging weakly* in with a particular emphasis on the so‐called normalized, ‐parametrized balanced viscosity solutions. By means of three counterexamples, it is shown that common solution concepts are not stable w.r.t. weak* and even intermediate (or strict) convergence of loads in the sense that a limit of a sequence of solutions associated with these loads need not be a solution corresponding to the load in the limit. We moreover introduce a new solution concept, which is stable in this sense, but our examples show that this concept necessarily allows “solutions” that are physically meaningless.
{"title":"On a lack of stability of parametrized BV solutions to rate‐independent systems with nonconvex energies and discontinuous loads","authors":"Merlin Andreia, Christian Meyer","doi":"10.1002/zamm.202300654","DOIUrl":"https://doi.org/10.1002/zamm.202300654","url":null,"abstract":"We consider a rate‐independent system with nonconvex energy under discontinuous external loading. The underlying space is finite‐dimensional and the loads are functions in . We investigate the stability of various solution concepts w.r.t. a sequence of loads converging weakly* in with a particular emphasis on the so‐called normalized, ‐parametrized balanced viscosity solutions. By means of three counterexamples, it is shown that common solution concepts are not stable w.r.t. weak* and even intermediate (or strict) convergence of loads in the sense that a limit of a sequence of solutions associated with these loads need not be a solution corresponding to the load in the limit. We moreover introduce a new solution concept, which is stable in this sense, but our examples show that this concept necessarily allows “solutions” that are physically meaningless.","PeriodicalId":501230,"journal":{"name":"ZAMM - Journal of Applied Mathematics and Mechanics","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140797969","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we design a decoupled, linear, unconditionally stable and fully discrete numerical scheme for a ferrohydrodynamics system with second‐order temporal accuracy. This scheme is based on a second‐order backward difference formula for time derivative terms and linearization extrapolation for nonlinear terms, which produces a series of decoupled linear equations and solves effectively this nonlinear and multiphysical coupled system. Meanwhile, we show that the scheme is unconditionally stable. Finally, some numerical experiments are provided to verify the theoretical finding and illustrate the accuracy and efficiency of the proposed scheme.
{"title":"Numerical simulation of the ferrohydrodynamics flow using an unconditionally stable second‐order scheme","authors":"Aytura Keram, Pengzhan Huang","doi":"10.1002/zamm.202400025","DOIUrl":"https://doi.org/10.1002/zamm.202400025","url":null,"abstract":"In this paper, we design a decoupled, linear, unconditionally stable and fully discrete numerical scheme for a ferrohydrodynamics system with second‐order temporal accuracy. This scheme is based on a second‐order backward difference formula for time derivative terms and linearization extrapolation for nonlinear terms, which produces a series of decoupled linear equations and solves effectively this nonlinear and multiphysical coupled system. Meanwhile, we show that the scheme is unconditionally stable. Finally, some numerical experiments are provided to verify the theoretical finding and illustrate the accuracy and efficiency of the proposed scheme.","PeriodicalId":501230,"journal":{"name":"ZAMM - Journal of Applied Mathematics and Mechanics","volume":"33 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140627392","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Anderson J. A. Ramos, Anderson L. A. Araujo, Mirelson M. Freitas, Manoel J. Dos Santos, Alberto S. Noé
In this paper, we study a porous thermoelastic system with microtemperature and strong time delay acting on the volume fraction equation. The thermal effect of microtemperature is based on the Lord–Shulman theory (J Mech Phys Solids. 15(5) (1967), 299–309.), while the strong delay is motivated by Makheloufi's et al. recent work (Math Meth Appl Sci. 44 (2021), 6301–6317.). To prove the well‐posedness of the system, lack of exponential stability and the polynomial decay with optimal rate, we use the semigroup theory of linear operators.
{"title":"Polynomial stability for Lord–Shulman porous elasticity with microtemperature and strong time delay","authors":"Anderson J. A. Ramos, Anderson L. A. Araujo, Mirelson M. Freitas, Manoel J. Dos Santos, Alberto S. Noé","doi":"10.1002/zamm.202300323","DOIUrl":"https://doi.org/10.1002/zamm.202300323","url":null,"abstract":"In this paper, we study a porous thermoelastic system with microtemperature and strong time delay acting on the volume fraction equation. The thermal effect of microtemperature is based on the Lord–Shulman theory (J Mech Phys Solids. 15(5) (1967), 299–309.), while the strong delay is motivated by Makheloufi's et al. recent work (Math Meth Appl Sci. 44 (2021), 6301–6317.). To prove the well‐posedness of the system, lack of exponential stability and the polynomial decay with optimal rate, we use the semigroup theory of linear operators.","PeriodicalId":501230,"journal":{"name":"ZAMM - Journal of Applied Mathematics and Mechanics","volume":"113 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140630702","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Ali Rehman, Ma Chau Khun, Mustafa Inc, Lakhdar Ragoub, Shahram Rezapour, Taseer Muhammad
In this study, we will look at the analytical characterization of water and motor oil‐based nanofluid flow and the effects of viscous dissipation and variable viscosity on stretching surfaces. The primary goal of this research is to improve heat transfer efficiency in a range of systems, including cooling applications, refrigeration systems, and heat exchangers. The addition of nanoparticles to the base fluid increases its thermal conductivity, which boosts heat transfer rates. The flow system considers the impact of viscous dissipation. In addition, this methodology accounts for temperature and velocity slips during stretching. We utilized the proper transformations to convert a set of PDEs to NLODEs. To solve this system of equations, we use hybrid nanofluid. The impact of different parameters obtained from temperature and velocity equations involving the porosity parameter, power law number, ratio velocity, dynamic viscosity, Forchheimer parameter, and Eckert number input factors are shown in the form of graphs.
{"title":"Analytical analysis of water and engine oil base nanofluid flow with the influence of viscous dissipation and variable viscosity on stretching surface","authors":"Ali Rehman, Ma Chau Khun, Mustafa Inc, Lakhdar Ragoub, Shahram Rezapour, Taseer Muhammad","doi":"10.1002/zamm.202300773","DOIUrl":"https://doi.org/10.1002/zamm.202300773","url":null,"abstract":"In this study, we will look at the analytical characterization of water and motor oil‐based nanofluid flow and the effects of viscous dissipation and variable viscosity on stretching surfaces. The primary goal of this research is to improve heat transfer efficiency in a range of systems, including cooling applications, refrigeration systems, and heat exchangers. The addition of nanoparticles to the base fluid increases its thermal conductivity, which boosts heat transfer rates. The flow system considers the impact of viscous dissipation. In addition, this methodology accounts for temperature and velocity slips during stretching. We utilized the proper transformations to convert a set of PDEs to NLODEs. To solve this system of equations, we use hybrid nanofluid. The impact of different parameters obtained from temperature and velocity equations involving the porosity parameter, power law number, ratio velocity, dynamic viscosity, Forchheimer parameter, and Eckert number input factors are shown in the form of graphs.","PeriodicalId":501230,"journal":{"name":"ZAMM - Journal of Applied Mathematics and Mechanics","volume":"55 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140602321","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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