An inverse problem is solved for identifying unknown force loadings on the inner surface of a finite‐length hollow cylinder using the variational method of homogeneous solutions. The problem is considered within the axisymmetric formulation, and the radial and axial displacements of the outer surface of the cylinder are used as the auxiliary data for solving the inverse problem. The accessible surfaces of the cylinder (the end‐faces and the outer surface) are assumed to be free of force loading. By making use of the variational method of homogeneous solutions, the problem is reduced to an infinite system of linear algebraic equations. The solution is verified numerically and its stability with respect to small errors in the input data is analyzed.
{"title":"Identification of force loadings on the inner circumference of a finite‐length elastic cylinder","authors":"L. Postolaki, Y. Tokovyy","doi":"10.1002/zamm.202300435","DOIUrl":"https://doi.org/10.1002/zamm.202300435","url":null,"abstract":"An inverse problem is solved for identifying unknown force loadings on the inner surface of a finite‐length hollow cylinder using the variational method of homogeneous solutions. The problem is considered within the axisymmetric formulation, and the radial and axial displacements of the outer surface of the cylinder are used as the auxiliary data for solving the inverse problem. The accessible surfaces of the cylinder (the end‐faces and the outer surface) are assumed to be free of force loading. By making use of the variational method of homogeneous solutions, the problem is reduced to an infinite system of linear algebraic equations. The solution is verified numerically and its stability with respect to small errors in the input data is analyzed.","PeriodicalId":23924,"journal":{"name":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","volume":null,"pages":null},"PeriodicalIF":2.3,"publicationDate":"2023-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82073113","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}
Sanjalee Maheshwari, Y. D. Sharma, Om Prakash Yadav
Targeted drug delivery is one of the most promising aspects of cancer diagnosis and treatment. Gold nanoparticles are widely used for drug delivery and in the treatment of tumors, but due to the low absorption of infrared light, tumor cells get destroyed. However, iron‐oxide‐coated gold nanoparticles could be used for drug delivery to a targeted spot with the help of an external magnetic field. The present article aims to investigate the thermal instability of the blood flow transporting gold and iron‐oxide nanoparticles through the artery. The Casson fluid model is used to characterize the blood flow, and Maxwell equations, together with Navier–Stokes equations, are used to describe the flow behavior. Further, the linear stability theory and normal mode analysis are used to obtain the secular equation of the thermal Rayleigh number. The influence of pertinent flow governing parameters such as heat source parameter, Chandrashekhar number, the diameter of nanoparticles, and volume fraction of nanoparticles are discussed graphically on the convective instability of the system. The addition of gold nanoparticles makes the system unstable due to their large size and heat generation within the system. On the other hand, the magnetic field stabilizes the system by controlling the trajectory of the nanoparticles injected into the blood vessels.
{"title":"Convective instability of blood‐based Au‐Fe3O4 hybrid nanoliquid under the presence of magnetic field with internal heat source: Application to cancer treatment","authors":"Sanjalee Maheshwari, Y. D. Sharma, Om Prakash Yadav","doi":"10.1002/zamm.202200518","DOIUrl":"https://doi.org/10.1002/zamm.202200518","url":null,"abstract":"Targeted drug delivery is one of the most promising aspects of cancer diagnosis and treatment. Gold nanoparticles are widely used for drug delivery and in the treatment of tumors, but due to the low absorption of infrared light, tumor cells get destroyed. However, iron‐oxide‐coated gold nanoparticles could be used for drug delivery to a targeted spot with the help of an external magnetic field. The present article aims to investigate the thermal instability of the blood flow transporting gold and iron‐oxide nanoparticles through the artery. The Casson fluid model is used to characterize the blood flow, and Maxwell equations, together with Navier–Stokes equations, are used to describe the flow behavior. Further, the linear stability theory and normal mode analysis are used to obtain the secular equation of the thermal Rayleigh number. The influence of pertinent flow governing parameters such as heat source parameter, Chandrashekhar number, the diameter of nanoparticles, and volume fraction of nanoparticles are discussed graphically on the convective instability of the system. The addition of gold nanoparticles makes the system unstable due to their large size and heat generation within the system. On the other hand, the magnetic field stabilizes the system by controlling the trajectory of the nanoparticles injected into the blood vessels.","PeriodicalId":23924,"journal":{"name":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","volume":null,"pages":null},"PeriodicalIF":2.3,"publicationDate":"2023-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85137697","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}
This proposed work aims to describe nonsimilar forced convection analysis for the flow of Maxwell nanofluids. The forced flow is commenced due to the stretching surface (SS) at an exponential rate. Heat and mass transmission is tackled with convective and zero mass flux at the surface. The fundamental laws of conservation governing the present flow problem are expressed mathematically in the form of a nonlinear partial differential system. The differential system is then remodeled into a system of nonlinear dimensionless partial differential equations (PDEs) under the implementation of suitable nonsimilar transformations. The resulting nonsimilar system is analytically approximated by applying local nonsimilarity (LNS) and then using the finite‐difference based bvp4c algorithm, it is numerically simulated to ascertain the influences of the various parameters—including the; Deborah number, Biot number, Schmidt number, Brownian diffusion parameter, Prandtl number, and thermophoresis diffusion parameters, on velocity and temperature. The reduced Nusselt numbers and the conduct of velocity and thermal distribution for varying parameters are illustrated graphically. The reduction of the boundary layer (BL) thickness is measured because‐of the Biot number while an increase is observed with an elevation in Deborah number. The velocity configuration is reduced with expanding Deborah number. It is remarked that as the values of the thermophoresis and Brownian motion parameter rise, the thermal BL thickness expands, and at the surface, the temperature gradient demises. An excellent comparison is noticed between present works with the already published article. The novelty of this article is that most of realworld BL flow problems are nonsimilar in nature, while many research have neglected this fact and treated the problem as similar. Therefore, we talked about the Maxwell problem's nonsimilar analysis here. The author's observations indicate that the analysis of the topic under discussion has not yet been declared in published literature.
{"title":"Nonsimilar forced convection analysis of maxwell nanofluid flow over an exponentially stretching sheet with convective boundary conditions","authors":"Raheela Razzaq, Umer Farooq, Hasan Raza Mirza","doi":"10.1002/zamm.202200623","DOIUrl":"https://doi.org/10.1002/zamm.202200623","url":null,"abstract":"This proposed work aims to describe nonsimilar forced convection analysis for the flow of Maxwell nanofluids. The forced flow is commenced due to the stretching surface (SS) at an exponential rate. Heat and mass transmission is tackled with convective and zero mass flux at the surface. The fundamental laws of conservation governing the present flow problem are expressed mathematically in the form of a nonlinear partial differential system. The differential system is then remodeled into a system of nonlinear dimensionless partial differential equations (PDEs) under the implementation of suitable nonsimilar transformations. The resulting nonsimilar system is analytically approximated by applying local nonsimilarity (LNS) and then using the finite‐difference based bvp4c algorithm, it is numerically simulated to ascertain the influences of the various parameters—including the; Deborah number, Biot number, Schmidt number, Brownian diffusion parameter, Prandtl number, and thermophoresis diffusion parameters, on velocity and temperature. The reduced Nusselt numbers and the conduct of velocity and thermal distribution for varying parameters are illustrated graphically. The reduction of the boundary layer (BL) thickness is measured because‐of the Biot number while an increase is observed with an elevation in Deborah number. The velocity configuration is reduced with expanding Deborah number. It is remarked that as the values of the thermophoresis and Brownian motion parameter rise, the thermal BL thickness expands, and at the surface, the temperature gradient demises. An excellent comparison is noticed between present works with the already published article. The novelty of this article is that most of realworld BL flow problems are nonsimilar in nature, while many research have neglected this fact and treated the problem as similar. Therefore, we talked about the Maxwell problem's nonsimilar analysis here. The author's observations indicate that the analysis of the topic under discussion has not yet been declared in published literature.","PeriodicalId":23924,"journal":{"name":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","volume":null,"pages":null},"PeriodicalIF":2.3,"publicationDate":"2023-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86201506","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 used linear stability theory based on the normal mode decomposition technique and nonlinear stability theory based on the minimum representation of double Fourier series to study the criterion of appearance of the stationary convection and the oscillatory convection; and the rate of heat and mass transfer in a binary viscoelastic fluid mixture in a rotating porous medium under the effect of helical force. We have determined the analytical expression of the Rayleigh number of the system as a function of the dimensionless parameters. Expressions for heat and mass transfer rates are determined as a function of Nusselt and Sherwood number, respectively. The transient behaviors of the Nusselt number and the Sherwood number are studied by solving the finite amplitude equations using the Runge‐Kutta method. Then, the effect of each dimensionless parameter on the system is studied pointed out interesting results. According to the analysis of the different results obtained, it appears that in a porous medium saturated by a binary mixture of viscoelastic fluid in rotation, the Taylor‐Darcy number TaD$Ta_D$ , the delay time parameter λ2 and the mass Rayleigh‐Darcy number RaCD$Ra_{CD}$ delay the onset of stationary and oscillatory convection. On the other hand, the helical force SD$S_{D}$ , the relaxation time parameter λ1, the ratio of diffusivities τ and the number of Vadasz Va$Va$ accelerate the onset of stationary and oscillatory convection. In the case of the nonlinear stability study, at steady state, the helical force SD$S_{D}$ accelerates the rate of heat and mass transfer. On the other hand, the Taylor‐Darcy number TaD$Ta_D$ , the diffusivity ratio τ and the mass Rayleigh‐Darcy number RaCD$Ra_{CD}$ retard the rate of heat and mass transfer. In the unsteady state, the helical force SD$S_{D}$ , the relaxation time parameter λ1 and the mass Rayleigh‐Darcy number RaCD$Ra_{CD}$ accelerate the rate of heat and mass transfer. This is not the case for the Taylor‐Darcy number TaD$Ta_D$ and the delay time parameter λ2.
{"title":"Combined effect of helical force and rotation on the double convection of a binary viscoelastic fluid in a porous medium: Linear and weakly nonlinear analysis","authors":"M. Kpossa, V. Monwanou","doi":"10.1002/zamm.202200363","DOIUrl":"https://doi.org/10.1002/zamm.202200363","url":null,"abstract":"We used linear stability theory based on the normal mode decomposition technique and nonlinear stability theory based on the minimum representation of double Fourier series to study the criterion of appearance of the stationary convection and the oscillatory convection; and the rate of heat and mass transfer in a binary viscoelastic fluid mixture in a rotating porous medium under the effect of helical force. We have determined the analytical expression of the Rayleigh number of the system as a function of the dimensionless parameters. Expressions for heat and mass transfer rates are determined as a function of Nusselt and Sherwood number, respectively. The transient behaviors of the Nusselt number and the Sherwood number are studied by solving the finite amplitude equations using the Runge‐Kutta method. Then, the effect of each dimensionless parameter on the system is studied pointed out interesting results. According to the analysis of the different results obtained, it appears that in a porous medium saturated by a binary mixture of viscoelastic fluid in rotation, the Taylor‐Darcy number TaD$Ta_D$ , the delay time parameter λ2 and the mass Rayleigh‐Darcy number RaCD$Ra_{CD}$ delay the onset of stationary and oscillatory convection. On the other hand, the helical force SD$S_{D}$ , the relaxation time parameter λ1, the ratio of diffusivities τ and the number of Vadasz Va$Va$ accelerate the onset of stationary and oscillatory convection. In the case of the nonlinear stability study, at steady state, the helical force SD$S_{D}$ accelerates the rate of heat and mass transfer. On the other hand, the Taylor‐Darcy number TaD$Ta_D$ , the diffusivity ratio τ and the mass Rayleigh‐Darcy number RaCD$Ra_{CD}$ retard the rate of heat and mass transfer. In the unsteady state, the helical force SD$S_{D}$ , the relaxation time parameter λ1 and the mass Rayleigh‐Darcy number RaCD$Ra_{CD}$ accelerate the rate of heat and mass transfer. This is not the case for the Taylor‐Darcy number TaD$Ta_D$ and the delay time parameter λ2.","PeriodicalId":23924,"journal":{"name":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","volume":null,"pages":null},"PeriodicalIF":2.3,"publicationDate":"2023-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81024822","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}
M. de Miranda, Marta de Miranda, A. Falocchi, A. Ferrero, Luca Marinini
Starting from an applied problem related to the modeling of an element of a cable‐stayed bridge, we compute the elasticity solution for a hollow circular cylinder under axial end loads. We prove results of symmetry for the solution and we expand it in proper Fourier series; computing the Fourier coefficients in adapted power series, we provide the explicit solution. We consider an engineering case of study, applying the corresponding approximate formula and giving some estimates on the error committed with respect to the truncation of the series.
{"title":"Elasticity solution for a hollow cylinder under axial end loads: Application to a blister of a stayed bridge","authors":"M. de Miranda, Marta de Miranda, A. Falocchi, A. Ferrero, Luca Marinini","doi":"10.1002/zamm.202300169","DOIUrl":"https://doi.org/10.1002/zamm.202300169","url":null,"abstract":"Starting from an applied problem related to the modeling of an element of a cable‐stayed bridge, we compute the elasticity solution for a hollow circular cylinder under axial end loads. We prove results of symmetry for the solution and we expand it in proper Fourier series; computing the Fourier coefficients in adapted power series, we provide the explicit solution. We consider an engineering case of study, applying the corresponding approximate formula and giving some estimates on the error committed with respect to the truncation of the series.","PeriodicalId":23924,"journal":{"name":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","volume":null,"pages":null},"PeriodicalIF":2.3,"publicationDate":"2023-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87568860","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}
Thirupathi Thumma, Subhajit Panda, S. Mishra, Surender Ontela
This study analyses the effect of Brownian motion and thermophoresis on the flow of nanofluid along an impermeable curved surface. The Darcy‐Forchheimer drag vis‐à‐vis the radiating heat and the heat source enriches the flow phenomena. This drag force has several applications such as in (i) biomedical engineering for the flow of blood through curved arteries and veins, (ii) civil engineering for the flow of water through porous materials such as soil or rock, etc. The convective heat and solutal transport properties embedded in boundary conditions develop the heat transport phenomena. The dimensional governing equations are transformed into non‐dimensional form by using suitable substitution of transformed variables and stream function. Further, numerical practice is adopted to handle the set of nonlinear differential equations. The simulation of the optimized heat and solutal transfer rate for various factors is carried out using the ‘central composite design’ (CCD) associated with the ‘response surface methodology’ (RSM). The regression analysis and residual error are computed through the statistical approach of analysis of variance and finally, the sensitivity analysis is proposed for the various factors. However, the enhanced properties and flow behaviour for the diversified values of the physical parameters are presented and described briefly via the corroboration of the present methodology with the published work in particular cases. The notable outcomes are the axial velocity profile enriches for the increasing curvature constraints and the regression analysis is presented for the optimizing heat transfer rate using response surface methodology.
{"title":"Mathematical modelling of heat and solutal rate with cross‐diffusion effect on the flow of nanofluid past a curved surface under the impact of thermal radiation and heat source: Sensitivity analysis","authors":"Thirupathi Thumma, Subhajit Panda, S. Mishra, Surender Ontela","doi":"10.1002/zamm.202300077","DOIUrl":"https://doi.org/10.1002/zamm.202300077","url":null,"abstract":"This study analyses the effect of Brownian motion and thermophoresis on the flow of nanofluid along an impermeable curved surface. The Darcy‐Forchheimer drag vis‐à‐vis the radiating heat and the heat source enriches the flow phenomena. This drag force has several applications such as in (i) biomedical engineering for the flow of blood through curved arteries and veins, (ii) civil engineering for the flow of water through porous materials such as soil or rock, etc. The convective heat and solutal transport properties embedded in boundary conditions develop the heat transport phenomena. The dimensional governing equations are transformed into non‐dimensional form by using suitable substitution of transformed variables and stream function. Further, numerical practice is adopted to handle the set of nonlinear differential equations. The simulation of the optimized heat and solutal transfer rate for various factors is carried out using the ‘central composite design’ (CCD) associated with the ‘response surface methodology’ (RSM). The regression analysis and residual error are computed through the statistical approach of analysis of variance and finally, the sensitivity analysis is proposed for the various factors. However, the enhanced properties and flow behaviour for the diversified values of the physical parameters are presented and described briefly via the corroboration of the present methodology with the published work in particular cases. The notable outcomes are the axial velocity profile enriches for the increasing curvature constraints and the regression analysis is presented for the optimizing heat transfer rate using response surface methodology.","PeriodicalId":23924,"journal":{"name":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","volume":null,"pages":null},"PeriodicalIF":2.3,"publicationDate":"2023-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76891261","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 work, we present the impacts of melting heat transfer phenomena on the steady, laminar, incompressible, two‐dimensional magnetohydrodynamic (MHD) Carreau nanofluid flow towards the stretching sheet. Additionally, in energy equation thermal radiation and variable thermal conductivity effects are also taken into consideration. By using similarity variables, governing non‐linear partial differential equations (PDEs) of the Carreau nanofluid flow model are transformed into dimensionless non‐linear ordinary differential equations (ODEs). Numerical solutions are then investigated and the results are illustrated through graphs and tables showing parameters effect on velocity, temperature, and concentration profiles of the fluid and on physical quantities including skin friction coefficient, Nusselt and Sherwood numbers, respectively. From the analysis, it is found that boosting melting heat transfer parameter leads to increasing behavior in velocity and concentration distributions, while the opposite trend is noticed for temperature distribution. Numerical results are found in close agreement and are accurate by carrying out its comparison with previous results for skin friction coefficient with different magnetic parameters while keeping other parameter values constant.
{"title":"Analysis of radiative MHD Carreau nanofluid flow with melting heat transfer and variable thermal conductivity","authors":"Zawar Khan, S. Zeb, Muhammad Yousaf","doi":"10.1002/zamm.202300017","DOIUrl":"https://doi.org/10.1002/zamm.202300017","url":null,"abstract":"In this work, we present the impacts of melting heat transfer phenomena on the steady, laminar, incompressible, two‐dimensional magnetohydrodynamic (MHD) Carreau nanofluid flow towards the stretching sheet. Additionally, in energy equation thermal radiation and variable thermal conductivity effects are also taken into consideration. By using similarity variables, governing non‐linear partial differential equations (PDEs) of the Carreau nanofluid flow model are transformed into dimensionless non‐linear ordinary differential equations (ODEs). Numerical solutions are then investigated and the results are illustrated through graphs and tables showing parameters effect on velocity, temperature, and concentration profiles of the fluid and on physical quantities including skin friction coefficient, Nusselt and Sherwood numbers, respectively. From the analysis, it is found that boosting melting heat transfer parameter leads to increasing behavior in velocity and concentration distributions, while the opposite trend is noticed for temperature distribution. Numerical results are found in close agreement and are accurate by carrying out its comparison with previous results for skin friction coefficient with different magnetic parameters while keeping other parameter values constant.","PeriodicalId":23924,"journal":{"name":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","volume":null,"pages":null},"PeriodicalIF":2.3,"publicationDate":"2023-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88339830","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 thermophysical properties of Ag−MOS2$Ag - MO{S_2}$ nanoparticles with water‐ethylene glycol mixture and its impact in augmenting of heat transport is presented. Boundary layer flow over a stretching surface with simultaneous effects of viscous dissipation, radiation, electric and magnetic field are taken into account. Self‐similarity transformation is utilized to modify the flow governing equations into system of differential equations and solved by shooting method. Program code is validated with existing results in literature and results shows good agreement. Influence of various physical parameters are visualized and Nusselt number, skin friction quantities are computed. We have observed that application of electric field increases Nusselt number. Eckert number decreases the Nusselt number for both nanofluid and hybrid nanofluid.
{"title":"Enhancing heat transfer with 50%–50% water‐ethylene glycol hybrid nanofluid flow over a nonlinear stretching sheet","authors":"C. Sulochana, Tiruamala Prasanna Kumar","doi":"10.1002/zamm.202200225","DOIUrl":"https://doi.org/10.1002/zamm.202200225","url":null,"abstract":"In this article thermophysical properties of Ag−MOS2$Ag - MO{S_2}$ nanoparticles with water‐ethylene glycol mixture and its impact in augmenting of heat transport is presented. Boundary layer flow over a stretching surface with simultaneous effects of viscous dissipation, radiation, electric and magnetic field are taken into account. Self‐similarity transformation is utilized to modify the flow governing equations into system of differential equations and solved by shooting method. Program code is validated with existing results in literature and results shows good agreement. Influence of various physical parameters are visualized and Nusselt number, skin friction quantities are computed. We have observed that application of electric field increases Nusselt number. Eckert number decreases the Nusselt number for both nanofluid and hybrid nanofluid.","PeriodicalId":23924,"journal":{"name":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","volume":null,"pages":null},"PeriodicalIF":2.3,"publicationDate":"2023-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84183134","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 problems of steady‐state and free oscillations of functionally graded hollow cylinders are considered in the present article, with the cylinders' properties considered changing along the radial or longitudinal coordinates. The stress–strain state was described using the model of an isotropic body with the variable Lamé parameters and density. The cylinders were assumed to be subjected to the normal and tangential loads. In order to obtain the numerical problem solutions, the finite element method was employed. The effect of variable properties on the amplitude–frequency characteristics and the resonant frequencies values for various cylinders types is estimated. Some features, which can be used in solving new inverse coefficient problems on material properties identification based on acoustic sounding data, are revealed.
{"title":"Functionally graded cylinders: Vibration analysis","authors":"A. Vatulyan, V. Dudarev, R. Mnukhin","doi":"10.1002/zamm.202200430","DOIUrl":"https://doi.org/10.1002/zamm.202200430","url":null,"abstract":"The problems of steady‐state and free oscillations of functionally graded hollow cylinders are considered in the present article, with the cylinders' properties considered changing along the radial or longitudinal coordinates. The stress–strain state was described using the model of an isotropic body with the variable Lamé parameters and density. The cylinders were assumed to be subjected to the normal and tangential loads. In order to obtain the numerical problem solutions, the finite element method was employed. The effect of variable properties on the amplitude–frequency characteristics and the resonant frequencies values for various cylinders types is estimated. Some features, which can be used in solving new inverse coefficient problems on material properties identification based on acoustic sounding data, are revealed.","PeriodicalId":23924,"journal":{"name":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","volume":null,"pages":null},"PeriodicalIF":2.3,"publicationDate":"2023-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75450753","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 current study focuses on the magnetohydrodynamic flow of fluids through two vertical, insulated walls. The influences of Newtonian heating/cooling, induced magnetic field (IMF), the Soret effect, radiative heat flux, and first‐order chemical reaction are considered. By solving the set of non‐dimensional linked governing equations, we were able to determine the expressions for the velocity, temperature, concentration, and IMF. The equations for Nusselt number, induced current density, and skin friction were also obtained. The graph displays the effects of several parameters on velocity, temperature, concentration, IMF, and induced current density (ICD). Additionally, a tabular analysis is done to see how these non‐dimensional parameters affect Nusselt number and skin frictions. It is seen that the Grashof number and Soret number improve the fluid velocity and skin friction whereas the chemical reaction parameter and Schmidt number reduces skin friction.
{"title":"A study of magnetohydrodynamic flow on a channel with induced magnetic field, Soret effect and heat radiation","authors":"U. Das, Nayan Mani Majumdar","doi":"10.1002/zamm.202200624","DOIUrl":"https://doi.org/10.1002/zamm.202200624","url":null,"abstract":"The current study focuses on the magnetohydrodynamic flow of fluids through two vertical, insulated walls. The influences of Newtonian heating/cooling, induced magnetic field (IMF), the Soret effect, radiative heat flux, and first‐order chemical reaction are considered. By solving the set of non‐dimensional linked governing equations, we were able to determine the expressions for the velocity, temperature, concentration, and IMF. The equations for Nusselt number, induced current density, and skin friction were also obtained. The graph displays the effects of several parameters on velocity, temperature, concentration, IMF, and induced current density (ICD). Additionally, a tabular analysis is done to see how these non‐dimensional parameters affect Nusselt number and skin frictions. It is seen that the Grashof number and Soret number improve the fluid velocity and skin friction whereas the chemical reaction parameter and Schmidt number reduces skin friction.","PeriodicalId":23924,"journal":{"name":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","volume":null,"pages":null},"PeriodicalIF":2.3,"publicationDate":"2023-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73790130","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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