Present article highlights the significance of Arrhenius activation energy along with viscous dissipation in Jeffrey fluid over a Riga plate. Riga plate is basically an actuator made up of array of magnets and electrodes scaled on a plane surface to tackle the weaker electrical conductivity during fluid flow. In order to ensure the novelty, a reliable melting heat surface condition has been incorporated on nonlinear stretching Riga plate of variable thickness to reconnoiter features of heat transfer. Moreover, stagnation point has been retained in this study. Adequate transformations are employed in order to attain system of nonlinear ordinary differential equations. A well known semi analytical technique (Homotopy analysis method) is utilized to obtain series solutions of prevailing dimensionless equations. Influence of several apposite parameters on velocity, thermal and concentration distributions is analyzed graphically. Physical evaluation and graphical sketch is presented for drag force coefficient and rate of heat transfer. Analysis of velocity as well as associated boundary layer thickness gives the growing up impact for the strength of modified Hartmann number. Enhancement of dimensionless reaction rate and endothermic/exothermic reaction parameter results in increment for heat flux over stretching Riga plate. Increase in thermal distribution takes place for higher Eckert number while thermal boundary layer thickness depicts opposite trend in this case. Concentration boundary layer thickness enhances while concentration profile declines for higher Schmidt number. Velocity distribution is found to be incremented for intense melting process. Higher dimensionless activation energy parameter is analyzed to be responsible for growing up concentration field.
{"title":"Insight of Jeffrey flow over a stretching Riga plate with activation energy and viscous dissipation: Melting heat transfer regime","authors":"Mubashar Javed","doi":"10.1002/zamm.202300611","DOIUrl":"https://doi.org/10.1002/zamm.202300611","url":null,"abstract":"Present article highlights the significance of Arrhenius activation energy along with viscous dissipation in Jeffrey fluid over a Riga plate. Riga plate is basically an actuator made up of array of magnets and electrodes scaled on a plane surface to tackle the weaker electrical conductivity during fluid flow. In order to ensure the novelty, a reliable melting heat surface condition has been incorporated on nonlinear stretching Riga plate of variable thickness to reconnoiter features of heat transfer. Moreover, stagnation point has been retained in this study. Adequate transformations are employed in order to attain system of nonlinear ordinary differential equations. A well known semi analytical technique (Homotopy analysis method) is utilized to obtain series solutions of prevailing dimensionless equations. Influence of several apposite parameters on velocity, thermal and concentration distributions is analyzed graphically. Physical evaluation and graphical sketch is presented for drag force coefficient and rate of heat transfer. Analysis of velocity as well as associated boundary layer thickness gives the growing up impact for the strength of modified Hartmann number. Enhancement of dimensionless reaction rate and endothermic/exothermic reaction parameter results in increment for heat flux over stretching Riga plate. Increase in thermal distribution takes place for higher Eckert number while thermal boundary layer thickness depicts opposite trend in this case. Concentration boundary layer thickness enhances while concentration profile declines for higher Schmidt number. Velocity distribution is found to be incremented for intense melting process. Higher dimensionless activation energy parameter is analyzed to be responsible for growing up concentration field.","PeriodicalId":501230,"journal":{"name":"ZAMM - Journal of Applied Mathematics and Mechanics","volume":"49 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140586505","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}
Shuguang Li, Nazia Shahmir, Muhammad Ramzan, N. Ameer Ahammad, Abdullah M. S. Alhuthali, C. Ahamed Saleel, Seifedine Kadry
The enhanced thermal characteristics of hybrid nanofluids make them more versatile compared to conventional fluids. These improved thermal properties render hybrid nanomaterials highly practical for a wide range of applications, including solar systems, energy production, and cooling processes. In line with this perspective, the current study concentrates on evaluating the thermal performance of two unique hybrid nanofluid flows that impinge obliquely on a stretched cylinder. Two base fluids, FC‐77 and a binary mixture of water and ethylene glycol (50:50)%, have been considered, with the addition of nanoparticles such as single‐walled carbon nanotubes (SWCNTs) and multiwalled carbon nanotubes (MWCNTs). The said model's novelty is enhanced by the temperature dependent viscosity and thermal conductivity. Appropriate transformations are applied to derive a system of ordinary differential equations (ODEs), which are then solved numerically using the bvp4c method. A thorough examination is conducted on the physical phenomenon of pertinent parameters, accompanied by graphical representations. The results revealed that, for the FC‐77 coolant‐based hybrid nanofluid, mounting the particle volume fraction leads to a significant reduction in temperature distribution. Additionally, it is perceived that the presence of a variable viscosity parameter causes a reduction in the surface drag coefficient as well as the axial and tangential velocities. The validity of the proposed flow model is demonstrated by comparing the results with those from an earlier study.
{"title":"Thermal inspection of hybrid nanofluid flows over a stretched cylinder at an oblique stagnation point with variable characteristics","authors":"Shuguang Li, Nazia Shahmir, Muhammad Ramzan, N. Ameer Ahammad, Abdullah M. S. Alhuthali, C. Ahamed Saleel, Seifedine Kadry","doi":"10.1002/zamm.202300837","DOIUrl":"https://doi.org/10.1002/zamm.202300837","url":null,"abstract":"The enhanced thermal characteristics of hybrid nanofluids make them more versatile compared to conventional fluids. These improved thermal properties render hybrid nanomaterials highly practical for a wide range of applications, including solar systems, energy production, and cooling processes. In line with this perspective, the current study concentrates on evaluating the thermal performance of two unique hybrid nanofluid flows that impinge obliquely on a stretched cylinder. Two base fluids, FC‐77 and a binary mixture of water and ethylene glycol (50:50)%, have been considered, with the addition of nanoparticles such as single‐walled carbon nanotubes (SWCNTs) and multiwalled carbon nanotubes (MWCNTs). The said model's novelty is enhanced by the temperature dependent viscosity and thermal conductivity. Appropriate transformations are applied to derive a system of ordinary differential equations (ODEs), which are then solved numerically using the bvp4c method. A thorough examination is conducted on the physical phenomenon of pertinent parameters, accompanied by graphical representations. The results revealed that, for the FC‐77 coolant‐based hybrid nanofluid, mounting the particle volume fraction leads to a significant reduction in temperature distribution. Additionally, it is perceived that the presence of a variable viscosity parameter causes a reduction in the surface drag coefficient as well as the axial and tangential velocities. The validity of the proposed flow model is demonstrated by comparing the results with those from an earlier study.","PeriodicalId":501230,"journal":{"name":"ZAMM - Journal of Applied Mathematics and Mechanics","volume":"96 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140586328","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}
This study sheds light on the complex dynamics of squeezing flow in Jeffrey fluids and highlights the significance of considering Cattaneo‐Christov heat flux and reactive Species. To simplify the mathematical formulation and facilitate numerical analysis, a similarity transformation is utilized to transform the governing partial differential equations into a collection of interconnected ordinary differential equations (ODEs). The transformed ODEs are subsequently resolved utilizing bvp4c technique. The application of the bvp4c technique enables accurate numerical analysis, offering valuable insights into the behavior of viscoelastic fluids under squeezing conditions with thermal effects and chemical reactions. Through numerical simulations, the temperature distribution, flow characteristics, and reaction kinetics within the Jeffrey fluid under squeezing conditions are examined.
{"title":"Role of squeezing phenomenon in the reactive dynamics of Jeffrey fluid","authors":"Shahida Rehman, Noor Muhammad","doi":"10.1002/zamm.202300749","DOIUrl":"https://doi.org/10.1002/zamm.202300749","url":null,"abstract":"This study sheds light on the complex dynamics of squeezing flow in Jeffrey fluids and highlights the significance of considering Cattaneo‐Christov heat flux and reactive Species. To simplify the mathematical formulation and facilitate numerical analysis, a similarity transformation is utilized to transform the governing partial differential equations into a collection of interconnected ordinary differential equations (ODEs). The transformed ODEs are subsequently resolved utilizing bvp4c technique. The application of the bvp4c technique enables accurate numerical analysis, offering valuable insights into the behavior of viscoelastic fluids under squeezing conditions with thermal effects and chemical reactions. Through numerical simulations, the temperature distribution, flow characteristics, and reaction kinetics within the Jeffrey fluid under squeezing conditions are examined.","PeriodicalId":501230,"journal":{"name":"ZAMM - Journal of Applied Mathematics and Mechanics","volume":"40 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140586651","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}
The current study is based on the effects of microrotational dynamics, microinertial effects, and temperature changes on electroosmotic peristalsis in a tapered microchannel. This has been addressed by an analytical study of heat transfer in the setting of electroosmotic peristaltic flow involving a micropolar fluid, specifically considering a symmetrically tapered channel. The Navier–Stokes equation, the Poisson–Boltzmann equation, the energy equation, and the micropolar fluid model are all included in the mathematical model. On the flow and temperature fields, a thorough parametric analysis is carried out, investigating the impacts of numerous variables, including the micropolar parameter, Prandtl number, Brinkman number, Grashof number, thermal conductivity ratio, and channel aspect ratio. The findings show that peristalsis and electroosmosis both contribute to higher heat transfer rates. Notably, the electroosmotic parameter and Brinkman number have a substantial impact on the distribution of temperature. The micropolar parameter and Brinkman number have a significant effect on the flow and temperature fields. Furthermore, electrokinetic phenomena are crucial in controlling the axial and spin velocities of the micropolar fluid. These findings have significant ramifications for the design and optimization of microfluidic devices in engineering and biomedical applications that employ the electroosmotic peristaltic flow of micropolar fluids.
{"title":"Exploring microrotational effects and temperature variations in electroosmotic peristalsis in tapered microchannel","authors":"Sidra Batool, Saima Noreen, Ali J. Chamkha","doi":"10.1002/zamm.202300779","DOIUrl":"https://doi.org/10.1002/zamm.202300779","url":null,"abstract":"The current study is based on the effects of microrotational dynamics, microinertial effects, and temperature changes on electroosmotic peristalsis in a tapered microchannel. This has been addressed by an analytical study of heat transfer in the setting of electroosmotic peristaltic flow involving a micropolar fluid, specifically considering a symmetrically tapered channel. The Navier–Stokes equation, the Poisson–Boltzmann equation, the energy equation, and the micropolar fluid model are all included in the mathematical model. On the flow and temperature fields, a thorough parametric analysis is carried out, investigating the impacts of numerous variables, including the micropolar parameter, Prandtl number, Brinkman number, Grashof number, thermal conductivity ratio, and channel aspect ratio. The findings show that peristalsis and electroosmosis both contribute to higher heat transfer rates. Notably, the electroosmotic parameter and Brinkman number have a substantial impact on the distribution of temperature. The micropolar parameter and Brinkman number have a significant effect on the flow and temperature fields. Furthermore, electrokinetic phenomena are crucial in controlling the axial and spin velocities of the micropolar fluid. These findings have significant ramifications for the design and optimization of microfluidic devices in engineering and biomedical applications that employ the electroosmotic peristaltic flow of micropolar fluids.","PeriodicalId":501230,"journal":{"name":"ZAMM - Journal of Applied Mathematics and Mechanics","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140586670","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}
The unsteady Poiseuille flow of Carreau‐Yasuda fluid in a pipe, caused by a variable pressure gradient, is studied theoretically. As a special case, the steady flow is considered separately. It is proved that at some values of the viscosity model parameters, the problem has a generalized solution, while at others ‐ a classical solution. For the latter, a necessary and sufficient condition is found, which depends on the maximum pressure gradient and the Carreau‐Yasuda model parameters.
{"title":"Poiseuille flow of Carreau‐Yasuda fluid at variable pressure gradient","authors":"Nilolay Kutev, Sonia Tabakova","doi":"10.1002/zamm.202300555","DOIUrl":"https://doi.org/10.1002/zamm.202300555","url":null,"abstract":"The unsteady Poiseuille flow of Carreau‐Yasuda fluid in a pipe, caused by a variable pressure gradient, is studied theoretically. As a special case, the steady flow is considered separately. It is proved that at some values of the viscosity model parameters, the problem has a generalized solution, while at others ‐ a classical solution. For the latter, a necessary and sufficient condition is found, which depends on the maximum pressure gradient and the Carreau‐Yasuda model parameters.","PeriodicalId":501230,"journal":{"name":"ZAMM - Journal of Applied Mathematics and Mechanics","volume":"9 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140586398","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}
This study highlights the significance of entropy generation in the Falkner–Skan flow of Casson fluid past a wedge. To investigate the energy analysis, the governing equations include the heat transport equation in the presence of internal heat source, and the energy transport accounts for heat dissipation using viscous dissipation and Joule heating effect. The mathematical formulation of the problem leads to a set of nonlinear coupled partial differential equations. To obtain a similarity solution, similarity variables are introduced. The resulting differential equations are solved numerically using the shooting technique in conjunction with the Runge–Kutta–Fehlberg 45 (RKF‐45) method. Graphical representations are utilized to demonstrate the physical significance of the relevant parameters. The study analyzes the impact of various parameters on the velocity, temperature, and entropy distributions for three wedge positions: stationary, forward‐moving, and backward‐moving. The results show that an increase in the wedge angle parameter and Casson parameter leads to an increase in fluid velocity, while fluid entropy increases rapidly with an increase in the Brinkmann number, power law Falkner–Skan parameter, and Reynolds number. Moreover, with an increment in the Prandtl and Eckert number, the Nusselt number coefficient decelerates for both static and moving wedge.
{"title":"Entropy generation due to MHD Falkner–Skan flow of Casson fluid over a wedge: A numerical study","authors":"Muhammad N. Abrar, Wang Yun, Mohamed Sharaf","doi":"10.1002/zamm.202300750","DOIUrl":"https://doi.org/10.1002/zamm.202300750","url":null,"abstract":"This study highlights the significance of entropy generation in the Falkner–Skan flow of Casson fluid past a wedge. To investigate the energy analysis, the governing equations include the heat transport equation in the presence of internal heat source, and the energy transport accounts for heat dissipation using viscous dissipation and Joule heating effect. The mathematical formulation of the problem leads to a set of nonlinear coupled partial differential equations. To obtain a similarity solution, similarity variables are introduced. The resulting differential equations are solved numerically using the shooting technique in conjunction with the Runge–Kutta–Fehlberg 45 (RKF‐45) method. Graphical representations are utilized to demonstrate the physical significance of the relevant parameters. The study analyzes the impact of various parameters on the velocity, temperature, and entropy distributions for three wedge positions: stationary, forward‐moving, and backward‐moving. The results show that an increase in the wedge angle parameter and Casson parameter leads to an increase in fluid velocity, while fluid entropy increases rapidly with an increase in the Brinkmann number, power law Falkner–Skan parameter, and Reynolds number. Moreover, with an increment in the Prandtl and Eckert number, the Nusselt number coefficient decelerates for both static and moving wedge.","PeriodicalId":501230,"journal":{"name":"ZAMM - Journal of Applied Mathematics and Mechanics","volume":"46 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140586498","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}
The study aims to investigate the effect of uniform inclined magnetic field on two‐dimensional flow of a steady, viscous incompressible fluid at low Reynolds number through a porous wavy channel. We consider a channel having sinusoidal walls filled with a fully saturated porous medium. The porous regime is assumed to be homogenous and isotropic. The viscous flow through a porous regime is governed by Brinkman equation, where the viscous forces are dominant. This allows us to assume the no‐slip boundary conditions at the walls of the wavy channel. Boundary element method (BEM) based on non‐primitive variables namely, stream function‐vorticity variables is used to solve the Brinkman equation. Further, we consider a very small magnetic Reynolds number to eliminate the magnetic‐induced equation. We analyzed that an increase in Hartman number, porosity, and reduction in inclination angle of magnetic field, wave amplitude, and Darcy number led to a reduction in horizontal velocity, whereas an increase in Hartman number, porosity, wave amplitude, and decrease in Darcy number and angle of inclination of magnetic field led to an increase in vertical velocity. Moreover, the flow reversal phenomena occur in the vicinity of the crest regime of the porous wavy channel for high wave amplitude and low Hartman number. The proposed investigation has widespread applications, such as drug delivery systems to target the drug precisely, magneto‐hydrodynamic pumps to regulate the blood flow in artificial hearts to reduce the risk of blood clotting, and so forth.
{"title":"Effect of magnetic field on viscous flow through porous wavy channel using boundary element method","authors":"Vishal Chhabra, Chandra Shekhar Nishad, Manoj Sahni","doi":"10.1002/zamm.202300416","DOIUrl":"https://doi.org/10.1002/zamm.202300416","url":null,"abstract":"The study aims to investigate the effect of uniform inclined magnetic field on two‐dimensional flow of a steady, viscous incompressible fluid at low Reynolds number through a porous wavy channel. We consider a channel having sinusoidal walls filled with a fully saturated porous medium. The porous regime is assumed to be homogenous and isotropic. The viscous flow through a porous regime is governed by Brinkman equation, where the viscous forces are dominant. This allows us to assume the no‐slip boundary conditions at the walls of the wavy channel. Boundary element method (BEM) based on non‐primitive variables namely, stream function‐vorticity variables is used to solve the Brinkman equation. Further, we consider a very small magnetic Reynolds number to eliminate the magnetic‐induced equation. We analyzed that an increase in Hartman number, porosity, and reduction in inclination angle of magnetic field, wave amplitude, and Darcy number led to a reduction in horizontal velocity, whereas an increase in Hartman number, porosity, wave amplitude, and decrease in Darcy number and angle of inclination of magnetic field led to an increase in vertical velocity. Moreover, the flow reversal phenomena occur in the vicinity of the crest regime of the porous wavy channel for high wave amplitude and low Hartman number. The proposed investigation has widespread applications, such as drug delivery systems to target the drug precisely, magneto‐hydrodynamic pumps to regulate the blood flow in artificial hearts to reduce the risk of blood clotting, and so forth.","PeriodicalId":501230,"journal":{"name":"ZAMM - Journal of Applied Mathematics and Mechanics","volume":"120 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140586596","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}
This article contains vital information on the internal heat generation effect on mixed convection slip flow past a vertical plate. The partial differential equations were first simplified to ordinary differential equations through similarity transformation. The simplified first‐order differential equations were integrated with Maple Software 2022 after utilizing the shooting technique. One of the most important discoveries is that the internal heat generation acts as a barrier to stop heat from flowing from the left to right plate edge. However, this could be averted by considering strong mixed convection to covet away the heat conducted through the left surface of the plate and the internal heat generated. However, for weak mixed convection, the movement of the fluid from the left to the right surface of the plate is achievable even with minimal internal heat generation. Since the right surface temperature is warmer (higher) than the left surface, the flow properties, in this case, are also affected by the internal heat generation, which also causes the reverse of heat flow from the plate. Particle injection could also be used to avert unwanted reversed flow for various momentum slip conditions considered. There is a marginal reverse flow at the plate surface, which may be related to the flow's mixed convective characteristics. Due to the plate surface's reinforcement, the rise in flow formation caused by the momentum slip parameter is more substantial close to the plate.
本文包含关于流经垂直板的混合对流滑移流的内部发热效应的重要信息。首先通过相似变换将偏微分方程简化为常微分方程。利用拍摄技术将简化后的一阶微分方程与 Maple 软件 2022 集成。最重要的发现之一是，内部发热起到了阻止热量从左侧板边缘流向右侧板边缘的作用。不过，如果考虑到强混合对流，就可以避免这种情况，因为强混合对流可以带走通过板左表面传导的热量和内部产生的热量。然而，对于弱混合对流，即使内部产生的热量极少，流体也可以从板的左表面流向右表面。由于右表面温度比左表面温度高，在这种情况下，流动特性也会受到内部发热的影响，这也会导致热量从板上反向流动。在所考虑的各种动量滑移条件下，粒子喷射也可用于避免不必要的反向流动。板表面存在边缘反向流，这可能与流动的混合对流特性有关。由于板面的强化作用，动量滑移参数引起的流动形成的上升在靠近板面的地方更为明显。
{"title":"On the implication of exponentially decaying internal heat generation on mixed convection flow from a vertical porous plate influenced by second‐order thermal and momentum slips","authors":"Basant K. Jha, Gabriel Samaila","doi":"10.1002/zamm.202300365","DOIUrl":"https://doi.org/10.1002/zamm.202300365","url":null,"abstract":"This article contains vital information on the internal heat generation effect on mixed convection slip flow past a vertical plate. The partial differential equations were first simplified to ordinary differential equations through similarity transformation. The simplified first‐order differential equations were integrated with Maple Software 2022 after utilizing the shooting technique. One of the most important discoveries is that the internal heat generation acts as a barrier to stop heat from flowing from the left to right plate edge. However, this could be averted by considering strong mixed convection to covet away the heat conducted through the left surface of the plate and the internal heat generated. However, for weak mixed convection, the movement of the fluid from the left to the right surface of the plate is achievable even with minimal internal heat generation. Since the right surface temperature is warmer (higher) than the left surface, the flow properties, in this case, are also affected by the internal heat generation, which also causes the reverse of heat flow from the plate. Particle injection could also be used to avert unwanted reversed flow for various momentum slip conditions considered. There is a marginal reverse flow at the plate surface, which may be related to the flow's mixed convective characteristics. Due to the plate surface's reinforcement, the rise in flow formation caused by the momentum slip parameter is more substantial close to the plate.","PeriodicalId":501230,"journal":{"name":"ZAMM - Journal of Applied Mathematics and Mechanics","volume":"9 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140586503","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, the anti‐plane stress analysis of a V‐notch with complex boundary conditions in a piezomagnetic half space is studied. Firstly, SH wave is considered as an external load acting on piezomagnetic half space, on the basis of repeated image superposition, the analytical expression of scattering wave is conducted, which satisfies the boundary conditions on the boundary of the half space. Then, the analytical expression of standing wave is established, which satisfies the stress free and magnetic insulation conditions on the boundaries of V‐notch by the fractional Bessel function expansion method and Graf addition theorem. Finally, Green's function method is applied, the half space is divided into two parts along the vertical interface, a pair of in‐plane magnetic field and out‐plane forces are applied on the vertical interface, and the first kind of Fredholm integral equations are set up and solved by applying orthogonal function expansion technique and effective truncation. Results clarified the influence on the dynamic stress concentration factor and magnetic field intensity concentration factor under proper conditions. Besides, the analytical solutions are compared with the finite element solutions to verify the accuracy of the conclusions in this article.
本文研究了压磁半空间中具有复杂边界条件的 V 型缺口的抗平面应力分析。首先，将 SH 波视为作用于压磁半空间的外部载荷，在重复图像叠加的基础上，进行散射波的解析表达，该解析表达满足半空间边界的边界条件。然后，通过分数贝塞尔函数展开法和格拉夫加法定理建立了驻波的解析表达式，它满足 V 型缺口边界上的无应力和磁绝缘条件。最后，应用格林函数法，沿垂直界面将半空间分为两部分，在垂直界面上施加一对平面内磁场和平面外力，建立第一类弗雷德霍姆积分方程，并应用正交函数展开技术和有效截断法求解。结果阐明了在适当条件下动态应力集中系数和磁场强度集中系数的影响。此外，还将分析解与有限元解进行了比较，以验证本文结论的准确性。
{"title":"Anti‐plane stress analysis for V‐notch in a piezomagnetic half space under SH wave","authors":"Xi‐Meng Zhang, Hui Qi","doi":"10.1002/zamm.202300924","DOIUrl":"https://doi.org/10.1002/zamm.202300924","url":null,"abstract":"In this paper, the anti‐plane stress analysis of a V‐notch with complex boundary conditions in a piezomagnetic half space is studied. Firstly, SH wave is considered as an external load acting on piezomagnetic half space, on the basis of repeated image superposition, the analytical expression of scattering wave is conducted, which satisfies the boundary conditions on the boundary of the half space. Then, the analytical expression of standing wave is established, which satisfies the stress free and magnetic insulation conditions on the boundaries of V‐notch by the fractional Bessel function expansion method and Graf addition theorem. Finally, Green's function method is applied, the half space is divided into two parts along the vertical interface, a pair of in‐plane magnetic field and out‐plane forces are applied on the vertical interface, and the first kind of Fredholm integral equations are set up and solved by applying orthogonal function expansion technique and effective truncation. Results clarified the influence on the dynamic stress concentration factor and magnetic field intensity concentration factor under proper conditions. Besides, the analytical solutions are compared with the finite element solutions to verify the accuracy of the conclusions in this article.","PeriodicalId":501230,"journal":{"name":"ZAMM - Journal of Applied Mathematics and Mechanics","volume":"78 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140602311","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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