Abstract An important rheological mathematical model is created to investigate the rheological impacts of slip velocity and varied zeta potentials in an inclined asymmetric channel. The flow is taken in an isotropic porous medium and is governed by Bingham‐Papanastasiou model. The membrane based pumping analysis is done in a wave frame of reference moving with the speed of the wave. Flow model is simplified by considering small wave number δ, small Reynolds number and small Peclet number . The emerging linearized non‐dimensional system of equations is evaluated for analytical and numerical methods. The effects of sundry parameters on pumping, temperature θ, axial velocity u and trapping have been studied graphically. The viscous model is retrieved for Bingham number or stress growth parameter . Finally, the effects of relevant parameters on heat transfer rate and shear stress at walls are discussed numerically. The results show that more pressure is required to flow same amount of fluid in an inclined channel. The temperature field θ is boosted by both the Bingham number and the continuation parameter M . It is also observed that different zeta potentials and velocity slip conditions are significant phenomena to influence channel flow. A pumping‐based device can be built using the existing model to combine and filter physiological samples and chemicals as well as to visualize the transit of physiological fluids.
{"title":"Electrokinetic peristaltic transport of Bingham‐Papanastasiou fluid via porous media","authors":"Farida Aslam, Saima Noreen","doi":"10.1002/zamm.202300070","DOIUrl":"https://doi.org/10.1002/zamm.202300070","url":null,"abstract":"Abstract An important rheological mathematical model is created to investigate the rheological impacts of slip velocity and varied zeta potentials in an inclined asymmetric channel. The flow is taken in an isotropic porous medium and is governed by Bingham‐Papanastasiou model. The membrane based pumping analysis is done in a wave frame of reference moving with the speed of the wave. Flow model is simplified by considering small wave number δ, small Reynolds number and small Peclet number . The emerging linearized non‐dimensional system of equations is evaluated for analytical and numerical methods. The effects of sundry parameters on pumping, temperature θ, axial velocity u and trapping have been studied graphically. The viscous model is retrieved for Bingham number or stress growth parameter . Finally, the effects of relevant parameters on heat transfer rate and shear stress at walls are discussed numerically. The results show that more pressure is required to flow same amount of fluid in an inclined channel. The temperature field θ is boosted by both the Bingham number and the continuation parameter M . It is also observed that different zeta potentials and velocity slip conditions are significant phenomena to influence channel flow. A pumping‐based device can be built using the existing model to combine and filter physiological samples and chemicals as well as to visualize the transit of physiological fluids.","PeriodicalId":23924,"journal":{"name":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135063113","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract In this manuscript, a two‐fluid magnetized plasma oscillator subjected to parametric excitation with square delayed feedback is studied both analytically and numerically. The Hamilton systems of triple‐well and narrow single‐well are discussed in detail. The scenarios of phase portraits and equilibria are given. Homoclinic and heteroclinic orbits are strictly derived. With the Melnikov method, the critical value of chaos arising from homoclinic or heteroclinic intersections is derived analytically. We have discovered some interesting dynamic phenomena, such as uncontrollable time delays with which chaos always occurs for this system. The influence of time‐delay on the chaotic property is also studied rigorously. On the basis of theoretical analysis, some numerical simulations including time histories, phase portraits, bifurcation diagrams, Poincaré sections, Lyapunov exponential spectrums and attractor basins are given. Numerical simulations are consistent with theoretical results.
{"title":"Orbits and chaos of a two‐fluid magnetized plasma oscillator subjected to parametric excitation with square delayed feedback","authors":"Sengen Hu, Liangqiang Zhou","doi":"10.1002/zamm.202300441","DOIUrl":"https://doi.org/10.1002/zamm.202300441","url":null,"abstract":"Abstract In this manuscript, a two‐fluid magnetized plasma oscillator subjected to parametric excitation with square delayed feedback is studied both analytically and numerically. The Hamilton systems of triple‐well and narrow single‐well are discussed in detail. The scenarios of phase portraits and equilibria are given. Homoclinic and heteroclinic orbits are strictly derived. With the Melnikov method, the critical value of chaos arising from homoclinic or heteroclinic intersections is derived analytically. We have discovered some interesting dynamic phenomena, such as uncontrollable time delays with which chaos always occurs for this system. The influence of time‐delay on the chaotic property is also studied rigorously. On the basis of theoretical analysis, some numerical simulations including time histories, phase portraits, bifurcation diagrams, Poincaré sections, Lyapunov exponential spectrums and attractor basins are given. Numerical simulations are consistent with theoretical results.","PeriodicalId":23924,"journal":{"name":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135207384","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Bioconvection in non‐Newtonian nanofluids has a wide range of contemporary applications in biotech, biomechanics, microbiology, computational biology, medical science, etc. Considering the Casson fluid model and inclined stretching geometry a mathematical model is developed to investigate the influence of chemical reactions on bioconvection characteristics of self‐propelled microbes in a non‐Newtonian nanofluid. Nanoparticles that can be dissolved in the blood (base fluid) include titanium oxide () and aluminium oxide (). The impacts of heat generation, magnetic field, and dissipation of viscosity are also included. To simplify the governing system of partial differential equations (PDEs), boundary layer assumptions are used. By using the proper transformations, the governing PDEs and the boundary conditions that correspond with them are further changed to a dimensionless form. Utilizing a local non‐similarity technique up to the second degree of truncation in conjunction with MATLAB's (bvp4c) built‐in finite difference code, the results of the altered model are gathered. Additionally, after achieving good alignment between calculated findings and published results, the influence of changing factors on the flow of fluids and heat transfer features of the envisioned flow problems is shown and examined in graphical configuration. Tables are designed to establish numerical variants of the drag coefficient and Nusselt number. The Outcome of this study is to highlight the important role that chemical reactions play in the bioconvection of Casson nanofluids, and how manipulating the chemical reaction parameter can impact the transport and heat/mass transfer properties of the fluid. It is noted that increasing the chemical reaction parameter leads to a fall in the concentration profile of the bioconvection Casson nanofluid. Enhancing the Casson fluid parameter enhances the velocity and temperature profile. When the Peclet number is altered, the propagation of microorganisms is constrained. Moreover, it was observed that the density of motile microorganisms increased as the bioconvective Lewis numbers became higher. The coefficient of friction on the inclined stretched surface is increased significantly by the porosity parameter and Lorentz forces, as they act as amplifiers.
{"title":"Non‐similar analysis of chemically reactive bioconvective Casson nanofluid flow over an inclined stretching surface","authors":"Umar Farooq, Muzamil Hussain, Umer Farooq","doi":"10.1002/zamm.202300128","DOIUrl":"https://doi.org/10.1002/zamm.202300128","url":null,"abstract":"Abstract Bioconvection in non‐Newtonian nanofluids has a wide range of contemporary applications in biotech, biomechanics, microbiology, computational biology, medical science, etc. Considering the Casson fluid model and inclined stretching geometry a mathematical model is developed to investigate the influence of chemical reactions on bioconvection characteristics of self‐propelled microbes in a non‐Newtonian nanofluid. Nanoparticles that can be dissolved in the blood (base fluid) include titanium oxide () and aluminium oxide (). The impacts of heat generation, magnetic field, and dissipation of viscosity are also included. To simplify the governing system of partial differential equations (PDEs), boundary layer assumptions are used. By using the proper transformations, the governing PDEs and the boundary conditions that correspond with them are further changed to a dimensionless form. Utilizing a local non‐similarity technique up to the second degree of truncation in conjunction with MATLAB's (bvp4c) built‐in finite difference code, the results of the altered model are gathered. Additionally, after achieving good alignment between calculated findings and published results, the influence of changing factors on the flow of fluids and heat transfer features of the envisioned flow problems is shown and examined in graphical configuration. Tables are designed to establish numerical variants of the drag coefficient and Nusselt number. The Outcome of this study is to highlight the important role that chemical reactions play in the bioconvection of Casson nanofluids, and how manipulating the chemical reaction parameter can impact the transport and heat/mass transfer properties of the fluid. It is noted that increasing the chemical reaction parameter leads to a fall in the concentration profile of the bioconvection Casson nanofluid. Enhancing the Casson fluid parameter enhances the velocity and temperature profile. When the Peclet number is altered, the propagation of microorganisms is constrained. Moreover, it was observed that the density of motile microorganisms increased as the bioconvective Lewis numbers became higher. The coefficient of friction on the inclined stretched surface is increased significantly by the porosity parameter and Lorentz forces, as they act as amplifiers.","PeriodicalId":23924,"journal":{"name":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135207382","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}
Tasawar Hayat, Muhammad Yazman, Khursheed Muhammad, Ahmed Alsaedi
Abstract The presented article aims to analyze the three‐dimensional electrically conducting flow induced by a rotating stretchable disk. A hybrid nanomaterial is generated by adding copper and graphene oxide nanoparticles to kerosene oil, which saturates through a Darcy–Forchheimer porous medium. The article also reports on entropy generation and the Bejan number. To solve the associated partial differential equations, appropriate transformations are applied to convert them into ordinary differential equations. These equations are then solved numerically to obtain the desired solutions. The significance of these nanoparticles in kerosene oil is due to their ability to enhance heat transfer and thermal conductivity, thereby optimizing the performance of the rotating stretchable disk system. The synergistic effects of these components lead to improved energy efficiency and overall system effectiveness. The results for various quantities of interest, such as velocity, entropy, temperature, and the Bejan number, are presented graphically and analyzed considering the influence of relevant parameters. Moreover, the comparative analysis indicated that hybrid nanofluid have dominating effect than base liquid (kerosene oil).
{"title":"Entropy generation in MHD Darcy–Forchheimer flow of hybrid nanomaterial: A numerical study of local similar solution","authors":"Tasawar Hayat, Muhammad Yazman, Khursheed Muhammad, Ahmed Alsaedi","doi":"10.1002/zamm.202200557","DOIUrl":"https://doi.org/10.1002/zamm.202200557","url":null,"abstract":"Abstract The presented article aims to analyze the three‐dimensional electrically conducting flow induced by a rotating stretchable disk. A hybrid nanomaterial is generated by adding copper and graphene oxide nanoparticles to kerosene oil, which saturates through a Darcy–Forchheimer porous medium. The article also reports on entropy generation and the Bejan number. To solve the associated partial differential equations, appropriate transformations are applied to convert them into ordinary differential equations. These equations are then solved numerically to obtain the desired solutions. The significance of these nanoparticles in kerosene oil is due to their ability to enhance heat transfer and thermal conductivity, thereby optimizing the performance of the rotating stretchable disk system. The synergistic effects of these components lead to improved energy efficiency and overall system effectiveness. The results for various quantities of interest, such as velocity, entropy, temperature, and the Bejan number, are presented graphically and analyzed considering the influence of relevant parameters. Moreover, the comparative analysis indicated that hybrid nanofluid have dominating effect than base liquid (kerosene oil).","PeriodicalId":23924,"journal":{"name":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135258305","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}
Seyyed Hassan Moussavian, Mohammad Jafari, Mojtaba Hajimohammadi
Abstract In this paper, a new analytical method is presented to determine the stress intensity factors (SIFs) of a generally orthotropic plate with cracks emanating from a circular hole. Therefore, using the Schwartz integration method, for the first time, the analytical solution is provided based on the complex variable method. In order to use the Schwartz's theorem in solving complex integrals, a new presentation of the mapping function has been presented, which leads to providing a simpler solution. After calculating the potential functions, the SIFs are determined for the circular hole with one and two cracks. Then, the effect of parameters such as fiber angle, different and unequal crack lengths, and different loadings are studied. To validate the results of the present analytical solution, some results have been compared with the results from other references. Comparing the results showed that the current solution has good accuracy and is reliable and the fiber angle has a significant effect on the mode II SIF. In the case that the fibers are along the crack length and the loading is perpendicular to the crack direction, the mode II SIF is zero, but if the fibers are not along the crack length, the value of the mode II SIF will not be zero. It is also shown that increasing the length of one crack increases the SIF of another crack as well.
{"title":"Analytical calculation of stress intensity factors for orthotropic plates containing cracks emanating from a circular hole using Schwarz integration","authors":"Seyyed Hassan Moussavian, Mohammad Jafari, Mojtaba Hajimohammadi","doi":"10.1002/zamm.202300429","DOIUrl":"https://doi.org/10.1002/zamm.202300429","url":null,"abstract":"Abstract In this paper, a new analytical method is presented to determine the stress intensity factors (SIFs) of a generally orthotropic plate with cracks emanating from a circular hole. Therefore, using the Schwartz integration method, for the first time, the analytical solution is provided based on the complex variable method. In order to use the Schwartz's theorem in solving complex integrals, a new presentation of the mapping function has been presented, which leads to providing a simpler solution. After calculating the potential functions, the SIFs are determined for the circular hole with one and two cracks. Then, the effect of parameters such as fiber angle, different and unequal crack lengths, and different loadings are studied. To validate the results of the present analytical solution, some results have been compared with the results from other references. Comparing the results showed that the current solution has good accuracy and is reliable and the fiber angle has a significant effect on the mode II SIF. In the case that the fibers are along the crack length and the loading is perpendicular to the crack direction, the mode II SIF is zero, but if the fibers are not along the crack length, the value of the mode II SIF will not be zero. It is also shown that increasing the length of one crack increases the SIF of another crack as well.","PeriodicalId":23924,"journal":{"name":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134970114","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}
Igor V. Andrianov, Jan Awrejcewicz, Steve G. Koblik, Galina A. Starushenko
Abstract In this paper, oscillations of the electrically actuated microbeam are considered, described by strongly nonlinear differential equations. One of the essentially nonlinear effects is the pull‐in phenomenon, that is, the transition of the oscillatory regime to the attraction regime. This effect is considered in the paper on the basis of various approximate models. In particular, the error of replacing the original nonlinearity by its expansion in the Maclaurin series is estimated. It is shown that such an approximation can only be used for voltage values that are far from critical. Estimates are also given for initial displacements and velocities, which guarantee an oscillating character of solutions. The electrically activated oscillations of the microbeam are considered taking into account the geometric nonlinearity within the framework of the Kirchhoff model. The dependence of pull‐in value on geometric nonlinearity is investigated.
{"title":"Nonlinear oscillation of a microbeam due to an electric actuation—Comparison of approximate models","authors":"Igor V. Andrianov, Jan Awrejcewicz, Steve G. Koblik, Galina A. Starushenko","doi":"10.1002/zamm.202300091","DOIUrl":"https://doi.org/10.1002/zamm.202300091","url":null,"abstract":"Abstract In this paper, oscillations of the electrically actuated microbeam are considered, described by strongly nonlinear differential equations. One of the essentially nonlinear effects is the pull‐in phenomenon, that is, the transition of the oscillatory regime to the attraction regime. This effect is considered in the paper on the basis of various approximate models. In particular, the error of replacing the original nonlinearity by its expansion in the Maclaurin series is estimated. It is shown that such an approximation can only be used for voltage values that are far from critical. Estimates are also given for initial displacements and velocities, which guarantee an oscillating character of solutions. The electrically activated oscillations of the microbeam are considered taking into account the geometric nonlinearity within the framework of the Kirchhoff model. The dependence of pull‐in value on geometric nonlinearity is investigated.","PeriodicalId":23924,"journal":{"name":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134969934","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}
Zakir Ullah, Gul Zaman, Ikram Ullah, Oluwole Daniel Makinde
Abstract This work presents a theoretical numerical study of the bioconvection flow of Prandtl–Eyring nanofluid through a stretching cylinder with gyrotactic microorganisms. The mathematical model developed also incorporated the inclined magnetic field and heat generation effects. Further, stratification conditions are considered at the boundary of the stretched cylinder. The described flow problem conducting coupled high‐order partial differential equations (PDEs) is first reduced to the nonlinear system of ordinary differential equations (ODEs) by introducing suitable mathematical transformations. The resulting highly nonlinear flow equations are treated numerically by applying the shooting method. A comparison of the adapted method with previously reported data is also made to validate the presented results. The comparisons are in excellent agreement. The individual effect of controlling flow parameters/numbers on the flow profiles and physical quantities of engineering interest are represented graphically with physical descriptions. The significant results of the present analysis revealed that a rise in bioconvection Rayleigh number, thermal Grashof number, and angle of inclination boosts the velocity profile. The study shows that thermal stratification, mass stratification, and motile density stratification parameters diminish the temperature, concentration, and microorganism profiles, respectively. The nondimensional Sherwood number is decelerated significantly by thermophoresis and mass stratification parameters.
{"title":"Bioconvection flow of Prandtl–Eyring nanofluid in the presence of gyrotactic microorganisms","authors":"Zakir Ullah, Gul Zaman, Ikram Ullah, Oluwole Daniel Makinde","doi":"10.1002/zamm.202300358","DOIUrl":"https://doi.org/10.1002/zamm.202300358","url":null,"abstract":"Abstract This work presents a theoretical numerical study of the bioconvection flow of Prandtl–Eyring nanofluid through a stretching cylinder with gyrotactic microorganisms. The mathematical model developed also incorporated the inclined magnetic field and heat generation effects. Further, stratification conditions are considered at the boundary of the stretched cylinder. The described flow problem conducting coupled high‐order partial differential equations (PDEs) is first reduced to the nonlinear system of ordinary differential equations (ODEs) by introducing suitable mathematical transformations. The resulting highly nonlinear flow equations are treated numerically by applying the shooting method. A comparison of the adapted method with previously reported data is also made to validate the presented results. The comparisons are in excellent agreement. The individual effect of controlling flow parameters/numbers on the flow profiles and physical quantities of engineering interest are represented graphically with physical descriptions. The significant results of the present analysis revealed that a rise in bioconvection Rayleigh number, thermal Grashof number, and angle of inclination boosts the velocity profile. The study shows that thermal stratification, mass stratification, and motile density stratification parameters diminish the temperature, concentration, and microorganism profiles, respectively. The nondimensional Sherwood number is decelerated significantly by thermophoresis and mass stratification parameters.","PeriodicalId":23924,"journal":{"name":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134969947","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}
Hussain Basha, Mahantesh M. Nandeppanavar, Gudala Janardhana Reddy
Abstract The novelty and main aim of the present numerical analysis is to explore the magneto‐thermo‐fluid characteristic features of incompressible, time‐dependent electrically conducting second‐grade fluid flow about a micro‐cantilever sensor sheet suspended in a squeezed regime between two parallel plates under the influence of Lorentz force field and viscous dissipation effects. Pertaining to this physical situation, the primitive forms of produced coupled nonlinear partial differential equations are rendered to non‐dimensional ordinary differential equations through appropriate scaling transformations. The resultant coupled nonlinear boundary value physical problem is solved by deploying a robust BVP4C Matlab function. The key features of the emerged different fluid flow parameters are documented in terms of extensive graphical visualization and tabular discussion. The current numerical investigation showed that, the increasing second‐grade fluid parameter significantly decreases the flow field and enhances the thermal and mass diffusion fields. Magnifying permeable velocity number decreases the velocity and increases the heat and concentration transport process. The thermal distribution over a sensor region is boosted with increasing Eckert number through viscous dissipation and magnetic Ohmic heating. Further, the elevating squeezing number decreases the skin friction and enhancing second‐grade fluid number boosted the skin‐friction coefficient. In addition to this, the increasing Schmidt and squeezing parameters decreases the local Sherwood number. Finally, a reasonable agreement between the present numerical solutions with the former results is presented.
{"title":"Dissipative Lorentz force influence on mass flow over a micro‐cantilever sensor sheet under magnetic Ohmic heating","authors":"Hussain Basha, Mahantesh M. Nandeppanavar, Gudala Janardhana Reddy","doi":"10.1002/zamm.202300055","DOIUrl":"https://doi.org/10.1002/zamm.202300055","url":null,"abstract":"Abstract The novelty and main aim of the present numerical analysis is to explore the magneto‐thermo‐fluid characteristic features of incompressible, time‐dependent electrically conducting second‐grade fluid flow about a micro‐cantilever sensor sheet suspended in a squeezed regime between two parallel plates under the influence of Lorentz force field and viscous dissipation effects. Pertaining to this physical situation, the primitive forms of produced coupled nonlinear partial differential equations are rendered to non‐dimensional ordinary differential equations through appropriate scaling transformations. The resultant coupled nonlinear boundary value physical problem is solved by deploying a robust BVP4C Matlab function. The key features of the emerged different fluid flow parameters are documented in terms of extensive graphical visualization and tabular discussion. The current numerical investigation showed that, the increasing second‐grade fluid parameter significantly decreases the flow field and enhances the thermal and mass diffusion fields. Magnifying permeable velocity number decreases the velocity and increases the heat and concentration transport process. The thermal distribution over a sensor region is boosted with increasing Eckert number through viscous dissipation and magnetic Ohmic heating. Further, the elevating squeezing number decreases the skin friction and enhancing second‐grade fluid number boosted the skin‐friction coefficient. In addition to this, the increasing Schmidt and squeezing parameters decreases the local Sherwood number. Finally, a reasonable agreement between the present numerical solutions with the former results is presented.","PeriodicalId":23924,"journal":{"name":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135879166","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Stephen Timoshenko was the author of numerous textbooks on various aspects of applied mechanics, and through them contributed to its rapid development in the world. As always, the community is also interested in the personal side of the scientists. This paper is devoted to a single statement made by Stephen Timoshenko in his autobiographical book. Specifically, it concerns Timoshenko's at least partial “explanation” of the Holocaust that took place during WWII. Whereas Timoshenko's statement constituted, to the present writer, open antisemitism, it does not seem to disturb many researchers who continue to honor him in various ways. “Nonsense is nonsense, but the history of nonsense is scholarship,” according to Saul Lieberman. Hence the present article presents an investigation of Timoshenko's nonsensical and overly antisemitic statement. This author corresponded with a number of historians of science all repudiating Timoshenko's assertions. Most importantly, the correspondents shed additional vivid light on the Holocaust as experienced by Jewish scientists.
{"title":"Was Stephen Timoshenko right about the Jewish scientists in Germany?","authors":"Isaac Elishakoff","doi":"10.1002/zamm.202300341","DOIUrl":"https://doi.org/10.1002/zamm.202300341","url":null,"abstract":"Abstract Stephen Timoshenko was the author of numerous textbooks on various aspects of applied mechanics, and through them contributed to its rapid development in the world. As always, the community is also interested in the personal side of the scientists. This paper is devoted to a single statement made by Stephen Timoshenko in his autobiographical book. Specifically, it concerns Timoshenko's at least partial “explanation” of the Holocaust that took place during WWII. Whereas Timoshenko's statement constituted, to the present writer, open antisemitism, it does not seem to disturb many researchers who continue to honor him in various ways. “Nonsense is nonsense, but the history of nonsense is scholarship,” according to Saul Lieberman. Hence the present article presents an investigation of Timoshenko's nonsensical and overly antisemitic statement. This author corresponded with a number of historians of science all repudiating Timoshenko's assertions. Most importantly, the correspondents shed additional vivid light on the Holocaust as experienced by Jewish scientists.","PeriodicalId":23924,"journal":{"name":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135885452","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}
Nasir Ali, Muhammad Waris Saeed Khan, Shahzad Saleem
Abstract The underlying intention of the present work is to elaborate the boundary layer flow of Carreau fluid over a non‐linear stretching curved surface. Firstly, we derived the equation of motion for a two‐dimensional curved surface using the Carreau constitutive relation. Employing the well‐known approximations of the boundary layer theory (order of magnitude analysis), the terms of higher and next order have been neglected. We developed an appropriate similarity transformation that reduced the considered partial differential equation into an ordinary differential equation (self‐similar formulation). The MATLAB built‐in function usually known as bvp5c is utilized to get the numerical solution of the considered problem. The impact of the power‐law index ( n ), Weissenberg number and curvature parameter ( k ) on velocity profile and skin friction are analyzed through several graphs and tables. The obtained results are also verified by employing the shooting method through Maple software. The results reveal that both boundary layer thickness and velocity profile increase by enlarging the dimensionless curvature parameter of the curved surface.
{"title":"Critical analysis of generalized Newtonian fluid flow past a non‐linearly stretched curved surface: A numerical solution for Carreau model","authors":"Nasir Ali, Muhammad Waris Saeed Khan, Shahzad Saleem","doi":"10.1002/zamm.202300100","DOIUrl":"https://doi.org/10.1002/zamm.202300100","url":null,"abstract":"Abstract The underlying intention of the present work is to elaborate the boundary layer flow of Carreau fluid over a non‐linear stretching curved surface. Firstly, we derived the equation of motion for a two‐dimensional curved surface using the Carreau constitutive relation. Employing the well‐known approximations of the boundary layer theory (order of magnitude analysis), the terms of higher and next order have been neglected. We developed an appropriate similarity transformation that reduced the considered partial differential equation into an ordinary differential equation (self‐similar formulation). The MATLAB built‐in function usually known as bvp5c is utilized to get the numerical solution of the considered problem. The impact of the power‐law index ( n ), Weissenberg number and curvature parameter ( k ) on velocity profile and skin friction are analyzed through several graphs and tables. The obtained results are also verified by employing the shooting method through Maple software. The results reveal that both boundary layer thickness and velocity profile increase by enlarging the dimensionless curvature parameter of the curved surface.","PeriodicalId":23924,"journal":{"name":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135879185","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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