Hossam A. Nabwey, Bakhtawar Bibi, Muhammad Ashraf, Ahmed M. Rashad, Miad Abu Hawsah
Thermal stratification improves coaxial pipe systems’ efficiency and stability. Thermal stratification enables accurate temperature maintenance, reduces thermal stress, optimizes heat transmission performance, and minimizes usage of energy to guarantee the system's long‐term performance. The main aim of the current study is to investigate the impacts of thermal stratification on buoyancy force flow and thermal transmission between coaxial fixed pipes. In the present research, the applications of thermally stratified medium on transient convective heat transfer between two coaxial fixed pipes are studied. A two‐dimensional mathematical formulation in terms of mutually nonlinear partial differential equations is used to analyze the unsteady flow and temperature field between the co‐axial pipes, when the internal pipe is uniformly heated and the outer wall of the external pipe is placed at infinity from the surface of the inner fixed pipe. Flow is assumed along the axial direction of the internal pipe and stationary boundary condition is assumed at the surface of the inner pipe. The coupled equations of the simulated model are solved numerically by applying the Implicit Finite Difference Technique. The computed outcomes in the form of geometrical interpretation are highlighted by using the technically advanced software TECHPLOT‐360. Comprehensive detail of the obtained results for the non‐dimensional parameters included in the flow formulation is predicted for steady state velocity, temperature distribution, time‐dependent surface shearness and time‐dependent energy shearness in results and discussion section of the manuscript. The emphasis is placed on the thermal stratification parameter in the above mentioned chief quantities. From the obtained results, it is predicted that the fluid flow pattern and thermal distribution are both reduced for rising values of the thermal stratification parameter S = 0.001, 0.03, 0.05, and 0.07. Minimum flow and thermal profile are observed at S = 0.07. Further, the amplitude of the time‐dependent surface shearness is uniformly distributed throughout the medium and the amplitude of the time‐dependent energy shearness is reduced effectively for S = 1.0, 5.0, and 10.0.
热分层提高了同轴管道系统的效率和稳定性。热分层可实现精确的温度维持、减少热应力、优化热传递性能并最大限度地减少能源消耗，从而保证系统的长期性能。本研究的主要目的是探讨热分层对同轴固定管道间浮力流和热传导的影响。本研究探讨了热分层介质对两根同轴固定管道间瞬态对流传热的影响。当内部管道被均匀加热，外部管道的外壁距离内部固定管道的表面无穷远时，使用互非线性偏微分方程的二维数学公式来分析同轴管道之间的非稳态流动和温度场。假定流体沿内管轴向流动，内管表面假定有静止边界条件。模拟模型的耦合方程采用隐式有限差分技术进行数值求解。利用技术先进的软件 TECHPLOT-360 对计算结果进行了几何解释。手稿的结果和讨论部分全面详细地预测了流动公式中包含的非尺寸参数的稳态速度、温度分布、随时间变化的表面剪切力和随时间变化的能量剪切力。重点是上述主要量中的热分层参数。根据所得结果预测，当热分层参数 S = 0.001、0.03、0.05 和 0.07 的值上升时，流体流动模式和热分布都会减小。当 S = 0.07 时，流量和热分布均为最小值。此外，当 S = 1.0、5.0 和 10.0 时，随时间变化的表面剪切振幅在整个介质中均匀分布，随时间变化的能量剪切振幅有效减小。
{"title":"Impacts of thermally stratified medium on transient convective heat transfer between co‐axial horizontal fixed pipes: Applications of the thermal stratification","authors":"Hossam A. Nabwey, Bakhtawar Bibi, Muhammad Ashraf, Ahmed M. Rashad, Miad Abu Hawsah","doi":"10.1002/zamm.202400052","DOIUrl":"https://doi.org/10.1002/zamm.202400052","url":null,"abstract":"Thermal stratification improves coaxial pipe systems’ efficiency and stability. Thermal stratification enables accurate temperature maintenance, reduces thermal stress, optimizes heat transmission performance, and minimizes usage of energy to guarantee the system's long‐term performance. The main aim of the current study is to investigate the impacts of thermal stratification on buoyancy force flow and thermal transmission between coaxial fixed pipes. In the present research, the applications of thermally stratified medium on transient convective heat transfer between two coaxial fixed pipes are studied. A two‐dimensional mathematical formulation in terms of mutually nonlinear partial differential equations is used to analyze the unsteady flow and temperature field between the co‐axial pipes, when the internal pipe is uniformly heated and the outer wall of the external pipe is placed at infinity from the surface of the inner fixed pipe. Flow is assumed along the axial direction of the internal pipe and stationary boundary condition is assumed at the surface of the inner pipe. The coupled equations of the simulated model are solved numerically by applying the Implicit Finite Difference Technique. The computed outcomes in the form of geometrical interpretation are highlighted by using the technically advanced software TECHPLOT‐360. Comprehensive detail of the obtained results for the non‐dimensional parameters included in the flow formulation is predicted for steady state velocity, temperature distribution, time‐dependent surface shearness and time‐dependent energy shearness in results and discussion section of the manuscript. The emphasis is placed on the thermal stratification parameter in the above mentioned chief quantities. From the obtained results, it is predicted that the fluid flow pattern and thermal distribution are both reduced for rising values of the thermal stratification parameter <jats:italic>S</jats:italic> = 0.001, 0.03, 0.05, and 0.07. Minimum flow and thermal profile are observed at <jats:italic>S</jats:italic> = 0.07. Further, the amplitude of the time‐dependent surface shearness is uniformly distributed throughout the medium and the amplitude of the time‐dependent energy shearness is reduced effectively for <jats:italic>S</jats:italic> = 1.0, 5.0, and 10.0.","PeriodicalId":501230,"journal":{"name":"ZAMM - Journal of Applied Mathematics and Mechanics","volume":"41 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141772941","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}
Noreen Sher Akbar, M. Fiaz Hussain, Taseer Muhammad
This study aims to explore a novel cross model for peristaltic flow, which has not been previously addressed. The focus is on investigating the peristaltic flow of an incompressible nanofluid within a vertically uniform channel. The current model has application in drug delivery, biomedical engineering, lab on chip etc. Utilizing peristaltic flow for drug delivery systems in symmetric channels offers precise control over fluid motion, non‐Newtonian fluids, such as polymer solutions used in drug formulations, exhibit complex flow behavior that can be manipulated through peristaltic pumping mechanisms. This application has the potential to revolutionize targeted drug delivery, enhancing therapeutic efficacy and minimizing side effects. Studying peristaltic flow in symmetric channels for non‐Newtonian fluids offers interdisciplinary insights and innovative applications. Understanding fluid rheology, channel geometry, and peristaltic pumping can lead to novel strategies for fluid control, with implications for healthcare, biotechnology, and materials science advancements. To simplify the complex system of nonlinear partial differential equations governing the flow, we consider long wavelengths and low Reynolds numbers. Subsequently, we employ Shooting methods to solve this system of equations, providing a comprehensive evaluation of the numerical results for key parameters such as velocity, temperature, concentration, and pressure gradient. The findings are presented through graphical representations of significant flow parameters.
{"title":"Numerical study of aphron drilling crosser fluids coating layer incorporated blood with zinc oxide (ZnO) nanoparticles injected in esophagus","authors":"Noreen Sher Akbar, M. Fiaz Hussain, Taseer Muhammad","doi":"10.1002/zamm.202400313","DOIUrl":"https://doi.org/10.1002/zamm.202400313","url":null,"abstract":"This study aims to explore a novel cross model for peristaltic flow, which has not been previously addressed. The focus is on investigating the peristaltic flow of an incompressible nanofluid within a vertically uniform channel. The current model has application in drug delivery, biomedical engineering, lab on chip etc. Utilizing peristaltic flow for drug delivery systems in symmetric channels offers precise control over fluid motion, non‐Newtonian fluids, such as polymer solutions used in drug formulations, exhibit complex flow behavior that can be manipulated through peristaltic pumping mechanisms. This application has the potential to revolutionize targeted drug delivery, enhancing therapeutic efficacy and minimizing side effects. Studying peristaltic flow in symmetric channels for non‐Newtonian fluids offers interdisciplinary insights and innovative applications. Understanding fluid rheology, channel geometry, and peristaltic pumping can lead to novel strategies for fluid control, with implications for healthcare, biotechnology, and materials science advancements. To simplify the complex system of nonlinear partial differential equations governing the flow, we consider long wavelengths and low Reynolds numbers. Subsequently, we employ Shooting methods to solve this system of equations, providing a comprehensive evaluation of the numerical results for key parameters such as velocity, temperature, concentration, and pressure gradient. The findings are presented through graphical representations of significant flow parameters.","PeriodicalId":501230,"journal":{"name":"ZAMM - Journal of Applied Mathematics and Mechanics","volume":"68 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141772978","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}
Wei Peng, Ashraf M. Zenkour, Yaru Gao, Xu Zhang, Tianhu He, Yan Li
Graphene nanoplatelets (GPLs) are considered to be a desirable reinforcing nanofillers for nanocomposite materials owing to their superior thermo‐mechanical properties. Meanwhile, thermoelastic damping (TED), as a dominant intrinsic dissipation mechanisms, is a major challenge in optimizing high‐performance micro/nano‐resonators. Nevertheless, the classical TED models fail at the micro/nano‐scale due to without considering the influences of the size‐dependent effect and the thermal lagging effect. The present work focuses on investigating TED analysis of functionally graded (FG) microplate resonators reinforced with GPLs based on the modified coupled stress theory (MCST) and the Moore–Gibson–Thompson (MGT) heat conduction model. Four patterns of GPLs distribution including the UD, FG‐O, FG‐X and FG‐A pattern distributions are taken into account and the effective mechanical properties of the plate‐type nanocomposite are evaluated based on the Halpin–Tsai model. The energy equation and the transverse motion equation in the Kirchhoff microplate model are formulated, and then, the closed‐from analytical solution of TED is solved by complex frequency method. The influences of the various parameters involving the material length‐scale parameter, the thermal phase lag of the heat flux and the total weight fraction of GPLs on the TED are discussed in detail. The obtained results show that the effects of the modified parameter on the TED are pronounced. This results provide a more reasonable theoretical approach to estimate TED in the design of FG microplate resonators reinforced with GPLs with high performance.
{"title":"Size‐dependent thermoelastic damping analysis in functionally graded graphene nanoplatelets reinforced composite microplate resonators based on Moore–Gibson–Thompson thermoelasticity","authors":"Wei Peng, Ashraf M. Zenkour, Yaru Gao, Xu Zhang, Tianhu He, Yan Li","doi":"10.1002/zamm.202301091","DOIUrl":"https://doi.org/10.1002/zamm.202301091","url":null,"abstract":"Graphene nanoplatelets (GPLs) are considered to be a desirable reinforcing nanofillers for nanocomposite materials owing to their superior thermo‐mechanical properties. Meanwhile, thermoelastic damping (TED), as a dominant intrinsic dissipation mechanisms, is a major challenge in optimizing high‐performance micro/nano‐resonators. Nevertheless, the classical TED models fail at the micro/nano‐scale due to without considering the influences of the size‐dependent effect and the thermal lagging effect. The present work focuses on investigating TED analysis of functionally graded (FG) microplate resonators reinforced with GPLs based on the modified coupled stress theory (MCST) and the Moore–Gibson–Thompson (MGT) heat conduction model. Four patterns of GPLs distribution including the UD, FG‐O, FG‐X and FG‐A pattern distributions are taken into account and the effective mechanical properties of the plate‐type nanocomposite are evaluated based on the Halpin–Tsai model. The energy equation and the transverse motion equation in the Kirchhoff microplate model are formulated, and then, the closed‐from analytical solution of TED is solved by complex frequency method. The influences of the various parameters involving the material length‐scale parameter, the thermal phase lag of the heat flux and the total weight fraction of GPLs on the TED are discussed in detail. The obtained results show that the effects of the modified parameter on the TED are pronounced. This results provide a more reasonable theoretical approach to estimate TED in the design of FG microplate resonators reinforced with GPLs with high performance.","PeriodicalId":501230,"journal":{"name":"ZAMM - Journal of Applied Mathematics and Mechanics","volume":"14 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141772982","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}
Manzoor Ahmad, Sami Ullah Khan, Qudsia Bibi, Muhammad Taj, Iskander Tlili, Faisal Mehmood Butt
Owing to the multidisciplinary applications of nanomaterials, a wide range of research has been conducted on this topic recently. The aim of current research is to analyze the enhancement of heat transfer due to the unsteady flow of Maxwell nanofluid associated with the zero mass thermal constraints. The applications of the radiated phenomenon and magnetic force are contributed to the current flow problem. The analysis is subject to the implementation of Robin and zero‐mass diffusion constraints. A bidirectional moving porous surface endorsed the flow. The appropriate variables are taken for simplifying the system. The homotopy analysis method (HAM) is used to compute the solution procedure. The obtained results are confirmed with already performed studies. It has been observed that the temperature and nanoparticle concentration distributions decrease for higher unsteady parameter values.
{"title":"Robin and zero‐mass diffusion analysis for radiated unsteady flow of Maxwell nanofluid due to porous stretched regime: Analytical simulations","authors":"Manzoor Ahmad, Sami Ullah Khan, Qudsia Bibi, Muhammad Taj, Iskander Tlili, Faisal Mehmood Butt","doi":"10.1002/zamm.202300421","DOIUrl":"https://doi.org/10.1002/zamm.202300421","url":null,"abstract":"Owing to the multidisciplinary applications of nanomaterials, a wide range of research has been conducted on this topic recently. The aim of current research is to analyze the enhancement of heat transfer due to the unsteady flow of Maxwell nanofluid associated with the zero mass thermal constraints. The applications of the radiated phenomenon and magnetic force are contributed to the current flow problem. The analysis is subject to the implementation of Robin and zero‐mass diffusion constraints. A bidirectional moving porous surface endorsed the flow. The appropriate variables are taken for simplifying the system. The homotopy analysis method (HAM) is used to compute the solution procedure. The obtained results are confirmed with already performed studies. It has been observed that the temperature and nanoparticle concentration distributions decrease for higher unsteady parameter values.","PeriodicalId":501230,"journal":{"name":"ZAMM - Journal of Applied Mathematics and Mechanics","volume":"47 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141772977","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}
Abdelmooty Mohamed Abd‐Alla, Esraa N. Thabet, Hany A. Hosham, S. M. M. El‐Kabeir
The present paper explores a two‐dimensional mixed bio‐convective unsteady viscous hydro‐magnetic Casson Williamson nanofluid flow model with heat and mass transport incorporating motile microorganisms towards a stretchy spinning disc. The flow concept is accomplished by rotating a stretched disc with a time‐varying angular velocity. By applying a magnetic field normal to the axial direction, a magnetic interaction is taken into consideration. The Casson Williamson nanofluid contains nanosized particles suspended with swimming motile microorganisms and the rotation of the disc is exhibited by buoyancy forces, thermophoresis, suction/injection, zero mass flux conditions, variable thermal conductivity, Joule heating and so forth. The obtained flow narrating differential equations of the model are transformed into ordinary differential system. This is accomplished by simulating boundary value problems using the shooting technique using the ‘ND‐Solve’ approach included in the Mathematica software (Mathematica 12). The implications of the engaged parameters such as Williamson fluid parameter, Casson fluid (CF) parameter, thermophoresis parameter, Brownian motion parameter and so forth, on both axial and radial velocities, temperature, concentration of nanoparticles and microorganisms are explained by means of graphical and tabular constructions. This paper's validity has been confirmed and its findings align with those of other previously published papers. Furthermore, it is found that both the axial and radial velocity profiles are seen to be diminishing functions of the CF parameter. The identified observation may have theoretical implications for a number of engineering procedures, solar energy systems, biofuel cells and extrusion system improvement. Moreover, this work finds application in micro‐fabrication techniques and the chemical industry.
{"title":"Significance of variable thermal conductivity and suction/injection in unsteady MHD mixed convection flow of Casson Williamson nanofluid through heat and mass transport with gyrotactic microorganisms","authors":"Abdelmooty Mohamed Abd‐Alla, Esraa N. Thabet, Hany A. Hosham, S. M. M. El‐Kabeir","doi":"10.1002/zamm.202300501","DOIUrl":"https://doi.org/10.1002/zamm.202300501","url":null,"abstract":"The present paper explores a two‐dimensional mixed bio‐convective unsteady viscous hydro‐magnetic Casson Williamson nanofluid flow model with heat and mass transport incorporating motile microorganisms towards a stretchy spinning disc. The flow concept is accomplished by rotating a stretched disc with a time‐varying angular velocity. By applying a magnetic field normal to the axial direction, a magnetic interaction is taken into consideration. The Casson Williamson nanofluid contains nanosized particles suspended with swimming motile microorganisms and the rotation of the disc is exhibited by buoyancy forces, thermophoresis, suction/injection, zero mass flux conditions, variable thermal conductivity, Joule heating and so forth. The obtained flow narrating differential equations of the model are transformed into ordinary differential system. This is accomplished by simulating boundary value problems using the shooting technique using the ‘ND‐Solve’ approach included in the Mathematica software (Mathematica 12). The implications of the engaged parameters such as Williamson fluid parameter, Casson fluid (CF) parameter, thermophoresis parameter, Brownian motion parameter and so forth, on both axial and radial velocities, temperature, concentration of nanoparticles and microorganisms are explained by means of graphical and tabular constructions. This paper's validity has been confirmed and its findings align with those of other previously published papers. Furthermore, it is found that both the axial and radial velocity profiles are seen to be diminishing functions of the CF parameter. The identified observation may have theoretical implications for a number of engineering procedures, solar energy systems, biofuel cells and extrusion system improvement. Moreover, this work finds application in micro‐fabrication techniques and the chemical industry.","PeriodicalId":501230,"journal":{"name":"ZAMM - Journal of Applied Mathematics and Mechanics","volume":"127 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141772979","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}
Rajdeep Bordoloi, Nazibuddin Ahmed, Kalyan Chamuah, Ali J. Chamkha
The article presents a solution to a complex problem involving a transient MHD‐free convective chemically reactive flow. The flow involves a viscous incompressible electrically conducting non‐Gray optically thick fluid moving past a semi‐infinite vertical plate that has suddenly started but is temporarily accelerated. The plate has nonlinear parabolic ramped conditions, and the flow is exposed to thermal radiation, heat absorbing sink, and diffusion‐thermo effect. For the current study, the model fluid being used is moist air. The governing equations are obtained using the Laplace transform technique with the help of the Heaviside step function. This study is the first to consider parabolic ramped motion, temperature and concentration simultaneously. Effects of the pertinent parameters on the Sherwood number and Nusselt number are visualized using 3D surface plotting. Findings of the problem manifest that concentration, temperature, and velocity profiles in case of ramped conditions are less than in isothermal conditions. The rate of heat transfer of mercury is less than oxygen, air, water, and ethanol at a room temperature of 22°C–25°C. The ramped plate has the tendency to augment the heat transfer rate. The present study is of great interest in numerous fields of industry and machine‐building applications.
{"title":"Exact analysis of hydromagnetic non‐Gray optically thick heat absorbing fluid with nonlinear parabolic ramped conditions","authors":"Rajdeep Bordoloi, Nazibuddin Ahmed, Kalyan Chamuah, Ali J. Chamkha","doi":"10.1002/zamm.202300451","DOIUrl":"https://doi.org/10.1002/zamm.202300451","url":null,"abstract":"The article presents a solution to a complex problem involving a transient MHD‐free convective chemically reactive flow. The flow involves a viscous incompressible electrically conducting non‐Gray optically thick fluid moving past a semi‐infinite vertical plate that has suddenly started but is temporarily accelerated. The plate has nonlinear parabolic ramped conditions, and the flow is exposed to thermal radiation, heat absorbing sink, and diffusion‐thermo effect. For the current study, the model fluid being used is moist air. The governing equations are obtained using the Laplace transform technique with the help of the Heaviside step function. This study is the first to consider parabolic ramped motion, temperature and concentration simultaneously. Effects of the pertinent parameters on the Sherwood number and Nusselt number are visualized using 3D surface plotting. Findings of the problem manifest that concentration, temperature, and velocity profiles in case of ramped conditions are less than in isothermal conditions. The rate of heat transfer of mercury is less than oxygen, air, water, and ethanol at a room temperature of 22°C–25°C. The ramped plate has the tendency to augment the heat transfer rate. The present study is of great interest in numerous fields of industry and machine‐building applications.","PeriodicalId":501230,"journal":{"name":"ZAMM - Journal of Applied Mathematics and Mechanics","volume":"9 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141772983","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}
Muhammad Hasnain Shahzad, Aziz Ullah Awan, Sohail Nadeem, N. Ameer Ahammad, Haneen Hamam, Ahmed Alamer, Sidra Shafique
This research venture comprehends a theoretical examination of non‐Newtonian fluid flowing peristaltic via an elliptical channel. Furthermore, the Prandtl fluid method for this elliptic duct problem is thoroughly considered. This mathematical inquiry adopts a non‐Newtonian Prandtl fluid model. A polynomial methodology is used to analyze partial differential equations that appear in nondimensional form and deliver an exact analytical solution for the temperature and velocity profile. This study is the first to utilize a novel order polynomial of degree eight having eleven constants to precisely solve the temperature equation for Prandtl fluid flow via an elliptic domain. A comprehensive graphical analysis is also provided to understand the mathematical conclusions fully. The graphs of the velocity profiles clearly show that the non‐Newtonian effects are more potent along the minor axis of the elliptical duct. The streamlined graphs accentuating the trapping phenomenon show specific closed contours close to the boundary wall of the peristaltic duct.
{"title":"Rheological effects in peristaltic flow of Prandtl fluid through elliptical duct: A comprehensive analysis","authors":"Muhammad Hasnain Shahzad, Aziz Ullah Awan, Sohail Nadeem, N. Ameer Ahammad, Haneen Hamam, Ahmed Alamer, Sidra Shafique","doi":"10.1002/zamm.202400094","DOIUrl":"https://doi.org/10.1002/zamm.202400094","url":null,"abstract":"This research venture comprehends a theoretical examination of non‐Newtonian fluid flowing peristaltic via an elliptical channel. Furthermore, the Prandtl fluid method for this elliptic duct problem is thoroughly considered. This mathematical inquiry adopts a non‐Newtonian Prandtl fluid model. A polynomial methodology is used to analyze partial differential equations that appear in nondimensional form and deliver an exact analytical solution for the temperature and velocity profile. This study is the first to utilize a novel order polynomial of degree eight having eleven constants to precisely solve the temperature equation for Prandtl fluid flow via an elliptic domain. A comprehensive graphical analysis is also provided to understand the mathematical conclusions fully. The graphs of the velocity profiles clearly show that the non‐Newtonian effects are more potent along the minor axis of the elliptical duct. The streamlined graphs accentuating the trapping phenomenon show specific closed contours close to the boundary wall of the peristaltic duct.","PeriodicalId":501230,"journal":{"name":"ZAMM - Journal of Applied Mathematics and Mechanics","volume":"33 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141772981","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we focus on scattering of non‐periodic incident fields in three‐dimensional bi‐periodic structures, as they can not be solved by the classical methods used for the quasi‐periodic scattering problems. To solve such non‐periodic scattering problems, the Floquet–Bloch transform, which decomposes the unbounded problem into a family of periodic problems in a bounded unit cell, has been applied together with a numerical method by Lechleiter and Zhang (2017). However, its theoretical result indicates that the computational order is too low. Hence, our aim is to propose a high‐order numerical approach by using the Floquet–Bloch transform. To this end, the first crucial part is to analyze the regularity of the transformed solution with respect to the Floquet parameter. The second challenging part is to propose a high‐order tailor‐made quadrature method adapted to singularities of the transformed solution formed by a finite number of circular arcs. Afterwards, we obtain the error estimation of the proposed numerical approach. Eventually, the accuracy and efficiency of the mentioned approach are revealed by several numerical examples.
{"title":"A high‐order numerical method for solving non‐periodic scattering problems in three‐dimensional bi‐periodic structures","authors":"Tilo Arens, Nasim Shafieeabyaneh, Ruming Zhang","doi":"10.1002/zamm.202300650","DOIUrl":"https://doi.org/10.1002/zamm.202300650","url":null,"abstract":"In this paper, we focus on scattering of non‐periodic incident fields in three‐dimensional bi‐periodic structures, as they can not be solved by the classical methods used for the quasi‐periodic scattering problems. To solve such non‐periodic scattering problems, the Floquet–Bloch transform, which decomposes the unbounded problem into a family of periodic problems in a bounded unit cell, has been applied together with a numerical method by Lechleiter and Zhang (2017). However, its theoretical result indicates that the computational order is too low. Hence, our aim is to propose a high‐order numerical approach by using the Floquet–Bloch transform. To this end, the first crucial part is to analyze the regularity of the transformed solution with respect to the Floquet parameter. The second challenging part is to propose a high‐order tailor‐made quadrature method adapted to singularities of the transformed solution formed by a finite number of circular arcs. Afterwards, we obtain the error estimation of the proposed numerical approach. Eventually, the accuracy and efficiency of the mentioned approach are revealed by several numerical examples.","PeriodicalId":501230,"journal":{"name":"ZAMM - Journal of Applied Mathematics and Mechanics","volume":"37 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141741101","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 present research focuses on the challenges engineers face in predicting the behavior of nonlinear vibration systems accurately. The nonperturbative method is highlighted as a solution that provides insights into chaos, bifurcation, resonance response, and stability attributes. Specifically, the study delves into the dynamic analysis of the nonlinear Mathieu equation. The research involves a complex and extensive analytical exploration, transitioning from a nonlinear state to a linear one through various stages. The introduced computational method aims to examine the resonance response of the nonlinear Mathieu equation and offer innovative solutions for the Mathieu–Duffing–type oscillator. The nonperturbative approach remains essential in gaining a deeper understanding of nonlinear vibration systems.
{"title":"A comprehensive study of stability analysis for nonlinear Mathieu equation without a perturbative technique","authors":"Yusry O. El‐Dib","doi":"10.1002/zamm.202400047","DOIUrl":"https://doi.org/10.1002/zamm.202400047","url":null,"abstract":"The present research focuses on the challenges engineers face in predicting the behavior of nonlinear vibration systems accurately. The nonperturbative method is highlighted as a solution that provides insights into chaos, bifurcation, resonance response, and stability attributes. Specifically, the study delves into the dynamic analysis of the nonlinear Mathieu equation. The research involves a complex and extensive analytical exploration, transitioning from a nonlinear state to a linear one through various stages. The introduced computational method aims to examine the resonance response of the nonlinear Mathieu equation and offer innovative solutions for the Mathieu–Duffing–type oscillator. The nonperturbative approach remains essential in gaining a deeper understanding of nonlinear vibration systems.","PeriodicalId":501230,"journal":{"name":"ZAMM - Journal of Applied Mathematics and Mechanics","volume":"56 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141741105","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 numerically treats the magnetic field impacts on the natural convection flow and entropy generation in a square cavity filled with hybrid nanofluid and induced by two isothermally heated semicircles at the bottom and left walls of the cavity. The cavity is filled by hybrid nanofluid (titanium oxide/silver‐water) and oriented under different inclination angles with the applied magnetic field. The simulations in this study were executed via a home‐made code written in the FORTRAN programing language. The numerical methodology considered to solve the coupled equations of continuity, momentum, energy, and entropy generation equations with the associated boundary conditions is the finite volume method and the full multigrid acceleration. Various wake parameters are considered in this research study, namely, the inclination angle of the cavity (α), the magnetic field inclination (γ), the Hartmann number (Ha), the Rayleigh number (Ra), the volume fraction of the hybrid nanofluid (ϕ) and the internal semicircles radii ratio (β). The major findings issued from the impact of these parameters on the fluid flow and heat transfer characteristics reveal that heat transfer and entropy generation are a decreasing function of the Hartmann parameter. Moreover, the total entropy generation is intensified by 85.23% from Ra = 103 to Ra = 106 for Ha = 10, by 85.818% for Ha = 50 and 83.813% for Ha = 100. Besides, the flow magnitude is found decreasing with increasing the radii ratio β of the semicircles. It is also found that optimal heat transfer rates deducted from the variation of average Nusselt number versus Ra for different volume fractions of the hybrid nanoparticles are obtained for the extreme values of the pertinent parameters (β = 1, ϕ = 8%, Ra = 106). Hence, the present work offers a useful tool and a parametric study for the research community and engineers on the design and optimization of thermal management systems used in a variety of industrial applications, such as heat exchangers, nuclear reactors, and energy systems.
{"title":"Thermal performance analysis of oriented MHD convective flow and entropy production of hybrid nanofluids in a cavity induced by semicircles at different radii ratios","authors":"Basma Souayeh","doi":"10.1002/zamm.202400015","DOIUrl":"https://doi.org/10.1002/zamm.202400015","url":null,"abstract":"The current study numerically treats the magnetic field impacts on the natural convection flow and entropy generation in a square cavity filled with hybrid nanofluid and induced by two isothermally heated semicircles at the bottom and left walls of the cavity. The cavity is filled by hybrid nanofluid (titanium oxide/silver‐water) and oriented under different inclination angles with the applied magnetic field. The simulations in this study were executed via a home‐made code written in the FORTRAN programing language. The numerical methodology considered to solve the coupled equations of continuity, momentum, energy, and entropy generation equations with the associated boundary conditions is the finite volume method and the full multigrid acceleration. Various wake parameters are considered in this research study, namely, the inclination angle of the cavity (<jats:italic>α</jats:italic>), the magnetic field inclination (<jats:italic>γ</jats:italic>), the Hartmann number (Ha), the Rayleigh number (Ra), the volume fraction of the hybrid nanofluid (<jats:italic>ϕ</jats:italic>) and the internal semicircles radii ratio (<jats:italic>β</jats:italic>). The major findings issued from the impact of these parameters on the fluid flow and heat transfer characteristics reveal that heat transfer and entropy generation are a decreasing function of the Hartmann parameter. Moreover, the total entropy generation is intensified by 85.23% from Ra = 10<jats:sup>3</jats:sup> to Ra = 10<jats:sup>6</jats:sup> for Ha = 10, by 85.818% for Ha = 50 and 83.813% for Ha = 100. Besides, the flow magnitude is found decreasing with increasing the radii ratio <jats:italic>β</jats:italic> of the semicircles. It is also found that optimal heat transfer rates deducted from the variation of average Nusselt number versus Ra for different volume fractions of the hybrid nanoparticles are obtained for the extreme values of the pertinent parameters (<jats:italic>β</jats:italic> = 1, <jats:italic>ϕ</jats:italic> = 8%, Ra = 10<jats:sup>6</jats:sup>). Hence, the present work offers a useful tool and a parametric study for the research community and engineers on the design and optimization of thermal management systems used in a variety of industrial applications, such as heat exchangers, nuclear reactors, and energy systems.","PeriodicalId":501230,"journal":{"name":"ZAMM - Journal of Applied Mathematics and Mechanics","volume":"62 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141741103","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：