In this article, we investigated the heat and mass transfer of immiscible fluid flow in symmetric two‐vertical regions with a porous matrix in region‐II. The properties of heat generation and absorption are discussed. The channel, consisting of two vertical regions, is filled with a porous matrix with viscous fluids. In both cases, we considered the fluids that undergo Newtonian heat generation and absorption. It was assumed that the porous matrix's channel wall was thermally stable and electrically non‐conducting. The analytical method is used to solve governing equations. Variations in Brinkman Number (Br), Biot Number (Bi), Grashof (Gr) number, viscosity ratio (m), heat generation, and thermal conductivity are illustrated graphically. And we examined the increase in Grashof number, which has effects on fluid flows in both regions. Similarly, the change of heat and momentum transmission in porous media is greatly affected by the viscosity, channel width, source, and sink. Also, when the Grashof number increases, buoyancy increases, leading to an increase in the fluid flow for heat generation and absorption.
{"title":"An investigation of the heat and mass transfer effects in vertical channels with immersible fluid flow through a porous matrix","authors":"Mangala Kandagal, Ramesh Kempepatil","doi":"10.1002/zamm.202300998","DOIUrl":"https://doi.org/10.1002/zamm.202300998","url":null,"abstract":"In this article, we investigated the heat and mass transfer of immiscible fluid flow in symmetric two‐vertical regions with a porous matrix in region‐II. The properties of heat generation and absorption are discussed. The channel, consisting of two vertical regions, is filled with a porous matrix with viscous fluids. In both cases, we considered the fluids that undergo Newtonian heat generation and absorption. It was assumed that the porous matrix's channel wall was thermally stable and electrically non‐conducting. The analytical method is used to solve governing equations. Variations in Brinkman Number (Br), Biot Number (Bi), Grashof (Gr) number, viscosity ratio (m), heat generation, and thermal conductivity are illustrated graphically. And we examined the increase in Grashof number, which has effects on fluid flows in both regions. Similarly, the change of heat and momentum transmission in porous media is greatly affected by the viscosity, channel width, source, and sink. Also, when the Grashof number increases, buoyancy increases, leading to an increase in the fluid flow for heat generation and absorption.","PeriodicalId":501230,"journal":{"name":"ZAMM - Journal of Applied Mathematics and Mechanics","volume":"30 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141937879","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}
Subhajit Panda, Pradyumna Kumar Pattnaik, Rupa Baithalu, Satya Ranjan Mishra
The pivotal role of Brownian and thermophoresis in investigating the flow characteristic of polar nanofluid is important nowadays due to various engineering applications. The enhanced thermal and transport properties in the field of biomedical nanomedicine for hyperthermia treatments, and for enhancing the efficiency of heat exchange processes in cooling electronic devices, heat exchangers, and automotive engines the use of Brownian and thermophoresis is important. Therefore, the present study reveals the importance of Darcy–Forchheimer inertial drag combined with the space‐ and temperature‐dependent heat generation/absorption on the flow of polar nanofluid over an elongating surface. The surface is considered to be permeable for which the hydromagnetic flow in the presence of thermal radiation specifically, Brownian and thermophoresis affects the flow phenomena significantly. The proposed flow model designed with the aforementioned physical properties is standardized into the set of nonlinear ordinary equations by the implementation of suitable similarity rules. Further, the characteristics of various physical quantities are deployed by solving the system by using traditional Rung–Kutta fourth‐order technique. Further, the analysis of several factors is deployed briefly via graphically, and simulation of rate coefficients is presented through tables. The important outcomes of the study are deployed as the inclusion of thermal and solutal buoyancy enhances the velocity distribution, whereas reverse impact is observed for the increasing inertial drag. Also, space‐ and temperature‐dependent heat source augments the temperature profile but Lewis number decelerates the fluid concentration significantly.
{"title":"Inertial drag combined with non‐uniform heat generation/absorption effects on the hydromagnetic flow of polar nanofluid over an elongating permeable surface due to the impose of chemical reaction","authors":"Subhajit Panda, Pradyumna Kumar Pattnaik, Rupa Baithalu, Satya Ranjan Mishra","doi":"10.1002/zamm.202301058","DOIUrl":"https://doi.org/10.1002/zamm.202301058","url":null,"abstract":"The pivotal role of Brownian and thermophoresis in investigating the flow characteristic of polar nanofluid is important nowadays due to various engineering applications. The enhanced thermal and transport properties in the field of biomedical nanomedicine for hyperthermia treatments, and for enhancing the efficiency of heat exchange processes in cooling electronic devices, heat exchangers, and automotive engines the use of Brownian and thermophoresis is important. Therefore, the present study reveals the importance of Darcy–Forchheimer inertial drag combined with the space‐ and temperature‐dependent heat generation/absorption on the flow of polar nanofluid over an elongating surface. The surface is considered to be permeable for which the hydromagnetic flow in the presence of thermal radiation specifically, Brownian and thermophoresis affects the flow phenomena significantly. The proposed flow model designed with the aforementioned physical properties is standardized into the set of nonlinear ordinary equations by the implementation of suitable similarity rules. Further, the characteristics of various physical quantities are deployed by solving the system by using traditional Rung–Kutta fourth‐order technique. Further, the analysis of several factors is deployed briefly via graphically, and simulation of rate coefficients is presented through tables. The important outcomes of the study are deployed as the inclusion of thermal and solutal buoyancy enhances the velocity distribution, whereas reverse impact is observed for the increasing inertial drag. Also, space‐ and temperature‐dependent heat source augments the temperature profile but Lewis number decelerates the fluid concentration significantly.","PeriodicalId":501230,"journal":{"name":"ZAMM - Journal of Applied Mathematics and Mechanics","volume":"95 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141937877","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 study presents an analysis of Ree–Eyring tri‐hybrid nanofluid flow between two expanding/contracting disks with permeable walls by applying the computing power of Levenberg–Marquardt supervised neural networks (LM‐SNNs). The effects of thermal radiation, Brownian motion, and thermophoresis were also thoroughly examined. The results are presented for tri‐hybrid nanofluid with SWCNT and MWCNT and Fe2O3 and H2O base fluid. The coupled non‐linear PDE system is transformed into a system of ODE associated with convective boundary conditions by applying the appropriate transformations. This is then accomplished numerically by using the finite difference‐based BVP‐4c MATLAB code that implements the three‐stage Lobatto IIIA formula. The results are novel and have been validated with LM‐SNNs outcomes. It has been observed that both numerical outcomes and LM‐SNNs produce equivalent results, and both approaches exhibit a drop in the velocity profile for the magnetic field near the lower plate and a rise near the upper plate. The skin friction against the Prandtl number increases, whereas the Nusselt number decreases at the upper disc. Compared to BVP‐4c numerical approaches, the given LM‐SNNs model is more dependable, efficient, and time‐saving because it requires less work and produces results quickly.
{"title":"Exploring the influence of morphology on magnetized Ree–Eyring tri‐hybrid nanofluid flow between orthogonally moving coaxial disks using artificial neural networks with Levenberg–Marquardt scheme","authors":"Abdul Rauf, Hafiza Khadija Khan, Nehad Ali Shah","doi":"10.1002/zamm.202400147","DOIUrl":"https://doi.org/10.1002/zamm.202400147","url":null,"abstract":"The present study presents an analysis of Ree–Eyring tri‐hybrid nanofluid flow between two expanding/contracting disks with permeable walls by applying the computing power of Levenberg–Marquardt supervised neural networks (LM‐SNNs). The effects of thermal radiation, Brownian motion, and thermophoresis were also thoroughly examined. The results are presented for tri‐hybrid nanofluid with SWCNT and MWCNT and Fe<jats:sub>2</jats:sub>O<jats:sub>3</jats:sub> and H<jats:sub>2</jats:sub>O base fluid. The coupled non‐linear PDE system is transformed into a system of ODE associated with convective boundary conditions by applying the appropriate transformations. This is then accomplished numerically by using the finite difference‐based BVP‐4c MATLAB code that implements the three‐stage Lobatto IIIA formula. The results are novel and have been validated with LM‐SNNs outcomes. It has been observed that both numerical outcomes and LM‐SNNs produce equivalent results, and both approaches exhibit a drop in the velocity profile for the magnetic field near the lower plate and a rise near the upper plate. The skin friction against the Prandtl number increases, whereas the Nusselt number decreases at the upper disc. Compared to BVP‐4c numerical approaches, the given LM‐SNNs model is more dependable, efficient, and time‐saving because it requires less work and produces results quickly.","PeriodicalId":501230,"journal":{"name":"ZAMM - Journal of Applied Mathematics and Mechanics","volume":"78 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141937878","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 research presents an analytical study of magnetohydrodynamics (MHD)‐free convective heat and mass transfer flow of a nanofluid bounded by a semi‐infinite flat plate. A magnetic field of strength is applied throughout the fluid region. The plate is moving with a constant velocity , temperature, and the concentration are assumed to be fluctuating with time harmonically from a constant mean at the plate. The frontier equations are assumed to be of an oscillatory nature and cracked analytically using the perturbation technique. The novelty of the present work is to examine the heat and mass transfer MHD flow for Cu‐water and TiO2‐water nanofluids in the presence of thermal radiation. The influence of physical parameters on the flow domain is described in the discussions by graphically and in tabular form. It was found that the fluid temperature and skin friction were reduced with the increased values of the radiation parameters for Cu‐water and TiO2‐water nanofluids. Also, it is noticed that the concentration boundary layer thickness decreases with an increase in chemical reaction parameters.
{"title":"MHD free convective heat and mass transfer flow passing through semi‐infinite plate for Cu‐water and TiO2‐water nanofluids in presence of radiation embedded in porous medium","authors":"Kangkan Choudhury, Sweety Sharma","doi":"10.1002/zamm.202300851","DOIUrl":"https://doi.org/10.1002/zamm.202300851","url":null,"abstract":"This research presents an analytical study of magnetohydrodynamics (MHD)‐free convective heat and mass transfer flow of a nanofluid bounded by a semi‐infinite flat plate. A magnetic field of strength is applied throughout the fluid region. The plate is moving with a constant velocity , temperature, and the concentration are assumed to be fluctuating with time harmonically from a constant mean at the plate. The frontier equations are assumed to be of an oscillatory nature and cracked analytically using the perturbation technique. The novelty of the present work is to examine the heat and mass transfer MHD flow for Cu‐water and TiO<jats:sub>2</jats:sub>‐water nanofluids in the presence of thermal radiation. The influence of physical parameters on the flow domain is described in the discussions by graphically and in tabular form. It was found that the fluid temperature and skin friction were reduced with the increased values of the radiation parameters for Cu‐water and TiO<jats:sub>2</jats:sub>‐water nanofluids. Also, it is noticed that the concentration boundary layer thickness decreases with an increase in chemical reaction parameters.","PeriodicalId":501230,"journal":{"name":"ZAMM - Journal of Applied Mathematics and Mechanics","volume":"20 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141937930","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}
Subrat Kumar Jena, S. Pradyumna, S. Chakraverty, Mohamed A. Eltaher
This research employs Chebyshev–Ritz method along with Navier's method to investigate the vibration characteristics of a nanobeam subject to a longitudinal magnetic field and linear hygroscopic environment. The nanobeam is characterized by a Winkler–Pasternak elastic foundation and follows the nonlocal Euler–Bernoulli beam theory. The governing equation of motion is derived using Hamilton's principle, and non‐dimensional frequency parameters are computed for Simply Supported‐Simply Supported (SS), Clamped‐Clamped (CC), and Clamped‐Free (CF) boundary conditions. The motivation behind this study is to provide a comprehensive and efficient analytical framework for understanding the dynamic behavior of nanobeams in complex environments. By investigating the influence of magnetic and hygroscopic factors on the vibration characteristics of nanobeams, this research aims to offer valuable insights for the design and optimization of nanoscale structures. Employing shifted Chebyshev polynomials as shape functions in Chebyshev–Ritz method offers several advantages in the proposed model. Firstly, these polynomials possess orthogonal properties, which can significantly enhance computational efficiency. The orthogonality of shifted Chebyshev polynomials allow for simpler and more streamlined numerical computations compared to non‐orthogonal basis functions. Additionally, the orthogonality ensures that the resulting system of equations is well‐conditioned, even for higher‐order polynomial approximations. A closed‐form solution for SS boundary condition is obtained through Navier's method. Convergence analysis is performed to validate the accuracy and effectiveness of the proposed model against existing models. The non‐dimensional frequency parameters obtained using both Navier's method and Chebyshev–Ritz method demonstrate strong agreement, further validating the proposed nanobeam model. Additionally, a comprehensive parametric study evaluates the impact of various characteristics, including the small‐scale parameter, Winkler modulus, shear modulus, magnetic parameter, and hygroscopic parameter. The findings contribute to a nuanced understanding of nanobeam vibrations under the influence of a magnetic field and hygroscopic environment, providing valuable insights for the design and optimization of nanoscale structures in practical applications.
本研究采用 Chebyshev-Ritz 方法和 Navier 方法研究了纳米梁在纵向磁场和线性吸湿环境下的振动特性。纳米梁以温克勒-帕斯捷尔纳克弹性基础为特征，并遵循非局部欧拉-伯努利梁理论。利用汉密尔顿原理推导了支配运动方程，并计算了简支-简支（SS）、夹紧-夹紧（CC）和无夹紧（CF）边界条件下的非尺寸频率参数。这项研究的动机是为理解纳米梁在复杂环境中的动态行为提供一个全面、高效的分析框架。通过研究磁性和吸湿性因素对纳米梁振动特性的影响，本研究旨在为纳米结构的设计和优化提供有价值的见解。在切比雪夫-里兹方法中采用移位切比雪夫多项式作为形状函数，为所提出的模型提供了几个优势。首先，这些多项式具有正交特性，可显著提高计算效率。与非正交基函数相比，移位切比雪夫多项式的正交性使数值计算更简单、更流畅。此外，正交性还能确保所得到的方程系统具有良好的条件，即使对于高阶多项式近似也是如此。通过纳维法，可以得到 SS 边界条件的闭式解。通过收敛分析，验证了所提模型与现有模型相比的准确性和有效性。使用纳维法和切比雪夫-里兹法获得的非尺寸频率参数显示出很强的一致性，进一步验证了所提出的纳米梁模型。此外，一项全面的参数研究评估了各种特性的影响，包括小尺度参数、温克勒模量、剪切模量、磁参数和吸湿参数。研究结果有助于深入理解纳米梁在磁场和吸湿环境影响下的振动，为实际应用中纳米结构的设计和优化提供了宝贵的见解。
{"title":"Chebyshev–Ritz and Navier's methods for hygro‐magneto vibration of Euler–Bernoulli nanobeam resting on Winkler–Pasternak elastic foundation","authors":"Subrat Kumar Jena, S. Pradyumna, S. Chakraverty, Mohamed A. Eltaher","doi":"10.1002/zamm.202400196","DOIUrl":"https://doi.org/10.1002/zamm.202400196","url":null,"abstract":"This research employs Chebyshev–Ritz method along with Navier's method to investigate the vibration characteristics of a nanobeam subject to a longitudinal magnetic field and linear hygroscopic environment. The nanobeam is characterized by a Winkler–Pasternak elastic foundation and follows the nonlocal Euler–Bernoulli beam theory. The governing equation of motion is derived using Hamilton's principle, and non‐dimensional frequency parameters are computed for Simply Supported‐Simply Supported (SS), Clamped‐Clamped (CC), and Clamped‐Free (CF) boundary conditions. The motivation behind this study is to provide a comprehensive and efficient analytical framework for understanding the dynamic behavior of nanobeams in complex environments. By investigating the influence of magnetic and hygroscopic factors on the vibration characteristics of nanobeams, this research aims to offer valuable insights for the design and optimization of nanoscale structures. Employing shifted Chebyshev polynomials as shape functions in Chebyshev–Ritz method offers several advantages in the proposed model. Firstly, these polynomials possess orthogonal properties, which can significantly enhance computational efficiency. The orthogonality of shifted Chebyshev polynomials allow for simpler and more streamlined numerical computations compared to non‐orthogonal basis functions. Additionally, the orthogonality ensures that the resulting system of equations is well‐conditioned, even for higher‐order polynomial approximations. A closed‐form solution for SS boundary condition is obtained through Navier's method. Convergence analysis is performed to validate the accuracy and effectiveness of the proposed model against existing models. The non‐dimensional frequency parameters obtained using both Navier's method and Chebyshev–Ritz method demonstrate strong agreement, further validating the proposed nanobeam model. Additionally, a comprehensive parametric study evaluates the impact of various characteristics, including the small‐scale parameter, Winkler modulus, shear modulus, magnetic parameter, and hygroscopic parameter. The findings contribute to a nuanced understanding of nanobeam vibrations under the influence of a magnetic field and hygroscopic environment, providing valuable insights for the design and optimization of nanoscale structures in practical applications.","PeriodicalId":501230,"journal":{"name":"ZAMM - Journal of Applied Mathematics and Mechanics","volume":"75 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141886799","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}
Ram Prakash Sharma, Pudhari Srilatha, Om Prakash, R. S. Varun Kumar
The present analysis considers the angular velocities of the free flow and the arbitrarily fluctuating cone over time, leading to an unsteady stream over a rotating cone in a rotating nanofluid. The effects of heat source/sink and magnetic field on an unsteady flow past a rotating cone in a rotating nanoliquid are considered in this examination. The dimensional governing equations are transformed into nondimensional ordinary differential equations (ODEs) using the similarity variables. The nonlinear system of ODEs has been solved using the Hosoya polynomial‐based collocation method (HPBCM), and the obtained values are compared with the numerical method Runge Kutta Fehlberg's fourth‐fifth order (RKF‐45) scheme. The effects of numerous factors on the momentum and thermal distributions are shown graphically. Results reveal that the ratio of the cone angular velocity to the free stream angular velocity increases the velocity profile but converse trend is seen for the thermal profile. The upsurge in the values of the magnetic parameter intensifies the velocity profile. The rise in the values of the heat source/sink parameter upsurges the thermal profile. As the unsteady parameter increases temperature profile declines.
{"title":"Influence of heat source/sink on a rotating cone in a rotating nanofluid with magnetic field impact: Application of Hosoya polynomial‐based collocation method","authors":"Ram Prakash Sharma, Pudhari Srilatha, Om Prakash, R. S. Varun Kumar","doi":"10.1002/zamm.202400294","DOIUrl":"https://doi.org/10.1002/zamm.202400294","url":null,"abstract":"The present analysis considers the angular velocities of the free flow and the arbitrarily fluctuating cone over time, leading to an unsteady stream over a rotating cone in a rotating nanofluid. The effects of heat source/sink and magnetic field on an unsteady flow past a rotating cone in a rotating nanoliquid are considered in this examination. The dimensional governing equations are transformed into nondimensional ordinary differential equations (ODEs) using the similarity variables. The nonlinear system of ODEs has been solved using the Hosoya polynomial‐based collocation method (HPBCM), and the obtained values are compared with the numerical method Runge Kutta Fehlberg's fourth‐fifth order (RKF‐45) scheme. The effects of numerous factors on the momentum and thermal distributions are shown graphically. Results reveal that the ratio of the cone angular velocity to the free stream angular velocity increases the velocity profile but converse trend is seen for the thermal profile. The upsurge in the values of the magnetic parameter intensifies the velocity profile. The rise in the values of the heat source/sink parameter upsurges the thermal profile. As the unsteady parameter increases temperature profile declines.","PeriodicalId":501230,"journal":{"name":"ZAMM - Journal of Applied Mathematics and Mechanics","volume":"6 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141880421","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}
Thimlapura Nagaraju Tanuja, Linganna Kavitha, Pudhari Srilatha, Umair Khan, Sibyala Vijaykumar Varma, Rangaswamy Naveen Kumar, Amal Abdulrahman, Mohammed Modather Mohammed Abdou
The magnetohydrodynamic (MHD) movement of fluids through a porous material has a variety of uses such as distillation towers, heat exchangers, catalytic processes, magnetic field‐based wound treatments, cancer therapy and hyperthermia. This paper explores the complex dynamics of a three‐phase flow utilizing MHD Jeffrey fluid, which sits in between nano and hybrid (molybdenum disulphide [MoS2] and multi‐walled carbon nanotubes [MWCNTs]) nanofluids. The governing differential equations are derived for the physical flow model. The equations are reduced to dimensionless equations by using dimensionless parameters. The resultant equations are solved by using the regular perturbation technique. The results are analysed for various physical pertinent parameters through 2D/3D graphs. The heat transfer rate and volume flow rate are calculated for the left and right plates. This analysis also considers how the system's overall behaviour would be affected by radiation and dissipation effects. The results indicate that the magnetic parameter, electric parameter, quadratic convective parameter, Brinkman number and Grashof number significantly affect heat transfer enhancement. Fluid velocity can be reduced using radiation parameters, porosity, electric and magnetic parameters and velocity declines by Jeffrey parameters.
{"title":"Effects of dissipation and radiation on the Jeffrey fluid flow in between nano and hybrid nanofluid subject to porous medium","authors":"Thimlapura Nagaraju Tanuja, Linganna Kavitha, Pudhari Srilatha, Umair Khan, Sibyala Vijaykumar Varma, Rangaswamy Naveen Kumar, Amal Abdulrahman, Mohammed Modather Mohammed Abdou","doi":"10.1002/zamm.202300852","DOIUrl":"https://doi.org/10.1002/zamm.202300852","url":null,"abstract":"The magnetohydrodynamic (MHD) movement of fluids through a porous material has a variety of uses such as distillation towers, heat exchangers, catalytic processes, magnetic field‐based wound treatments, cancer therapy and hyperthermia. This paper explores the complex dynamics of a three‐phase flow utilizing MHD Jeffrey fluid, which sits in between nano and hybrid (molybdenum disulphide [MoS<jats:sub>2</jats:sub>] and multi‐walled carbon nanotubes [MWCNTs]) nanofluids. The governing differential equations are derived for the physical flow model. The equations are reduced to dimensionless equations by using dimensionless parameters. The resultant equations are solved by using the regular perturbation technique. The results are analysed for various physical pertinent parameters through 2D/3D graphs. The heat transfer rate and volume flow rate are calculated for the left and right plates. This analysis also considers how the system's overall behaviour would be affected by radiation and dissipation effects. The results indicate that the magnetic parameter, electric parameter, quadratic convective parameter, Brinkman number and Grashof number significantly affect heat transfer enhancement. Fluid velocity can be reduced using radiation parameters, porosity, electric and magnetic parameters and velocity declines by Jeffrey parameters.","PeriodicalId":501230,"journal":{"name":"ZAMM - Journal of Applied Mathematics and Mechanics","volume":"78 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141886800","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}
Flank D. M. Bezerra, Severino H. da Silva, Vando Narciso
In this paper, we consider a peridynamic model with energy damping inspired by the works of Balakrishnan and Taylor on “damping models” based on the instantaneous total energy of the system. We study the asymptotic behavior of solutions, in the sense of attractors, of these peridynamic models in suitable phase space; more precisely, we prove a result of existence and characterization of compact global attractors with a nonlinear strongly continuous semigroup approach based in the asymptotic smoothness property thanks to Chueshov and Lasiecka and Nakao's lemma.
{"title":"Asymptotic smoothness effects and global attractor for a peridynamic model with energy damping","authors":"Flank D. M. Bezerra, Severino H. da Silva, Vando Narciso","doi":"10.1002/zamm.202400187","DOIUrl":"https://doi.org/10.1002/zamm.202400187","url":null,"abstract":"In this paper, we consider a peridynamic model with energy damping inspired by the works of Balakrishnan and Taylor on “damping models” based on the instantaneous total energy of the system. We study the asymptotic behavior of solutions, in the sense of attractors, of these peridynamic models in suitable phase space; more precisely, we prove a result of existence and characterization of compact global attractors with a nonlinear strongly continuous semigroup approach based in the asymptotic smoothness property thanks to Chueshov and Lasiecka and Nakao's lemma.","PeriodicalId":501230,"journal":{"name":"ZAMM - Journal of Applied Mathematics and Mechanics","volume":"146 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141862981","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}
Sourav Kumar Panja, Samim Alam, Subhas Chandra Mandal
This article presents an extensive analytical solution addressing the interaction between two non‐identical edge cracks in an infinite orthotropic strip under anti‐plane shear waves. Most studies assume identical cracks or single edge crack in a strip, but this research breaks new ground by considering cracks of different sizes. By incorporating mixed‐type boundary conditions, the study derives dual integral equations. These equations are then transformed into a singular integral equation of Cauchy type with the aid of a trial solution and contour integration technique. The singular integral equation is further converted into a system of integral equations, which are solved numerically utilizing Jacobi polynomials. The obtained solutions are utilized to derive expressions for the stress intensity factor (SIF) and crack opening displacement (COD) at the crack tip using Krenk's interpolation formulae. The derived results are presented graphically and compared against existing solutions for single edge crack and symmetric edge cracks in static scenario.
{"title":"Analytical solution of two non‐identical edge cracks in an infinite strip under anti‐plane shear wave","authors":"Sourav Kumar Panja, Samim Alam, Subhas Chandra Mandal","doi":"10.1002/zamm.202400162","DOIUrl":"https://doi.org/10.1002/zamm.202400162","url":null,"abstract":"This article presents an extensive analytical solution addressing the interaction between two non‐identical edge cracks in an infinite orthotropic strip under anti‐plane shear waves. Most studies assume identical cracks or single edge crack in a strip, but this research breaks new ground by considering cracks of different sizes. By incorporating mixed‐type boundary conditions, the study derives dual integral equations. These equations are then transformed into a singular integral equation of Cauchy type with the aid of a trial solution and contour integration technique. The singular integral equation is further converted into a system of integral equations, which are solved numerically utilizing Jacobi polynomials. The obtained solutions are utilized to derive expressions for the stress intensity factor (SIF) and crack opening displacement (COD) at the crack tip using Krenk's interpolation formulae. The derived results are presented graphically and compared against existing solutions for single edge crack and symmetric edge cracks in static scenario.","PeriodicalId":501230,"journal":{"name":"ZAMM - Journal of Applied Mathematics and Mechanics","volume":"75 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141862980","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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