Pub Date : 2024-09-26DOI: 10.1016/j.padiff.2024.100934
A.A. Kashchenko, I.S. Luzin
In this paper, we study the dynamics of a system of nonlinear differential equations with delay. We find stable equilibrium states and regions of attraction to them in the phase space of the system, as well as stable and unstable homogeneous and inhomogeneous cycles. We find conditions on the parameters of the system for multistability. We show that the coupling parameter has a decisive influence on the dynamics of the system. We find regions of the parameters of the system and extensive sets of initial conditions such that if we take these values of the parameters and any initial conditions from these sets, the system will have simple dynamics.
{"title":"Dynamics of the system of delay differential equations with nonlinearity having a simple behavior at infinity","authors":"A.A. Kashchenko, I.S. Luzin","doi":"10.1016/j.padiff.2024.100934","DOIUrl":"10.1016/j.padiff.2024.100934","url":null,"abstract":"<div><div>In this paper, we study the dynamics of a system of nonlinear differential equations with delay. We find stable equilibrium states and regions of attraction to them in the phase space of the system, as well as stable and unstable homogeneous and inhomogeneous cycles. We find conditions on the parameters of the system for multistability. We show that the coupling parameter has a decisive influence on the dynamics of the system. We find regions of the parameters of the system and extensive sets of initial conditions such that if we take these values of the parameters and any initial conditions from these sets, the system will have simple dynamics.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"12 ","pages":"Article 100934"},"PeriodicalIF":0.0,"publicationDate":"2024-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142419539","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-25DOI: 10.1016/j.padiff.2024.100942
Rasel Islam, M. Abul Kawser, M. Sohel Rana, M. Nurul Islam
In this article, we investigate the space-time Klein-Gordon (KG) model, a significant framework in quantum field theory and quantum mechanics, which also describes phenomena such as wave propagation in crystal dislocations. This model is particularly important in high-energy particle physics. The novelty of this article is to examine the sufficient, useful in optical fibers, and further general soliton solutions of the nonlinear KG model using the generalized exponential rational function method (GERFM), which do not exist in the recent literature. The fractional complex wave transformation is utilized to turn the model into a nonlinear form, and the accuracy of the acquired solutions is confirmed by reintroducing them into the original models using Mathematica. The obtained solutions are expressed in hyperbolic, exponential, rational, and trigonometric forms. We elucidate the fractional effects for specific parameter values, accompanied by illustrative figures. Our results demonstrate that GERFM is effective, powerful, and versatile, providing exact traveling wave solutions for various nonlinear models in engineering and mathematical physics. Our findings reveal that the characteristics of soliton-shaped waves in both three-dimensional and two-dimensional contexts are profoundly influenced by fractional order derivative. This study advances the understanding of nonlinear wave dynamics and offers a robust method for solving complex physical models.
在这篇文章中，我们研究了时空克莱因-戈登（KG）模型，它是量子场论和量子力学的一个重要框架，也描述了晶体位错中的波传播等现象。该模型在高能粒子物理学中尤为重要。本文的新颖之处在于利用广义指数有理函数法（GERFM）研究了非线性 KG 模型的充分解、光纤中的有用解以及进一步的一般孤子解，而这些解在最近的文献中并不存在。利用分数复波变换将模型转化为非线性形式，并通过使用 Mathematica 将获得的解重新引入原始模型来确认其准确性。获得的解以双曲、指数、有理和三角形式表示。我们阐明了特定参数值的分数效应，并附有说明性数字。我们的研究结果表明，GERFM 有效、强大且用途广泛，能为工程和数学物理中的各种非线性模型提供精确的行波解。我们的研究结果表明，孤子形波在三维和二维环境中的特性深受分数阶导数的影响。这项研究加深了人们对非线性波动力学的理解，并为复杂物理模型的求解提供了一种稳健的方法。
{"title":"Mathematical analysis of soliton solutions in space-time fractional Klein-Gordon model with generalized exponential rational function method","authors":"Rasel Islam, M. Abul Kawser, M. Sohel Rana, M. Nurul Islam","doi":"10.1016/j.padiff.2024.100942","DOIUrl":"10.1016/j.padiff.2024.100942","url":null,"abstract":"<div><div>In this article, we investigate the space-time Klein-Gordon (KG) model, a significant framework in quantum field theory and quantum mechanics, which also describes phenomena such as wave propagation in crystal dislocations. This model is particularly important in high-energy particle physics. The novelty of this article is to examine the sufficient, useful in optical fibers, and further general soliton solutions of the nonlinear KG model using the generalized exponential rational function method (GERFM), which do not exist in the recent literature. The fractional complex wave transformation is utilized to turn the model into a nonlinear form, and the accuracy of the acquired solutions is confirmed by reintroducing them into the original models using Mathematica. The obtained solutions are expressed in hyperbolic, exponential, rational, and trigonometric forms. We elucidate the fractional effects for specific parameter values, accompanied by illustrative figures. Our results demonstrate that GERFM is effective, powerful, and versatile, providing exact traveling wave solutions for various nonlinear models in engineering and mathematical physics. Our findings reveal that the characteristics of soliton-shaped waves in both three-dimensional and two-dimensional contexts are profoundly influenced by fractional order derivative. This study advances the understanding of nonlinear wave dynamics and offers a robust method for solving complex physical models.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"12 ","pages":"Article 100942"},"PeriodicalIF":0.0,"publicationDate":"2024-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142357948","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
HIV/AIDS remains one of the main global causes of morbidity and mortality. While antiretroviral drugs are still the only treatment for HIV patients, their accessibility and efficient delivery in resource-poor nations constitute a major concern, and no epidemiological model has considered this. Based on this, we create a model for HIV/AIDS that considers condoms and vaginal microbicides alongside saturated treatment. We consider the constant control case, in which theoretical results show that the delay factor in the antiretroviral therapy (ART) regimen can induce backward bifurcation, which consequently distorts the global effort to end HIV incidence. We use the Castillo-Chavez stability to ensure that the disease-free equilibrium is globally asymptotically stable whenever the associated reproduction number is less than one. Uncertainty and sensitivity analysis using the Latin hypercube sampling technique was also carried out on the parameters and state variables of the model equations, and the result shows that half of the most highly influential parameters are capable of reducing cases of HIV and AIDS. For time-dependent control cases, our findings suggest that, in countries with low income, directing resources to either condom use or vaginal microbicides is more effective than a regular intake of antiretrovirals alone. Furthermore, results without ART delay have shown to be more effective in HIV control than others where the inaccessibility of the therapy encouraged outbursts of AIDS cases. Thus, as reliable as antiretrovirals are in HIV/AIDS treatment, early administration and regular intake are key to their continued success.
{"title":"Nonlinear dynamics model of HIV/AIDS: Assessing the impacts of condoms, vaginal microbicides, and optimized treatment","authors":"Reuben Iortyer Gweryina , Cicik Alfiniyah , Chinwendu Emilian Madubueze , Kenneth Ojotogba Achema","doi":"10.1016/j.padiff.2024.100933","DOIUrl":"10.1016/j.padiff.2024.100933","url":null,"abstract":"<div><div>HIV/AIDS remains one of the main global causes of morbidity and mortality. While antiretroviral drugs are still the only treatment for HIV patients, their accessibility and efficient delivery in resource-poor nations constitute a major concern, and no epidemiological model has considered this. Based on this, we create a model for HIV/AIDS that considers condoms and vaginal microbicides alongside saturated treatment. We consider the constant control case, in which theoretical results show that the delay factor in the antiretroviral therapy (ART) regimen can induce backward bifurcation, which consequently distorts the global effort to end HIV incidence. We use the Castillo-Chavez stability to ensure that the disease-free equilibrium is globally asymptotically stable whenever the associated reproduction number is less than one. Uncertainty and sensitivity analysis using the Latin hypercube sampling technique was also carried out on the parameters and state variables of the model equations, and the result shows that half of the most highly influential parameters are capable of reducing cases of HIV and AIDS. For time-dependent control cases, our findings suggest that, in countries with low income, directing resources to either condom use or vaginal microbicides is more effective than a regular intake of antiretrovirals alone. Furthermore, results without ART delay have shown to be more effective in HIV control than others where the inaccessibility of the therapy encouraged outbursts of AIDS cases. Thus, as reliable as antiretrovirals are in HIV/AIDS treatment, early administration and regular intake are key to their continued success.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"12 ","pages":"Article 100933"},"PeriodicalIF":0.0,"publicationDate":"2024-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142357949","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-24DOI: 10.1016/j.padiff.2024.100918
Mutaz Mohammad , Alexander Trounev
This paper presents innovative numerical methodologies designed to solve challenging time fractional partial differential equations, with a focus on the Burgers’, Fisher–KPP, and nonlinear Schrödinger equations. By employing advanced wavelet techniques integrated with fractional calculus, we achieve highly accurate solutions, surpassing conventional methods with minimal absolute error in numerical simulations. A thorough series of numerical experiments validates the robustness and effectiveness of our approach across various parameter regimes and initial conditions. The results underscore significant advancements in the computational modeling of complex physical phenomena governed by time fractional dynamics and offering a powerful tool for a wide range of applications in science and engineering.
{"title":"Computational precision in time fractional PDEs: Euler wavelets and novel numerical techniques","authors":"Mutaz Mohammad , Alexander Trounev","doi":"10.1016/j.padiff.2024.100918","DOIUrl":"10.1016/j.padiff.2024.100918","url":null,"abstract":"<div><div>This paper presents innovative numerical methodologies designed to solve challenging time fractional partial differential equations, with a focus on the Burgers’, Fisher–KPP, and nonlinear Schrödinger equations. By employing advanced wavelet techniques integrated with fractional calculus, we achieve highly accurate solutions, surpassing conventional methods with minimal absolute error in numerical simulations. A thorough series of numerical experiments validates the robustness and effectiveness of our approach across various parameter regimes and initial conditions. The results underscore significant advancements in the computational modeling of complex physical phenomena governed by time fractional dynamics and offering a powerful tool for a wide range of applications in science and engineering.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"12 ","pages":"Article 100918"},"PeriodicalIF":0.0,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142357869","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-24DOI: 10.1016/j.padiff.2024.100941
Rupa Baithalu , Subhajit Panda , P.K. Pattnaik , S.R. Mishra
Magnetized hybrid nanofluid combined with ferrite and silver in a blood-based liquid presents their vital role in several aspects such as artificial heart pumping system, drug delivery process, the flow of blood in the artery, etc. This is because the high heat transportation rate of the nanofluid is caused by the inclusion of nanoparticles. The current investigation is based on the characteristic of particle concentration comprised of Fe3O4 and Ag in the base liquid blood that passed in between two infinite parallel disks filled with porous matrix. The electrically conducting fluid associated to maximum of 1.5 % of volume concentration from each of the solid particles affects the flow phenomena. However, the impact of thermal radiation vis-à-vis the heat dissipation provides efficient heat transport properties with the inclusion of the effective thermal conductivity assumed from the Hamilton-Crosser model. The proposed conductivity model describes the role of particle shapes on the enhanced thermal properties. Further, numerical treatment is obtained for the transformed designed problem following similarity rules that are used for the conversion of the governing equations into their non-dimensional form. The computation of various flow profiles leads to get the entropy generation due to the irreversibility processes. Along with the fluid velocity and temperature distributions, the study is carried out for the entropy as well as the computation of Bejan number and afterwards the simulation of the shear and heat transportation rate are also depicted graphically. The main finding of the proposed study is that solid particle concentrations have a substantial impact to increasing fluid velocity in magnitude, resulting in a narrower wall thickness at both channel walls. Thermal radiation was shown to be more effective at increasing entropy generation and Bejan value.
在血液基液体中加入铁氧体和银的磁化混合纳米流体在人工心脏泵送系统、药物输送过程、动脉血流等多个方面发挥了重要作用。这是因为纳米粒子的加入导致了纳米流体的高热传输率。目前的研究基于在两个充满多孔基质的无限平行圆盘之间流动的血液基液中由 Fe3O4 和 Ag 组成的颗粒浓度特征。每种固体颗粒体积浓度最大为 1.5% 的导电流体会影响流动现象。然而，热辐射对散热的影响通过加入汉密尔顿-克罗斯模型假定的有效热传导率提供了有效的热传输特性。所提出的导热模型描述了颗粒形状对增强热特性的作用。此外，还根据相似性规则对转化后的设计问题进行了数值处理，这些规则用于将控制方程转换为非维度形式。通过对各种流动剖面的计算，可以得到由于不可逆过程而产生的熵。在研究流体速度和温度分布的同时，还研究了熵和贝扬数的计算，之后还以图形方式描述了剪切力和热传输率的模拟。拟议研究的主要发现是，固体颗粒浓度对增加流体速度的幅度有很大影响，导致两个通道壁的壁厚变窄。热辐射在增加熵生成和贝扬值方面更为有效。
{"title":"Entropy analysis in magnetized blood-based hybrid nanofluid flow via parallel disks","authors":"Rupa Baithalu , Subhajit Panda , P.K. Pattnaik , S.R. Mishra","doi":"10.1016/j.padiff.2024.100941","DOIUrl":"10.1016/j.padiff.2024.100941","url":null,"abstract":"<div><div>Magnetized hybrid nanofluid combined with ferrite and silver in a blood-based liquid presents their vital role in several aspects such as artificial heart pumping system, drug delivery process, the flow of blood in the artery, etc. This is because the high heat transportation rate of the nanofluid is caused by the inclusion of nanoparticles. The current investigation is based on the characteristic of particle concentration comprised of Fe<sub>3</sub>O<sub>4</sub> and Ag in the base liquid blood that passed in between two infinite parallel disks filled with porous matrix. The electrically conducting fluid associated to maximum of 1.5 % of volume concentration from each of the solid particles affects the flow phenomena. However, the impact of thermal radiation vis-à-vis the heat dissipation provides efficient heat transport properties with the inclusion of the effective thermal conductivity assumed from the Hamilton-Crosser model. The proposed conductivity model describes the role of particle shapes on the enhanced thermal properties. Further, numerical treatment is obtained for the transformed designed problem following similarity rules that are used for the conversion of the governing equations into their non-dimensional form. The computation of various flow profiles leads to get the entropy generation due to the irreversibility processes. Along with the fluid velocity and temperature distributions, the study is carried out for the entropy as well as the computation of Bejan number and afterwards the simulation of the shear and heat transportation rate are also depicted graphically. The main finding of the proposed study is that solid particle concentrations have a substantial impact to increasing fluid velocity in magnitude, resulting in a narrower wall thickness at both channel walls. Thermal radiation was shown to be more effective at increasing entropy generation and Bejan value.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"12 ","pages":"Article 100941"},"PeriodicalIF":0.0,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142357870","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-24DOI: 10.1016/j.padiff.2024.100940
Pradeep Kumar , A Felicita , Ajaykumar AR , Qasem Al-Mdallal
The current article discloses the influence of the hyperbolic tangent nanofluid on time dependent flow through a microchannel when a magnetic field is applied. The porous medium was incorporated using the Darcy–Forchheimer model. The chemical reaction is explained by Arrhenius activation energy. Temperature is determined by convective boundary conditions. The irreversibility occurring in the flow is analyzed. The modeled problem gives rise to partial differential equations, which are computed by finite difference method. Response surface methodology, an optimization technique, is used to attain the optimal conditions for entropy generated for the flow of fluid. Results of the analysis reveal that concentration decreases with the rise in reaction rate parameter and increases with activation energy parameter. Prandtl and Eckert numbers, with their increase, enhance entropy, and fluid friction irreversibility is at its highest. Perfect co-relation is attained for the model by the response surface methodology, with a co-relation coefficient of 100 %. The Weissenberg number is highly sensitive to change in the present modeling, followed by Darcy and Reynolds numbers. The Reynolds number and Darcy number show positive sensitivity, while the Weissenberg number shows negative sensitivity to the entropy generated.
{"title":"Numerical illustration using finite difference method for the transient flow through porous microchannel and statistical interpretation of entropy using response surface methodology","authors":"Pradeep Kumar , A Felicita , Ajaykumar AR , Qasem Al-Mdallal","doi":"10.1016/j.padiff.2024.100940","DOIUrl":"10.1016/j.padiff.2024.100940","url":null,"abstract":"<div><div>The current article discloses the influence of the hyperbolic tangent nanofluid on time dependent flow through a microchannel when a magnetic field is applied. The porous medium was incorporated using the Darcy–Forchheimer model. The chemical reaction is explained by Arrhenius activation energy. Temperature is determined by convective boundary conditions. The irreversibility occurring in the flow is analyzed. The modeled problem gives rise to partial differential equations, which are computed by finite difference method. Response surface methodology, an optimization technique, is used to attain the optimal conditions for entropy generated for the flow of fluid. Results of the analysis reveal that concentration decreases with the rise in reaction rate parameter and increases with activation energy parameter. Prandtl and Eckert numbers, with their increase, enhance entropy, and fluid friction irreversibility is at its highest. Perfect co-relation is attained for the model by the response surface methodology, with a co-relation coefficient of 100 %. The Weissenberg number is highly sensitive to change in the present modeling, followed by Darcy and Reynolds numbers. The Reynolds number and Darcy number show positive sensitivity, while the Weissenberg number shows negative sensitivity to the entropy generated.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"12 ","pages":"Article 100940"},"PeriodicalIF":0.0,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142419538","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-23DOI: 10.1016/j.padiff.2024.100937
Md. Asaduzzaman , Faruk Özger , Md. Zulfikar Ali
In this article, we construct and investigate a new fractional variational iteration technique which is named as AFVI method. After that, we formulate some IVPs corresponding to the fractional nonlinear evolution equations NLTFFWE, mNLTFFWE, TFmCHE and TFmDPE. The Caputo fractional order derivative has been used to fractionalize the considered NLEEs. Then, we solve the considered IVPs by applying the formulated AFVI method. Lastly, we check the accuracy of the attained AASs by making some graphical and numerical comparisons with their corresponding exact solutions and other existing equivalent AASs. The result of this article confirm that the efficiency, appropriateness and time spent capability of the newly constructed AFVI method are better than that of the other existing analogous fractional analytical approximation methods. Here, we apply the Maple 2021 programming software to obtain the AASs of the formulated IVPs and drawing the 3D graphs of the attained AASs. Finally, in this article we validate the applicability of the Caputo fractional order derivative to form a novel analytical approximation method as well as to fractionalize some essential NLEEs of Mathematical physics.
{"title":"Analytical approximate solutions of some fractional nonlinear evolution equations through AFVI method","authors":"Md. Asaduzzaman , Faruk Özger , Md. Zulfikar Ali","doi":"10.1016/j.padiff.2024.100937","DOIUrl":"10.1016/j.padiff.2024.100937","url":null,"abstract":"<div><div>In this article, we construct and investigate a new fractional variational iteration technique which is named as AFVI method. After that, we formulate some IVPs corresponding to the fractional nonlinear evolution equations NLTFFWE, mNLTFFWE, TFmCHE and TFmDPE. The Caputo fractional order derivative has been used to fractionalize the considered NLEEs. Then, we solve the considered IVPs by applying the formulated AFVI method. Lastly, we check the accuracy of the attained AASs by making some graphical and numerical comparisons with their corresponding exact solutions and other existing equivalent AASs. The result of this article confirm that the efficiency, appropriateness and time spent capability of the newly constructed AFVI method are better than that of the other existing analogous fractional analytical approximation methods. Here, we apply the Maple 2021 programming software to obtain the AASs of the formulated IVPs and drawing the 3D graphs of the attained AASs. Finally, in this article we validate the applicability of the Caputo fractional order derivative to form a novel analytical approximation method as well as to fractionalize some essential NLEEs of Mathematical physics.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"12 ","pages":"Article 100937"},"PeriodicalIF":0.0,"publicationDate":"2024-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142328354","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-22DOI: 10.1016/j.padiff.2024.100927
Shahid Rafiq , Muhammad Mustahsan , Muhammad Asim , M. Ijaz Khan , Sami Ullah Khan , Furqan Ahmad , M. Waqas , Barno Abdullaeva
This research aims to presents the free convective flow power law fluid due to vertical cone. The investigation for observing the heat transfer phenomenon is accounted to heat generation and radiative effects. The assumption of variable viscosity is taken into account. A vertical cone induced the flow. The dimensionless variables are followed to attains the simplified form. The numerical computations are performed with help of famous finite element method (FEM). The FEM algorithm is supported with applications of quadratic Lagrange polynomials. The results are confirmed with peak accuracy. The physical aspect of problem is presented in view of shear thickening, shear thinning and viscous material case. A comparative thermal reflection in absence and presence of heat generation have been endorsed. Moreover, the insight of various parameters on Nusselt number is also presented.
{"title":"Computational analysis of radiative flow of power law fluid with heat generation effects: Galerkin finite element simulations","authors":"Shahid Rafiq , Muhammad Mustahsan , Muhammad Asim , M. Ijaz Khan , Sami Ullah Khan , Furqan Ahmad , M. Waqas , Barno Abdullaeva","doi":"10.1016/j.padiff.2024.100927","DOIUrl":"10.1016/j.padiff.2024.100927","url":null,"abstract":"<div><div>This research aims to presents the free convective flow power law fluid due to vertical cone. The investigation for observing the heat transfer phenomenon is accounted to heat generation and radiative effects. The assumption of variable viscosity is taken into account. A vertical cone induced the flow. The dimensionless variables are followed to attains the simplified form. The numerical computations are performed with help of famous finite element method (FEM). The FEM algorithm is supported with applications of quadratic Lagrange polynomials. The results are confirmed with peak accuracy. The physical aspect of problem is presented in view of shear thickening, shear thinning and viscous material case. A comparative thermal reflection in absence and presence of heat generation have been endorsed. Moreover, the insight of various parameters on Nusselt number is also presented.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"12 ","pages":"Article 100927"},"PeriodicalIF":0.0,"publicationDate":"2024-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142419541","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-22DOI: 10.1016/j.padiff.2024.100936
S.R. Mishra , P.K. Pattnaik , Rupa Baithalu , P.K. Ratha , Subhajit Panda
An efficient heat transfer phenomenon using nanofluid have greater challenges in various industries, engineering application the recent trend. Keeping this in present scenario, this study aims to optimize the heat transmission rate in the magnetized flow of nanomaterials through a rotating, spinning sphere. The heat transfer phenomena in the time-dependent fluid are enhanced by the incorporation of nonlinear radiation and a variable heat source. Additionally, the free convective flow is influenced by the effects of thermal buoyancy and a transverse magnetic field. The proposed model along with several factors is standardized through adequate transformation rules. Further, shooting-based Runge-Kutta technique is adopted with the help of built-in MATLAB function bvp4c for the solution of the transformed system. The prime focus of the proposed work is the optimizing heat transfer rate combined with regression analysis using artificial neural network and then it uses Levenberg Marquardt algorithm with well-posed training, testing, and validation data. The error analysis also presented briefly and the variation of characterizing parameters is depicted via graphs. Further, the important outcomes are; the particle concentration of carbon nanotubes contributes to decelerating the velocity profiles, leading to an increase in boundary layer thickness. In contrast, increasing magnetization has the opposite effect. Both nonlinear radiative heat and an additional heat source enhance the heat transfer phenomenon.
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Pub Date : 2024-09-21DOI: 10.1016/j.padiff.2024.100930
V. Alekseev
We study a fully connected network of Mackey–Glass generators, each described by the Mackey–Glass delay differential equation. This system can exhibit non-trivial behaviour over time. One interesting scenario of such behaviour is cluster synchronization—regimes in which all components are divided into several groups, each oscillating in the same mode. Cluster synchronization can appear in various systems, such as neural networks and biological systems. In this work, we investigate the case of two-cluster synchronization and prove the existence of such modes.
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