Partial Differential Equations in Applied Mathematics最新文献

{"title":"Hiemenz flow of ternary hybrid nanofluid over a linear stretching/shrinking sheet: Duality and stability analysis","authors":"Khaled Matarneh ,&nbsp;Adnan Asghar ,&nbsp;Raja'i Aldiabat ,&nbsp;Liaquat Ali Lund ,&nbsp;Zahir Shah","doi":"10.1016/j.padiff.2025.101165","DOIUrl":"10.1016/j.padiff.2025.101165","url":null,"abstract":"<div><div>The Hiemenz flow of a ternary hybrid nanofluid (THNF) consisting of <em>H</em>₂<em>O</em>/<em>Al</em>₂<em>O</em>₃ + <em>Cu</em> + <em>TiO</em>₂ has been successfully realised over a linear stretching or shrinking sheet, taking into account the effects of heat radiation. Nanofluids are composed of three distinct kinds of nanoparticles that are spread throughout a base fluid. These nanoparticles display a variety of sophisticated thermophysical properties. Ternary hybrid nanofluids are advantageous for usage in the cooling of electronic devices, microchips, and nuclear reactors due to their increased thermal conductivity. The stretching/shrinking sheet models the behavior of cooling surfaces in high-performance heat exchangers. When applied to a stretching sheet, the Hiemenz flow model replicates the process of cooling thin, flexible surfaces that are contained inside microchannels. As a result of the radiative heat effect, these fluids are able to absorb more heat, which results in an improvement in the cooling performance of electronic devices that create large thermal loads. The equations of Navier–Stokes have been transformed into equations of self-similarity by applying appropriate transformations of similarity variables. These equations have been numerically resolved by using the three-stage Labatto-three-A method. Dual solutions are achieved in specific ranges of parameter. There is no discernible increase or reduction in the values of skin coefficients, friction, and heat transfer rate in the dual solutions domain when the solid volume percent of titanium dioxide is increased. In the presence of an increase in the value of the solid volume fraction of titanium dioxide, the rate of heat transfer improved. The thickness of the thermal boundary layer (BL) increased with thermal radiation but decreased with the Prandtl number. Furthermore, temporal stability analysis reveals that the first solution exhibits superior long-term stability.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"14 ","pages":"Article 101165"},"PeriodicalIF":0.0,"publicationDate":"2025-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143737891","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}

{"title":"Velocity slip impact with inertial drag and Darcy dissipation on the radiative flow of micropolar fluid over an elongating surface","authors":"S.R. Mishra ,&nbsp;P.K. Ratha ,&nbsp;Rupa Baithalu ,&nbsp;Subhajit Panda","doi":"10.1016/j.padiff.2025.101168","DOIUrl":"10.1016/j.padiff.2025.101168","url":null,"abstract":"<div><div>The current scenario of the research depends upon the effective heat transfer properties of various fluids that have significant applications in different sectors like engineering, biomedical, industries, etc. From the various investigations, the flow of conducting micropolar fluid under the action of inertial drag over an elongating surface packed within a porous matrix is presented in this article. The model is equipped with inertial drag and the combined effect of Joule with Darcy dissipation energies in the flow spectacles. Furthermore, the velocity slip impact also affects the flow profiles significantly. Appropriate similarity rules are adopted to translate governing phenomena into dimensionless forms. The proposed transformed set of equations is solved employing a numerical technique called “Runge-Kutta fourth-order” combined with the “shooting method” and the simulation is carried out by utilizing MATLAB. The confirmation of the past examination is presented numerically with a good agreement in particular cases. Further, the physical consequence of several factors involved in the flow phenomena is presented graphically and elaborated in the discussion section. The major outcomes of this study are: Lorentz force resistivity reduces velocity-boundary thickness, while micropolar effects enhance velocity but show dual behavior in angular velocity. Darcy-Forchheimer drag lowers velocity, and heat dissipation raises temperature while controlling the gradient. Radiative heat significantly boosts temperature and the Nusselt number.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"14 ","pages":"Article 101168"},"PeriodicalIF":0.0,"publicationDate":"2025-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143761042","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}

{"title":"Numerical investigation of ion-slip current and stratification on MHD flow through high porosity medium with Soret and Dufour effects in a turning scheme","authors":"M.D. Hossain ,&nbsp;M. Eaqub Ali ,&nbsp;M.A. Samad ,&nbsp;M.M. Alam ,&nbsp;M.G. Hafez","doi":"10.1016/j.padiff.2025.101158","DOIUrl":"10.1016/j.padiff.2025.101158","url":null,"abstract":"<div><div>The study examines the effects of stratification, Hall and ion-slip currents, viscous dissipation in a magnetic field, and high porosity medium, considering Soret and Dufour effects in a turning flow scheme. The governing mathematical equations are transformed into ordinary differential equations using non-dimensional similarity variables. Numerical results are obtained using the Sixth-order Runge–Kutta method combined with the Nachtsheim–Swigert shooting iteration technique. The influence of various parameters on velocity, temperature, and concentration is presented graphically, while the effects on shear stress, Nusselt number, and Sherwood number are summarized in tabular form. The key findings show that primary velocity (PV) and secondary velocity (SV) increase with higher Hall parameter, Dufour number, and Eckert number. The porosity parameter enhances both PV and SV in the boundary layer, while the magnetic parameter reduces PV and increases SV. The Prandtl number decreases PV and increases SV. The Soret number enhances PV of concentration and reduces SV of temperature. Thermal stratification reduces PV and increases SV of concentration, whereas mass stratification decreases both PV and SV. Additionally, shear stress and heat/mass transfer are influenced by Dufour number, Eckert number, and Soret number, with higher values improving heat and mass transfer. Comparisons with previous studies show a good agreement with observed trends.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"14 ","pages":"Article 101158"},"PeriodicalIF":0.0,"publicationDate":"2025-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143737883","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}

{"title":"Modelling heat and mass transfer in electro-osmosis flow of williamson nano-fluids using a hybrid scheme","authors":"Muhammad Shoaib Arif ,&nbsp;Kamaleldin Abodayeh ,&nbsp;Yasir Nawaz","doi":"10.1016/j.padiff.2025.101164","DOIUrl":"10.1016/j.padiff.2025.101164","url":null,"abstract":"<div><div>This paper presents a computational scheme for solving time-dependent partial differential equations (PDEs) arising from the study of electro-osmosis flow of Williamson nano-fluids, which is significant for optimizing microfluidic and biomedical applications. The scheme employs a two-stage approach: the first stage modifies the time integrator using an exponential time integration technique. In contrast, the second stage implements the second-order Runge-Kutta method. This combination utilizes the efficacy of exponential integrators for stiff equations and the reliability of the Runge-Kutta method for time stepping. The stability of the scheme is examined using a scalar PDE as a benchmark. In addition to the time integrator, spatial discretization is performed using a high-order compact scheme, providing fourth or sixth-order accuracy for space-dependent terms. The mathematical model demonstrates that increasing Helmholtz–Smoluchowski velocity enhances fluid velocity, which is crucial for improving electrokinetic performance. This study's findings have potential applications in designing advanced lab-on-a-chip devices for efficient fluid transport in microchannels.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"14 ","pages":"Article 101164"},"PeriodicalIF":0.0,"publicationDate":"2025-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143704500","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}

{"title":"Dynamic analysis of competitive marketing strategies using differential game models and Runge–Kutta solutions","authors":"Awad Talal Alabdala ,&nbsp;Asmaa Alhassan ,&nbsp;Maan T. Alabdullah ,&nbsp;Waleed Adel","doi":"10.1016/j.padiff.2025.101156","DOIUrl":"10.1016/j.padiff.2025.101156","url":null,"abstract":"<div><div>This study presents a comprehensive mathematical and computational analysis of a competitive market model, incorporating Pontryagin’s Maximum Principle, the Hamiltonian formulation, and the Runge–Kutta (RK4) numerical method. The proposed model accounts for market share dynamics, pricing strategies, and advertising efforts, capturing real-world competitive interactions through logistic growth functions and nonlinear incidence rates. By formulating the problem as a differential game, we analyze the optimal control strategies of firms aiming to maximize their long-term market positions while minimizing operational costs. The results indicate that firms implementing aggressive pricing strategies initially experience rapid market share growth but later face diminishing returns due to market saturation and competitive responses. Conversely, firms adopting moderate strategies achieve sustained growth and long-term stability. Numerical simulations reveal the impact of damping effects, demonstrating that firms must balance short-term profitability with sustainable competitive positioning to maintain market dominance. The study also explores the role of advertising intensity, highlighting the nonlinear relationship between promotional expenditures and market gains. These findings provide valuable insights for firms seeking to refine their strategic decision-making in highly competitive environments. The research also emphasizes the importance of numerical optimization techniques in addressing real-world economic challenges, paving the way for future studies that integrate stochastic modeling, adaptive learning, and hybrid computational methods to enhance predictive accuracy in competitive market dynamics.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"14 ","pages":"Article 101156"},"PeriodicalIF":0.0,"publicationDate":"2025-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143725426","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}

{"title":"Brownian motion effects and thermophoresis on heat transmission mechanism of hybrid nano liquid flow over a stretched wedge surface","authors":"Sharanayya Swami ,&nbsp;Suresh Biradar ,&nbsp;Jagadish V Tawade ,&nbsp;Vediyappan Govindan ,&nbsp;Haewon Byeon ,&nbsp;Busayamas Pimpunchat","doi":"10.1016/j.padiff.2025.101157","DOIUrl":"10.1016/j.padiff.2025.101157","url":null,"abstract":"<div><div>The current study observes the impact of thermophoresis, Brownian motion, and magnetic fields on the flow and heat transfer properties of a hybrid nanofluid containing Al₂O₃, CuO, and ethylene glycol over a wedge-shaped surface undergoing horizontal stretching. The study addresses the critical need to enhance energy transfer and thermal management systems, which have significant technical and industrial applications. To model the problem, flow equations were transformed into ordinary differential equations using similarity transformations and solved numerically via the Runge-Kutta-Fehlberg method. The results reveal that the wedge angle and magnetic field strength are crucial factors influencing the flow and thermal behavior. Specifically, increasing the wedge angle enhances the Nusselt number but reduces the thermal and diffusion profiles. The suction and injection of the fluid significantly impact the local heat transfer rates and boundary layer thickness. Additionally, the Buongiorno slip parameter reduces the rate of energy transfer while amplifying thermal distributions. The thermophoresis parameter was found to influence both concentration and thermal boundary layers. A comparative analysis between Newtonian and non-Newtonian fluids showed that hybrid nanofluids improve mass and energy transfer rates in both cases, with enhanced effects observed in non-Newtonian fluids. The study's novelty lies in its comprehensive exploration of magneto-flow dynamics and hybrid nanofluid behavior in the context of wedge geometries and external magnetic fields. The findings extend previous research by offering quantitative insights into how key parameters like wedge angles, thermophoresis, and Brownian motion affect heat and mass transfer processes, providing a robust framework for optimizing hybrid nanofluid applications in engineering and industrial systems. The results align well with existing literature, validating the study's contributions to the field.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"14 ","pages":"Article 101157"},"PeriodicalIF":0.0,"publicationDate":"2025-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143704499","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}

{"title":"The Yamada-Ota model-based Casson quadra hybrid nanofluid stagnation flow configured by ohmic heating, heat source, and Newtonian boundary heating across an exponentially stretched cylinder","authors":"Tusar Kanti Das ,&nbsp;Ashish Paul ,&nbsp;Jintu Mani Nath ,&nbsp;Neelav Sarma","doi":"10.1016/j.padiff.2025.101159","DOIUrl":"10.1016/j.padiff.2025.101159","url":null,"abstract":"<div><div>An engine oil-driven Yamada-Ota model-based Casson quadra hybrid nanofluid flow, comprising spherical-shaped Silver, Copper, Graphene, and Molybdenum sulfide nanoparticles, is studied over a stretched cylinder in a porous medium. The investigation focuses on enhancing thermal efficiency by incorporating ohmic heating, boundary heating, velocity ratio, viscous dissipation, and heat source effects, which are pivotal for applications in thermal exchangers, bioengineering devices, and material processing. The contrast between Casson fluid and Casson quadra hybrid nanofluid flows is analyzed. Using the bvp4c method, numerical simulations reveal the impact of magnetic fields, inclination angles, porosity, Biot numbers, viscous dissipation, and heat sources on velocity and temperature profiles, tangential stress, and heat transmission rates. Results indicate a noTable 38.4 % enhancement in heat transfer for Casson quadra hybrid nanofluid compared to Casson fluid, attributed to the synergistic properties of the nanoparticles. Thermal profiles are significantly influenced by magnetic effects, inclination, porosity, and boundary heating. The heat transmission rate in the convective region increases with higher values of the Eckert number, heat source, porous factor, and Biot number. Conversely, it decreases as the Casson parameter, Reynolds number, and velocity ratio parameter rise. This study highlights the potential of Casson quadra hybrid nanofluids in improving thermal performance for engineering applications. It suggests future optimization opportunities by selecting suitable nanofluids, adjusting magnetic fields, and modifying system geometry, thus presenting these fluids as effective solutions for advanced heat transfer systems.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"14 ","pages":"Article 101159"},"PeriodicalIF":0.0,"publicationDate":"2025-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143686869","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}

{"title":"Significance of slip velocity and viscosity variation on squeezed film couple-stress properties between a rough plate and a cylinder","authors":"Arshiya Kousar K ,&nbsp;Salma A ,&nbsp;Saja Abdulrahman Althobaiti ,&nbsp;Hanumagowda BN ,&nbsp;Jagadish V Tawade ,&nbsp;Dilsora Abduvalieva ,&nbsp;M. Waqas ,&nbsp;Mohammed Azeez Saeed ,&nbsp;Manish Gupta","doi":"10.1016/j.padiff.2025.101160","DOIUrl":"10.1016/j.padiff.2025.101160","url":null,"abstract":"<div><div>This study examines the impact of surface roughness and viscosity variation on the couple stress squeeze film characteristics between a cylinder and a rough plate with slip velocity. Two distinct one-dimensional roughness patterns—longitudinal and transverse—are considered. Using Christensen's theory, the stochastic modified Reynolds equation is derived for Stokes couple stress fluid, incorporating viscosity variation with pressure. The standard perturbation technique is applied to solve the average Reynolds equation, yielding closed-form expressions for the mean fluid film pressure, load-carrying capacity, and squeeze film time. Various parameters are varied, and the results are discussed through graphical representations in 2D and 3D. This study highlights the importance of viscosity variation, couple stresses, and surface roughness in optimizing squeeze film performance. While increased viscosity and couple stresses enhance load-bearing capacity and film time, slip velocity detracts from these properties. Additionally, surface roughness has a significant impact, with transverse roughness improving, and longitudinal roughness reducing, the squeeze film characteristics. Applications of this study include improving the design and performance of bearing systems, lubrication in mechanical seals, and hydraulic systems where surface roughness and viscosity variation play a significant role in operational efficiency.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"14 ","pages":"Article 101160"},"PeriodicalIF":0.0,"publicationDate":"2025-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143697710","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}

{"title":"Analysis of MHD viscous fluid flow under the influence of viscous dissipation force over vertically moving plate with innovative constant proportional Caputo derivative","authors":"Muhammad Kazim,&nbsp;Safder Hussain,&nbsp;Saima Muhammad,&nbsp;Munawwar Ali Abbas","doi":"10.1016/j.padiff.2025.101163","DOIUrl":"10.1016/j.padiff.2025.101163","url":null,"abstract":"<div><div>In this study, magnetohydrodynamic viscous fluid is considered unsteady and incompressible, considering the effect of inclined magnetic field. Assessing the impact of viscous dissipation force in the fluid, the fractional model is proposed. This scenario has real-world applicability in a variety of scientific and technical domains and incorporates many physical phenomena. Fluid is considered as flowing over a vertically oriented plate moving about its own plane. Constant Proportional Caputo (CPC) derivative operator is obtained while developing the fractional model by transforming the governed equations into a dimensionless form. We solved these transformed equations analytically by employing the technique of Laplace transform and got solutions for momentum equation and energy equation in series form. For computational analysis we employed MATHCAD software and discussed the impact of pertinent parameters on flow. One of the important significances of this study is the use of a new kind of fractional operator, i.e., CPC with power law, and comparing the obtained results with previously published results. This research showed that for greater values of fractional parameters both velocity and temperature profiles reduce while they attain the maximum values for lower values of fractional parameters. Another important significance of this study is the use of viscous dissipation term in the mathematical model. It has also been found that viscous dissipation reduces the fluid temperature. Further, comparison graphs for temperature and velocity profiles are provided to validate our model.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"14 ","pages":"Article 101163"},"PeriodicalIF":0.0,"publicationDate":"2025-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143697711","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}

{"title":"A study on fractional-order mathematical and parameter analysis for CAR T-cell therapy for leukemia using homotopy perturbation method","authors":"Rezaul Karim ,&nbsp;M. Ali Akbar ,&nbsp;M. A. Bkar Pk ,&nbsp;Pinakee Dey","doi":"10.1016/j.padiff.2025.101152","DOIUrl":"10.1016/j.padiff.2025.101152","url":null,"abstract":"<div><div>Leukemia is a malignant blood cancer that originates in the bone marrow is typified by the uncontrolled proliferation of aberrant blood cells. Globally, it is one of the main causes of health issues. In this study, we present a fractional-order four compartmental mathematical model (MM) of leukemia, which includes susceptible blood cells <em>S</em>₁(<em>t</em>), infected blood cells <em>I</em>₁(<em>t</em>), cancer cells <em>C</em>₁(<em>t</em>), and immune blood cells <em>W</em>₁(<em>t</em>), and we analyze the dynamics of transmission of the disease. We use the homotopy perturbation method (HPM) to develop analytical solutions and classical fourth-order Runge-Kutta (RK4) approach to obtain numerical solutions for the mathematical model (MM) of leukemia. Moreover, the concerned solutions which have been found using the methods are compared. For the fractional parameter of α = 0.25, the result shows that the fractional order (FO) model gives better accuracy and stability compared to the conventional integer-order model. For that reason, we emphasize the significance of FO modeling in understanding the spread of leukemia.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"14 ","pages":"Article 101152"},"PeriodicalIF":0.0,"publicationDate":"2025-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143697706","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}