Mangala Kandagal , Ramesh Kempepatil , Jagadish V. Tawade , Nodira Nazarova , Manish Gupta , M. Khan
{"title":"The impact of carbon nanotubes (CNT) on heat generation and absorption, the behaviour of water and blood suspensions in an inclined channel with a porous matrix","authors":"Mangala Kandagal , Ramesh Kempepatil , Jagadish V. Tawade , Nodira Nazarova , Manish Gupta , M. Khan","doi":"10.1016/j.padiff.2025.101241","DOIUrl":"10.1016/j.padiff.2025.101241","url":null,"abstract":"<div><div>The study investigates the heat generation and absorption of engine oil, human blood and single wall carbon Nano tube (SWCNT) in an inclined channel filled with a porous matrix. Two regions are considered, both regions are of porous medium. Due to their enhanced thermal conductivity, are utilized to improve heat transfer efficiency in various applications. Formulation of the problem is framed using conservation of mass, energy and momentum in both regions. The flow of oil, human blood through a porous medium is analysed, considering the effects of both heat generation and absorption within the system. Key parameters such as the inclination angle of the channel, the porosity and the type of fluids are examined to understand their impact on the overall heat transfer process and velocity. To solve the problem regular perturbation method is applied for non-dimensional quantities; The presence of CNTs significantly improves the thermal conductivity of both engine oil and blood suspensions, leading to improved heat dissipation or absorption capabilities, which are influenced by the inclination and the porous structure. This study offers valuable insights into fluid flow processes in the human body using Nanotubes. Influence of CNTs on the fluid flow of human body and heat generation/absorption with porous matrix in both regions is unsolved problem.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101241"},"PeriodicalIF":0.0,"publicationDate":"2025-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144571613","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}
{"title":"Detailed analysis under fully constrained and relaxed boundary conditions of linear fields in the vicinity of a corner","authors":"Ayelet Goldstein, Ofer Eyal, Jorge Berger","doi":"10.1016/j.padiff.2025.101244","DOIUrl":"10.1016/j.padiff.2025.101244","url":null,"abstract":"<div><div>This work examines the behavior of fields near corners under various boundary conditions (BCs), focusing on singularities arising from fully constrained and relaxed BCs. We analyze this behavior across diverse physical systems governed by similar equations, including electromagnetism, superconductivity, and two-phase fluid flow. The corner geometry presents a challenge due to potentially diverging field solutions as the corner is approached (r<span><math><mo>→</mo></math></span> 0). This motivates the investigation of relaxed BCs, which regularize the field by introducing a characteristic length (Ls) that relates the field’s value to its normal derivative at the boundary.</div><div>We explore both single-medium (single-phase) and double-medium (two-phase) systems. While prior research has addressed relaxed BCs in specific contexts, their application to corners, particularly in diverse physical systems, remains under-explored. We develop a series solution method to analyze the field behavior near the corner under different BCs. Concrete examples illustrate the theoretical framework, examining both fully constrained and relaxed scenarios. The implications of this work extend to fields such as fluid mechanics, electromagnetism, and heat transfer.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101244"},"PeriodicalIF":0.0,"publicationDate":"2025-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144557625","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}
{"title":"An iterative method for solving sparse linear algebraic systems with continuum solution dependent right-hand side for elliptic partial differential equations","authors":"Sudipta Lal Basu , Kirk M. Soodhalter , Breiffni Fitzgerald , Biswajit Basu","doi":"10.1016/j.padiff.2025.101236","DOIUrl":"10.1016/j.padiff.2025.101236","url":null,"abstract":"<div><div>Krylov subspace iterative methods such as bi-conjugate gradients stabilized (BiCGStab) to approximately solve sparse linear algebraic systems are well known. However, there are certain instances in real-world engineering applications with underlying governing partial differential equation where the discretized right-hand side can only be exactly determined using the unavailable continuum solution. In such cases, an iterative method such as BiCGStab may not converge to a physically correct solution or may diverge completely. Such a method must be modified to accommodate inexact knowledge of the discrete right-hand side, using an updating scheme as the iteration proceeds. In this paper, we present such an updating strategy for physical problems governed by elliptic partial differential equations. This strategy must be performed in a numerically stable manner, which we also discuss. We present this as a modified BiCGStab iteration and investigate its effectiveness on both test problems, wherein it is shown to perform well and agrees with the analytical solutions, and on some more realistic problems arising in the study of Hele-Shaw flow, composite materials and power generation from wind farms.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101236"},"PeriodicalIF":0.0,"publicationDate":"2025-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144513917","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}
{"title":"An enhanced Artificial Neural Network approach for solving nonlinear fractional-order differential equations","authors":"Nikhil Sharma , Sunil Joshi , Pranay Goswami","doi":"10.1016/j.padiff.2025.101230","DOIUrl":"10.1016/j.padiff.2025.101230","url":null,"abstract":"<div><div>This paper introduces a hybrid Chebyshev Collocation Method (CCM) and Artificial Neural Network (ANN) approach to address the computational challenges of nonlinear Caputo fractional differential equations. The purpose is to improve accuracy for static solutions by approximating the fractional derivative spatially. The methodology leverages CCM for spatial discretization and ANN for residual minimization, achieving low MSEs (e.g., <span><math><mrow><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mo>−</mo><mn>5</mn></mrow></msup></mrow></math></span>) in three examples. The findings confirm improved convergence with increasing node count, with implications for efficient fractional PDE solvers. The novelty lies in the static CCM+ANN integration, offering a practical alternative to dynamic methods.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101230"},"PeriodicalIF":0.0,"publicationDate":"2025-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144330659","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 Kazim, Mubashir Abbas, Safder Hussain, Munawwar Ali Abbas
{"title":"Fractional modelling of heat transfer through porous media for incompressible MHD fluid flow with laplace transform approach","authors":"Muhammad Kazim, Mubashir Abbas, Safder Hussain, Munawwar Ali Abbas","doi":"10.1016/j.padiff.2025.101242","DOIUrl":"10.1016/j.padiff.2025.101242","url":null,"abstract":"<div><div>In this paper, we investigate a fractional model of an incompressible and unstable MHD viscous fluid with heat transfer pass across a porous medium. To quantify this, we used a vertical plate with a fluid connected to it. When an angled magnetic field is supplied, the plate moves in its own plane. The required nonlinear partial differential equations are used to convert the governing equations into a non-dimensional form. To find the solution of the simplified nonlinear partial differential equations, the Constant Proportional Caputo fractional derivatives are utilized. The Laplace transform techniques are used to simplify the non-dimensional governing equations of the model and the boundary conditions we discovered explicit formulations for each field. The resultant equation is solved for momentum and energy, and the solutions are given as series. The performance of velocity and temperature values are graphically plotted using MATHCAD software. In numerical simulation, the Local Skin fraction and local Nusselt number are considered and evaluated additionally. It has been concluded that the fluid’s temperature and velocity decreases by increasing the value of fractional parameter. It has also been found that the velocity and temperature increase with increasing values of<span><math><msub><mi>Q</mi><mn>0</mn></msub></math></span>.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101242"},"PeriodicalIF":0.0,"publicationDate":"2025-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144472180","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}
{"title":"Dynamical analysis and numerous signal transmission behavior of the nonlinear Pochhammer-Chree (PC) model via two consistent schemes","authors":"M. Al-Amin , M․Nurul Islam , M․Ali Akbar","doi":"10.1016/j.padiff.2025.101248","DOIUrl":"10.1016/j.padiff.2025.101248","url":null,"abstract":"<div><div>This investigation conducts a comprehensive analytical analysis of the renowned nonlinear Pochhammer-Chree (PC) model by utilizing two efficient methods. The nonlinear PC model stands as a robust tool for the analysis of movement of traveling waves in a substantially long cylindrical rod with a circular cross-section, and longitudinal wave such as sound and particle wave propagation through elastic medium. The PC model also plays very important role in explaining various natural and engineering applications. To establish these results, we employ the generalized exponential rational function (GERF) method and the auxiliary equation (AE) method. The obtain results uncover numerous secrete dynamical characteristics of the model. Here, we also examine the influences of wave propagation velocity parameter on the attained solutions to understand the inner mechanism and dynamical signal transmission behavior of the related phenomenon. The gestures of obtained results are explained by representing the 3-dimensional (3D) and 2-dimensional (2D) shapes. The attained solutions demonstrate that the employed techniques are straightforward, reliable, functional and more effective to extracting soliton solutions of numerous nonlinear models.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101248"},"PeriodicalIF":0.0,"publicationDate":"2025-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144472220","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}
{"title":"Exploring mixed convection in porous media: Thermal and flow behaviour","authors":"Shreedevi Kalyan , Mangala Kandagal , Jagadish V. Tawade , Nitin Satpute , M. Ijaz Khan , Nitiraj Kulkarni , Nargiza Kamolova , Manish Gupta","doi":"10.1016/j.padiff.2025.101239","DOIUrl":"10.1016/j.padiff.2025.101239","url":null,"abstract":"<div><div>This study explores mixed convective flow within a porous medium, considering scenarios of heat generation or absorption. The focus is on solving the nonlinear differential equations that describe concentration, temperature, and velocity profiles, with graphical representations provided for each. Notably, this research addresses an area previously unexamined. By employing the regular perturbation method, solutions to the nonlinear ordinary differential equations, derived from the nondimensionalized governing equations, are achieved. Various factors significantly influence fluid flow parameters, revealing intriguing phenomena. The results offer valuable insights into velocity and temperature distributions across diverse porous characteristics, including thermal temperature, viscosity ratio, width ratio, conductivity ratio, and Grashof number. A decrease in velocity is observed due to factors such as the porous structure, viscosity variations, and conductance differences. Conversely, an increase in flow velocity is noted with higher Grashof numbers and width-to-height ratios.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101239"},"PeriodicalIF":0.0,"publicationDate":"2025-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144513918","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}
Swathi H R , Indira Ramarao , Jagadeesha S , Ganesh Kumar K , Prakasha D G
{"title":"Peristaltic flow of nanofluid with temperature dependent viscosity in an annulus","authors":"Swathi H R , Indira Ramarao , Jagadeesha S , Ganesh Kumar K , Prakasha D G","doi":"10.1016/j.padiff.2025.101240","DOIUrl":"10.1016/j.padiff.2025.101240","url":null,"abstract":"<div><div>Peristaltic flow in an annular region bounded by a concentric cylindrical tube is considered. The current study focuses on understanding enhancement of heat transfer in presence of nanoparticles. It also studies the effect of peristaltic motion on enhancement of heat transfer. The outer tube is subjected to a sinusoidal wave, and inner tube is rigid. Nanofluid has a variable viscosity which depends on temperature. Analytical solutions for temperature, velocity, and pressure gradient are evaluated and the effect of carbon nanotube is represented graphically. A method of regular perturbation is adopted to get an analytical solution. The impact of having single-walled carbon nanotubes (SNT) and multi-walled carbon nanotubes (MNT) on the parameters like pressure gradient, temperature, and velocity. Long wavelength approximation is assumed on a low Reynold’s flow. The impact of inner tube radius, amplitude of sinusoidal wave, and rate of flow on pressure gradient are analyzed for both SNT and MNT.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101240"},"PeriodicalIF":0.0,"publicationDate":"2025-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144365842","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}
{"title":"Optical soliton solutions of M-fractional modified complex Ginzburg-Landau equation using unified method: A comparative study","authors":"Md. Mamunur Roshid, Sayma Akter, Bithi Akter","doi":"10.1016/j.padiff.2025.101245","DOIUrl":"10.1016/j.padiff.2025.101245","url":null,"abstract":"<div><div>The current research investigates the M-fractional modified complex Ginzburg-Landau equation, a crucial nonlinear model for characterizing the behavior and evolution of optical solitary waves in dynamic fiber optics. Examining wave propagation in nonlinear dispersive media is essential since it promotes progress in data transmission for communication systems and allows for generating ultrafast optical pulses. the M-fractional derivative for the MCGL model is applied for the first time, which is more meaningful. The equation is converted into an ordinary differential equation via wave transformation, enabling the use of a unified technique to get many soliton solutions. By applying the unified method, we obtain more solutions than other methods, such as the function transformation technique.<sup>23</sup> The solutions are expressed as <em>tanh</em>, <em>sec</em>, <em>tan</em>, <em>sech</em> functions and their combinations. For the special values of free parameters, we have periodic waves, kinky-periodic waves, periodic lump waves, periodic waves with lump waves, interactions of anti-kink and periodic waves, double periodic waves, and multi-kink waves. This work's innovative component is applying this approach to derive various soliton structures, analyzed using 2D, 3D, and contour representations. Additionally, the influence of fractional parameter presents with 3D plots for γ = 0.1, 0.4, 0.8. we also compare the fractional effect with the classical form in 2D plots. The results highlight the efficacy of this approach in examining soliton solutions in diverse nonlinear models, hence enhancing the comprehension of wave dynamics in mediums with differing stability.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101245"},"PeriodicalIF":0.0,"publicationDate":"2025-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144614844","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}
{"title":"Transport properties of viscous fluid through moving permeable walls in fuzzy enviormnent","authors":"Anuradha Sahoo, S.R. Mishra","doi":"10.1016/j.padiff.2025.101237","DOIUrl":"10.1016/j.padiff.2025.101237","url":null,"abstract":"<div><div>The current flow phenomena characterized by several flow properties depend on their physical behavior and the geometry of the problem. The present investigation deals with the flow of viscous two-dimensional liquid through an expanding/contracting surface where the walls are moving and also permeable. The differential equation governing the two-dimensional viscous flow is also fuzzified. Here, some parameters appeared in the differential equation are considered as triangular fuzzy numbers (TFN). The fuzzified “<em>Boundary Value Problem</em>” (BVP) is defuzzified by using “<em>Signed Distance Method</em>”. Finally, numerical solutions are for both crisp and fuzzy model are obtained and presented via graphs and tables. Further, the results are obtained by employing approximate analytical technique known as “Differential Transform Method” (DTM) and the refinement of these are verified with Pade approximant of order [4/4]. Finally, the numerical simulations by using traditional numerical technique and the current approximate analytical technique are compared for both the crisp and the fuzzified solutions of the BVP showing a good correlation among themselves. Moreover, the important outcomes of the study are; the enhanced Reynolds number the flow profile augments significantly and this enhancement is observed near the first region that is closed to the lower wall of the channel but the impact is reversed in the second. The interesting fact is that for the higher wall dilation parameter the fuzzified values of the Reynolds number shows its reverse impact.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101237"},"PeriodicalIF":0.0,"publicationDate":"2025-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144365841","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}