Pub Date : 2025-09-01Epub Date: 2025-07-14DOI: 10.1016/j.padiff.2025.101255
N. Nithya , B. Vennila , K. Loganathan , R. Shobika , K. Senthilvadivu , S. Eswaramoorthi
This paper examines how a ternary hybrid nanofluid made by combining , , and in water behaves when flowing across a stretching sheet with varying thickness. The motivation comes from real world needs in systems like solar collectors, biomedical devices, and industrial cooling, where better heat transfer with minimal drag is essential. Using a blend of the Differential Transformation Method (DTM) and statistical optimization techniques like Response Surface Methodology (RSM) and Central Composite Design (CCD), we study how magnetic field, radiation, nanoparticle volume fraction, and activation energy affects the system. The hybrid nanofluid’s improved thermal behavior is a key focus. It is found that the increasing sheet thickness leads to higher temperatures, while velocity and concentration drop. Greater thermal radiation and more silicon dioxide particles enhance the heat transfer, improving efficiency by 12% and reducing drag (skin friction) by 15% under optimized conditions. Thermal conductivity improves with more nanoparticles, raising the Nusselt number. Meanwhile, mass diffusion behavior captured by the Sherwood number is influenced by activation energy and the Schmidt number. Magnetic field and nanoparticle volume fraction effects together help lower surface drag.
{"title":"Exploration of the Arrhenius activation energy in unsteady ternary hybrid nanofluid flow past a slendering stretching sheet: RSM analysis","authors":"N. Nithya , B. Vennila , K. Loganathan , R. Shobika , K. Senthilvadivu , S. Eswaramoorthi","doi":"10.1016/j.padiff.2025.101255","DOIUrl":"10.1016/j.padiff.2025.101255","url":null,"abstract":"<div><div>This paper examines how a ternary hybrid nanofluid made by combining <span><math><msub><mrow><mtext>TiO</mtext></mrow><mrow><mn>2</mn></mrow></msub></math></span>, <span><math><msub><mrow><mtext>SiO</mtext></mrow><mrow><mn>2</mn></mrow></msub></math></span>, and <span><math><mrow><msub><mrow><mtext>Al</mtext></mrow><mrow><mn>2</mn></mrow></msub><msub><mrow><mtext>O</mtext></mrow><mrow><mn>3</mn></mrow></msub></mrow></math></span> in water behaves when flowing across a stretching sheet with varying thickness. The motivation comes from real world needs in systems like solar collectors, biomedical devices, and industrial cooling, where better heat transfer with minimal drag is essential. Using a blend of the Differential Transformation Method (DTM) and statistical optimization techniques like Response Surface Methodology (RSM) and Central Composite Design (CCD), we study how magnetic field, radiation, nanoparticle volume fraction, and activation energy affects the system. The hybrid nanofluid’s improved thermal behavior is a key focus. It is found that the increasing sheet thickness leads to higher temperatures, while velocity and concentration drop. Greater thermal radiation and more silicon dioxide particles enhance the heat transfer, improving efficiency by 12% and reducing drag (skin friction) by 15% under optimized conditions. Thermal conductivity improves with more nanoparticles, raising the Nusselt number. Meanwhile, mass diffusion behavior captured by the Sherwood number is influenced by activation energy and the Schmidt number. Magnetic field and nanoparticle volume fraction effects together help lower surface drag.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101255"},"PeriodicalIF":0.0,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144680602","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 study is a machine learning investigation of the advance level nanofluidic coolant through a cone in a two-dimensional transitory boundary layer. The model accounts for both radiation absorption and the Arrhenius activation energy. Synthetic datasets from governing mathematical model are used in Artificial Intelligence (AI) based Levenberg Marquardt Back Propagation algorithm (LM-BP). Multiple scenarios of Tangent Hyperbolic Nanofluidic (THNF) coolant are framed with variation of influencing characteristics like Magnetic field M, power law index n, permeability k, Radiation absorption Q, Prandtl ratio Pr, Brownian motion Nb, Lewis number Le and Chemical reaction parameter γ. Convergence parameters of AI-based feed routing Neural Network computing is presented through graphs and numerical tables. Results indicate that flow slows when the Lorentz force and surface permeability grow, but it gets stronger when thermal absorption and momentum to thermal diffusivity ratio Pr increase. Meanwhile, the temperature increases when thermal absorption rises and drops when thermal to mass diffusivity ratio Le increases so that temperature falls for greater chemical reaction influence.
{"title":"Machine learning analysis of tangent hyperbolic nanofluid with radiation and Arrhenius activation energy over falling cone under gravity","authors":"Muhammad Zubair , Hamid Qureshi , Usman Khaliq , Taoufik Saidani , Waqar Azeem Khan","doi":"10.1016/j.padiff.2025.101280","DOIUrl":"10.1016/j.padiff.2025.101280","url":null,"abstract":"<div><div>This study is a machine learning investigation of the advance level nanofluidic coolant through a cone in a two-dimensional transitory boundary layer. The model accounts for both radiation absorption and the Arrhenius activation energy. Synthetic datasets from governing mathematical model are used in Artificial Intelligence (AI) based Levenberg Marquardt Back Propagation algorithm (LM-BP). Multiple scenarios of Tangent Hyperbolic Nanofluidic (THNF) coolant are framed with variation of influencing characteristics like Magnetic field <em>M</em>, power law index <em>n</em>, permeability <em>k</em>, Radiation absorption <em>Q</em>, Prandtl ratio <em>Pr</em>, Brownian motion <em>Nb</em>, Lewis number <em>Le</em> and Chemical reaction parameter γ. Convergence parameters of AI-based feed routing Neural Network computing is presented through graphs and numerical tables. Results indicate that flow slows when the Lorentz force and surface permeability grow, but it gets stronger when thermal absorption and momentum to thermal diffusivity ratio Pr increase. Meanwhile, the temperature increases when thermal absorption rises and drops when thermal to mass diffusivity ratio Le increases so that temperature falls for greater chemical reaction influence.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101280"},"PeriodicalIF":0.0,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144920092","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}
Pub Date : 2025-09-01Epub Date: 2025-07-04DOI: 10.1016/j.padiff.2025.101252
B. Yu. Irgashev , H.H. Pulatova
In the article a non-trivial solution of the homogeneous Cauchy problem for a homogeneous high-order equation with a fractional Caputo derivative is constructed.
本文构造了具有分数阶Caputo导数的齐次高阶方程的齐次Cauchy问题的非平凡解。
{"title":"Non-uniqueness of the solution of the Cauchy problem for one higher-order equation with a fractional derivative","authors":"B. Yu. Irgashev , H.H. Pulatova","doi":"10.1016/j.padiff.2025.101252","DOIUrl":"10.1016/j.padiff.2025.101252","url":null,"abstract":"<div><div>In the article a non-trivial solution of the homogeneous Cauchy problem for a homogeneous high-order equation with a fractional Caputo derivative is constructed.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101252"},"PeriodicalIF":0.0,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144571098","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}
Pub Date : 2025-09-01Epub Date: 2025-08-25DOI: 10.1016/j.padiff.2025.101296
T. Gunasekar , K. Nithyanandhan , Hanumagowda B. N , Jagadish V. Tawade , Nashwan Adnan Othman , Barno Abdullaeva , Nadia Batool , Khayrilla Kurbonov
This paper investigates the existence and uniqueness of solutions for a nonlocal intuitionistic fuzzy impulsive integro-differential equation, employing intuitionistic fuzzy semigroups and the contraction mapping principle. Through a systematic theoretical framework, it establishes that, under certain conditions, a distinct solution is ensured. Additionally, the study expands its analysis to explore the existence results for intuitionistic fuzzy impulsive neutral integro-differential equations, broadening its research focus. This approach introduces a new perspective on understanding intuitionistic fuzzy integro-differential equations, introducing innovative methodologies and significant discoveries that advance theoretical exploration in this field. The findings underscore that, subject to specific assumptions, a singular fuzzy solution emerges for these problems marked by nonlocal conditions, effectively addressing crucial challenges in the analysis of fuzzy systems.
{"title":"A study on intuitionistic fuzzy neutral functional integro-differential PDEs with impulses","authors":"T. Gunasekar , K. Nithyanandhan , Hanumagowda B. N , Jagadish V. Tawade , Nashwan Adnan Othman , Barno Abdullaeva , Nadia Batool , Khayrilla Kurbonov","doi":"10.1016/j.padiff.2025.101296","DOIUrl":"10.1016/j.padiff.2025.101296","url":null,"abstract":"<div><div>This paper investigates the existence and uniqueness of solutions for a nonlocal intuitionistic fuzzy impulsive integro-differential equation, employing intuitionistic fuzzy semigroups and the contraction mapping principle. Through a systematic theoretical framework, it establishes that, under certain conditions, a distinct solution is ensured. Additionally, the study expands its analysis to explore the existence results for intuitionistic fuzzy impulsive neutral integro-differential equations, broadening its research focus. This approach introduces a new perspective on understanding intuitionistic fuzzy integro-differential equations, introducing innovative methodologies and significant discoveries that advance theoretical exploration in this field. The findings underscore that, subject to specific assumptions, a singular fuzzy solution emerges for these problems marked by nonlocal conditions, effectively addressing crucial challenges in the analysis of fuzzy systems.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101296"},"PeriodicalIF":0.0,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144931557","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}
Pub Date : 2025-09-01Epub Date: 2025-07-11DOI: 10.1016/j.padiff.2025.101250
Miguel Uh Zapata , Reymundo Itza Balam , Silvia Jerez
This paper provides an initial framework for developing high-order numerical methods to solve interface problems for nonlinear elliptic partial differential equations. The proposed formulation is based on the immersed interface method dealing with a discontinuous coefficient problem. The algorithm introduces new schemes for points near the interface, whereas standard central finite difference schemes are used in smooth regions. As a consequence, a global second-order accurate solution is guaranteed. First, theoretical results on the truncation error are given for one-dimensional linear problems. Next, the algorithm is generalized to deal with nonlinear convection and diffusion cases using the using Levenberg–Marquardt algorithm. Numerical simulations for several benchmark problems show the robustness and efficiency of the proposed scheme.
{"title":"An immersed interface method for nonlinear convection–diffusion equations with interfaces","authors":"Miguel Uh Zapata , Reymundo Itza Balam , Silvia Jerez","doi":"10.1016/j.padiff.2025.101250","DOIUrl":"10.1016/j.padiff.2025.101250","url":null,"abstract":"<div><div>This paper provides an initial framework for developing high-order numerical methods to solve interface problems for nonlinear elliptic partial differential equations. The proposed formulation is based on the immersed interface method dealing with a discontinuous coefficient problem. The algorithm introduces new schemes for points near the interface, whereas standard central finite difference schemes are used in smooth regions. As a consequence, a global second-order accurate solution is guaranteed. First, theoretical results on the truncation error are given for one-dimensional linear problems. Next, the algorithm is generalized to deal with nonlinear convection and diffusion cases using the using Levenberg–Marquardt algorithm. Numerical simulations for several benchmark problems show the robustness and efficiency of the proposed scheme.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101250"},"PeriodicalIF":0.0,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144614845","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}
Pub Date : 2025-09-01Epub Date: 2025-06-18DOI: 10.1016/j.padiff.2025.101230
Nikhil Sharma , Sunil Joshi , Pranay Goswami
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., ) 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.
{"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":"2025-09-01","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}
This study presents a comprehensive theoretical investigation into the influence of surface roughness, magnetohydrodynamics (MHD), and micropolar fluid dynamics on the squeeze film behavior between two wide, parallel rectangular plates. A modified Reynolds equation is derived by incorporating Eringen’s microcontinuum theory, Christensen’s stochastic surface roughness model, and classical hydrodynamic principles. The model accounts for the effects of a perpendicular magnetic field and longitudinal surface irregularities. Key performance parameters—namely pressure distribution, load-carrying capacity, and squeeze film duration—are obtained analytically and evaluated using dimensionless groups such as the Hartmann number, coupling number, fluid gap interaction number, and surface roughness parameter. The results demonstrate that incorporating micropolar fluid properties and MHD effects significantly enhances squeeze film performance compared to the Newtonian fluid case. Surface roughness is also found to play a beneficial role in improving load support and film retention. The findings offer valuable insights for designing advanced lubrication systems in engineering applications where microstructural effects and magnetic fields are present.
{"title":"Stochastic reynolds equation for magnetohydrodynamics micropolar fluid and surface roughness in squeeze-film lubrication characteristics of rough parallel rectangular plates","authors":"B.S. Asha , H.M. Shivakumar , B.N. Hanumagowda , Jagadish V. Tawade , Barno Abdullaeva , Manish Gupta , Murali Gundagani , Taoufik Saidani , Nadia Batool","doi":"10.1016/j.padiff.2025.101269","DOIUrl":"10.1016/j.padiff.2025.101269","url":null,"abstract":"<div><div>This study presents a comprehensive theoretical investigation into the influence of surface roughness, magnetohydrodynamics (MHD), and micropolar fluid dynamics on the squeeze film behavior between two wide, parallel rectangular plates. A modified Reynolds equation is derived by incorporating Eringen’s microcontinuum theory, Christensen’s stochastic surface roughness model, and classical hydrodynamic principles. The model accounts for the effects of a perpendicular magnetic field and longitudinal surface irregularities. Key performance parameters—namely pressure distribution, load-carrying capacity, and squeeze film duration—are obtained analytically and evaluated using dimensionless groups such as the Hartmann number, coupling number, fluid gap interaction number, and surface roughness parameter. The results demonstrate that incorporating micropolar fluid properties and MHD effects significantly enhances squeeze film performance compared to the Newtonian fluid case. Surface roughness is also found to play a beneficial role in improving load support and film retention. The findings offer valuable insights for designing advanced lubrication systems in engineering applications where microstructural effects and magnetic fields are present.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101269"},"PeriodicalIF":0.0,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144830958","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}
Pub Date : 2025-09-01Epub Date: 2025-09-02DOI: 10.1016/j.padiff.2025.101281
Ilia Kashchenko, Igor Maslenikov
We study the nonlinear dynamics of second-order differential equation with delayed feedback depending on the derivative. The problem in question contains a small multiplier at the highest derivative, so it is singularly perturbed. We determine the stability of equilibrium depending on the parameters and find critical (bifurcation) cases. In each critical case, asymptotic approximations for the spectrum points (roots of the characteristic equation) are determined. The main feature of the problem under consideration is that in critical cases the spectrum consists of two parts: an infinite chain of points that tend to the imaginary axis and one or two more points located near the imaginary axis.
Using methods of asymptotic analysis to study bifurcations, in the critical cases we construct special equations – quasinormal forms. Quasinormal form is an analog of normal form. It does not depends on small parameter and its solutions provide the main part of the asymptotic approximation of the solutions of the original problem. Each quasinormal form is a partial differential equation with an antiderivative operator and integral term in nonlinearity. For the constructed forms stable periodic solutions are determined, asymptotic approximations on stable periodic solutions of original problem is obtained and the bifurcations that occur are described.
Also, the situation where two successive bifurcations occur in the system was described.
{"title":"Local dynamics of second-order differential equation with delayed derivative","authors":"Ilia Kashchenko, Igor Maslenikov","doi":"10.1016/j.padiff.2025.101281","DOIUrl":"10.1016/j.padiff.2025.101281","url":null,"abstract":"<div><div>We study the nonlinear dynamics of second-order differential equation with delayed feedback depending on the derivative. The problem in question contains a small multiplier at the highest derivative, so it is singularly perturbed. We determine the stability of equilibrium depending on the parameters and find critical (bifurcation) cases. In each critical case, asymptotic approximations for the spectrum points (roots of the characteristic equation) are determined. The main feature of the problem under consideration is that in critical cases the spectrum consists of two parts: an infinite chain of points that tend to the imaginary axis and one or two more points located near the imaginary axis.</div><div>Using methods of asymptotic analysis to study bifurcations, in the critical cases we construct special equations – quasinormal forms. Quasinormal form is an analog of normal form. It does not depends on small parameter and its solutions provide the main part of the asymptotic approximation of the solutions of the original problem. Each quasinormal form is a partial differential equation with an antiderivative operator and integral term in nonlinearity. For the constructed forms stable periodic solutions are determined, asymptotic approximations on stable periodic solutions of original problem is obtained and the bifurcations that occur are described.</div><div>Also, the situation where two successive bifurcations occur in the system was described.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101281"},"PeriodicalIF":0.0,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144987919","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}
Pub Date : 2025-09-01Epub Date: 2025-08-29DOI: 10.1016/j.padiff.2025.101273
Takafumi Akahori
The intermediate nonlinear Schrödinger equation (abbreviated to (INS)) is a model equation for envelope waves in a deep stratified fluid and can be thought of as a generalization of the defocusing nonlinear Schrödinger equation. Furthermore, it possesses dark multi-solitons as well as the defocusing nonlinear Schrödinger equation. In this paper, we reveal the asymptotic behavior of dark multi-solitons to (INS). We also give the asymptotic behavior of bright multi-solitons to the intermediate long wave equation. Our analysis relies only on the explicit forms of multi-solitons obtained by Hirota’s bilinear method.
{"title":"Asymptotic behavior of dark multi-solitons to the intermediate nonlinear Schrödinger equation","authors":"Takafumi Akahori","doi":"10.1016/j.padiff.2025.101273","DOIUrl":"10.1016/j.padiff.2025.101273","url":null,"abstract":"<div><div>The intermediate nonlinear Schrödinger equation (abbreviated to (INS)) is a model equation for envelope waves in a deep stratified fluid and can be thought of as a generalization of the defocusing nonlinear Schrödinger equation. Furthermore, it possesses dark multi-solitons as well as the defocusing nonlinear Schrödinger equation. In this paper, we reveal the asymptotic behavior of dark multi-solitons to (INS). We also give the asymptotic behavior of bright multi-solitons to the intermediate long wave equation. Our analysis relies only on the explicit forms of multi-solitons obtained by Hirota’s bilinear method.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101273"},"PeriodicalIF":0.0,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144919986","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}
Pub Date : 2025-09-01Epub Date: 2025-06-26DOI: 10.1016/j.padiff.2025.101241
Mangala Kandagal , Ramesh Kempepatil , Jagadish V. Tawade , Nodira Nazarova , Manish Gupta , M. Khan
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.
{"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":"2025-09-01","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}
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