Pub Date : 2025-07-29DOI: 10.1016/j.padiff.2025.101261
Abderrahim El Ayboudi , Radoine Belkanoufi , Abdelkarim Hajjaj
This paper investigates the indirect boundary observability properties of one-dimensional strongly coupled wave equations in an approximated setting. Classical numerical discretization methods, such as finite differences and finite elements, typically fail to maintain uniform observability inequalities when applied to wave systems. This failure is primarily attributed to the emergence of high-frequency numerical solutions. The present work demonstrates a different approach through the implementation of these discretization schemes on a carefully designed non-uniform mesh. This study successfully establishes uniform observability inequalities for the coupled system. This methodology effectively recovers the system’s total energy through boundary observations, overcoming the well-documented limitations of traditional numerical approaches in wave equation systems.
{"title":"Uniform indirect boundary observability for a spatial discretization of strongly coupled wave equations","authors":"Abderrahim El Ayboudi , Radoine Belkanoufi , Abdelkarim Hajjaj","doi":"10.1016/j.padiff.2025.101261","DOIUrl":"10.1016/j.padiff.2025.101261","url":null,"abstract":"<div><div>This paper investigates the indirect boundary observability properties of one-dimensional strongly coupled wave equations in an approximated setting. Classical numerical discretization methods, such as finite differences and finite elements, typically fail to maintain uniform observability inequalities when applied to wave systems. This failure is primarily attributed to the emergence of high-frequency numerical solutions. The present work demonstrates a different approach through the implementation of these discretization schemes on a carefully designed non-uniform mesh. This study successfully establishes uniform observability inequalities for the coupled system. This methodology effectively recovers the system’s total energy through boundary observations, overcoming the well-documented limitations of traditional numerical approaches in wave equation systems.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101261"},"PeriodicalIF":0.0,"publicationDate":"2025-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144772096","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 : 2025-07-28DOI: 10.1016/j.padiff.2025.101257
Thokozani Blessing Shiba, Khadijo Rashid Adem
This study examines the Camassa–Holm–Kadomtsev–Petviashvili equation with power law nonlinearity in (3+1)-D. The highlighted equation appears in mathematical physics, particularly in the study of nonlinear optics, plasma, integrable systems, and soliton theory, among other areas. The integration of the underlying equation is done using Lie symmetry analysis. To get more precise answers, the ansatz approach is applied. Traveling wave solutions are then obtained. The multiplier approach will be used to obtain conservation laws for the underlying equation.
{"title":"On the exact explicit solutions and conservation laws of the generalized (3+1)-D Camassa–Holm–Kadomtsev–Petviashvili equation with power law nonlinearity","authors":"Thokozani Blessing Shiba, Khadijo Rashid Adem","doi":"10.1016/j.padiff.2025.101257","DOIUrl":"10.1016/j.padiff.2025.101257","url":null,"abstract":"<div><div>This study examines the Camassa–Holm–Kadomtsev–Petviashvili equation with power law nonlinearity in (3+1)-D. The highlighted equation appears in mathematical physics, particularly in the study of nonlinear optics, plasma, integrable systems, and soliton theory, among other areas. The integration of the underlying equation is done using Lie symmetry analysis. To get more precise answers, the ansatz approach is applied. Traveling wave solutions are then obtained. The multiplier approach will be used to obtain conservation laws for the underlying equation.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101257"},"PeriodicalIF":0.0,"publicationDate":"2025-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144779770","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 : 2025-07-26DOI: 10.1016/j.padiff.2025.101264
Ali Ahadi , Seyed Mostafa Mousavi , Amir Mohammad Alinia , Hossein Khademi
Partial differential equations (PDEs), particularly those involving fractional derivatives, have garnered considerable attention due to their ability to model complex systems with memory and hereditary properties. This paper focuses on the generalized Caputo fractional equation and presents a comparative analysis of three powerful solution techniques: the Homotopy Perturbation Method (HPM), the Variational Iteration Method (VIM), and the Akbari-Ganji Method (AGM). These methods are applied to fractional differential equations (FDEs) to derive approximate solutions. The accuracy and effectiveness of the methods are demonstrated through detailed comparisons with exact solutions and previous works in the field.
The study highlights the strengths of each technique in handling non-linear and fractional-order problems, providing reliable results with minimal error. Specifically, the HPM and VIM show remarkable convergence properties, while the AGM proves efficient in solving both linear and non-linear equations. These methods are validated by comparing the results with known solutions, which shows that these techniques work for a wide range of FDEs. The present study underscores the applicability of these approaches in several scientific and technological domains, hence promoting more advancements in the numerical examination of fractional systems.
{"title":"Analytical simulation of the nonlinear Caputo fractional equations","authors":"Ali Ahadi , Seyed Mostafa Mousavi , Amir Mohammad Alinia , Hossein Khademi","doi":"10.1016/j.padiff.2025.101264","DOIUrl":"10.1016/j.padiff.2025.101264","url":null,"abstract":"<div><div>Partial differential equations (PDEs), particularly those involving fractional derivatives, have garnered considerable attention due to their ability to model complex systems with memory and hereditary properties. This paper focuses on the generalized Caputo fractional equation and presents a comparative analysis of three powerful solution techniques: the Homotopy Perturbation Method (HPM), the Variational Iteration Method (VIM), and the Akbari-Ganji Method (AGM). These methods are applied to fractional differential equations (FDEs) to derive approximate solutions. The accuracy and effectiveness of the methods are demonstrated through detailed comparisons with exact solutions and previous works in the field.</div><div>The study highlights the strengths of each technique in handling non-linear and fractional-order problems, providing reliable results with minimal error. Specifically, the HPM and VIM show remarkable convergence properties, while the AGM proves efficient in solving both linear and non-linear equations. These methods are validated by comparing the results with known solutions, which shows that these techniques work for a wide range of FDEs. The present study underscores the applicability of these approaches in several scientific and technological domains, hence promoting more advancements in the numerical examination of fractional systems.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101264"},"PeriodicalIF":0.0,"publicationDate":"2025-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144724410","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 : 2025-07-25DOI: 10.1016/j.padiff.2025.101263
P. Kumar , AR. Ajaykumar , F. Almeida , S. Saranya , Qasem Al-Mdallal
Statistical and numerical approach is provided in the current article for Casson-Carreau nanofluid transient flow over continuously elongated sheet of curved feature. The flow is subjected under the various generation, Joule heating, non-linear thermal radiation, activation energy, second order slip, and convective peripheral conditions. Identifying the parameters that optimize the heat transfer rate and using those parameters applying the appropriate statistical tool to optimize the heat transfer rate are the two motives behind this study. A regression analysis is executed on the entropy generated; it has analyzed statistically using response surface methodology. For the issue under consideration, a Runge-Kutta-Fehlberg 4–5th order scheme has been implemented. Here, the study shows that although the Darcy number and first order slip decelerates velocity, the second order slip improves the velocity regime. Additionally, the study has showed that the activation energy parameter leverages the same, while chemical reaction parameter has negative effect on mass dispersion. With an increase in Brinkmann number, entropy production likewise rises, and fluid friction irreversibilities become more prevalent. As unsteadiness and activation energy parameters increase, Sherwood number declines. The visual representation of isotherms and streamlines is presented to display the flow and temperature pattern as a summary of the study. For the experimental setup by RSM, the better correlation coefficient is 99.93 % attained. The Pareto-chart specifies 2.2 to be the vital point for the statistical experimental design considered. For all the levels of heat source parameter and Eckert number, Radiation parameter exhibits positive sensitivity.
{"title":"Statistical and numerical investigation of irreversibility for time-dependent Casson-Carreau nanofluid flow driven by curved surface: Regression analysis","authors":"P. Kumar , AR. Ajaykumar , F. Almeida , S. Saranya , Qasem Al-Mdallal","doi":"10.1016/j.padiff.2025.101263","DOIUrl":"10.1016/j.padiff.2025.101263","url":null,"abstract":"<div><div>Statistical and numerical approach is provided in the current article for Casson-Carreau nanofluid transient flow over continuously elongated sheet of curved feature. The flow is subjected under the various generation, Joule heating, non-linear thermal radiation, activation energy, second order slip, and convective peripheral conditions. Identifying the parameters that optimize the heat transfer rate and using those parameters applying the appropriate statistical tool to optimize the heat transfer rate are the two motives behind this study. A regression analysis is executed on the entropy generated; it has analyzed statistically using response surface methodology. For the issue under consideration, a Runge-Kutta-Fehlberg 4–5th order scheme has been implemented. Here, the study shows that although the Darcy number and first order slip decelerates velocity, the second order slip improves the velocity regime. Additionally, the study has showed that the activation energy parameter leverages the same, while chemical reaction parameter has negative effect on mass dispersion. With an increase in Brinkmann number, entropy production likewise rises, and fluid friction irreversibilities become more prevalent. As unsteadiness and activation energy parameters increase, Sherwood number declines. The visual representation of isotherms and streamlines is presented to display the flow and temperature pattern as a summary of the study. For the experimental setup by RSM, the better correlation coefficient is 99.93 % attained. The Pareto-chart specifies 2.2 to be the vital point for the statistical experimental design considered. For all the levels of heat source parameter and Eckert number, Radiation parameter exhibits positive sensitivity.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101263"},"PeriodicalIF":0.0,"publicationDate":"2025-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144829639","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}
Data analysis (DA) is crucial in materials science and engineering for optimizing heat and mass transport processes. This study investigates the impact of magneto-hydrodynamics (MHD), quadratic radiation, and chemical reactions on entropy generation in Williamson fluid over an inclined porous sheet (IPS). It uses a numerical approach that integrates the 6th-order Runge-Kutta (R-K) method with the Nachtsheim-Swigert (N-S) shooting technique after transforming the governing equations into ordinary differential equations (ODEs). The research aims to elucidate the entropy generation dynamics of the Williamson fluid, examining the effects of quadratic radiative MHD chemical reactions. The key novelty of this work is that for 0.5 ≤ Kr ≤ 2.5, entropy production increases by 90.09% with linear radiation and by 114.60% with quadratic radiation, with the increase being higher for quadratic radiation. However, entropy generation for quadratic radiation is 14.10% lower than for linear radiation at Kr = 0.5. For an inclined sheet, it is 8.14% less than for a flat sheet at K = 2.5, and for Williamson fluid, it is 3.76% less than for Newtonian fluid at a diffusion coefficient of ϑ = 1.0. Additionally, the temperature increases in both the linear as well as quadratic radiation situations when the Williamson and radiation parameters increase. Regression analysis confirms the model's durability and accuracy at a 95% confidence level, with an R2 value of 99.92% and a strong positive correlation of over 99% between chemical processes and entropy creation. Understanding entropy production is crucial for optimizing cooling systems and heat exchangers, including biotechnology.
{"title":"Data analysis of entropy generation in quadratic radiative with chemically reactive Williamson fluid flow past an inclined porous sheet","authors":"Md. Yousuf Ali, Mizanur Rahman, Md. Shakib Hossain, Mst. Sharmin Akter, Noor Muhammad, Atia Sanjida Talukder","doi":"10.1016/j.padiff.2025.101266","DOIUrl":"10.1016/j.padiff.2025.101266","url":null,"abstract":"<div><div>Data analysis (DA) is crucial in materials science and engineering for optimizing heat and mass transport processes. This study investigates the impact of magneto-hydrodynamics (MHD), quadratic radiation, and chemical reactions on entropy generation in Williamson fluid over an inclined porous sheet (IPS). It uses a numerical approach that integrates the 6th-order Runge-Kutta (R-K) method with the Nachtsheim-Swigert (N-S) shooting technique after transforming the governing equations into ordinary differential equations (ODEs). The research aims to elucidate the entropy generation dynamics of the Williamson fluid, examining the effects of quadratic radiative MHD chemical reactions. The key novelty of this work is that for 0.5 ≤ <em>Kr</em> ≤ 2.5, entropy production increases by 90.09% with linear radiation and by 114.60% with quadratic radiation, with the increase being higher for quadratic radiation. However, entropy generation for quadratic radiation is 14.10% lower than for linear radiation at <em>Kr</em> = 0.5. For an inclined sheet, it is 8.14% less than for a flat sheet at <em>K</em> = 2.5, and for Williamson fluid, it is 3.76% less than for Newtonian fluid at a diffusion coefficient of <em>ϑ</em> = 1.0. Additionally, the temperature increases in both the linear as well as quadratic radiation situations when the Williamson and radiation parameters increase. Regression analysis confirms the model's durability and accuracy at a 95% confidence level, with an <em>R</em><sup>2</sup> value of 99.92% and a strong positive correlation of over 99% between chemical processes and entropy creation. Understanding entropy production is crucial for optimizing cooling systems and heat exchangers, including biotechnology.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101266"},"PeriodicalIF":0.0,"publicationDate":"2025-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144724411","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The present work focuses on the exploration of MHD ternary hybrid nanofluid (THNF) flow of boundary layer past a porous stretching surface. In this investigation, we have analysed how various sources such as magnetic field, porosity, heat generation, radiation affect the flow dynamics. The novelty of the work is to understand the heat transfer phenomenon of hybrid nanofluid subjected to magnetic field, viscous dissipation, radiation and porosity effects. of To understand the flow behaviour better associated partial differential equations were transformed to ordinary differential equations via similarity transformations. We have explored this resulting system through MATLAB bvp4c. The results showed that thermal radiation, solid volume fraction improved heat transfer in THNFs as compared to HNFs. By varying the values of various parameters of flow like solid volume fraction, magnetic field parameter, radiation parameter, permeability parameter we have thoroughly studied and compared the flow dynamics with the previously established results. The study has real world applications involving solar plants, applications demanding improved heat transfer and energy saving applications such as air coolers etc.
{"title":"Analysis of MHD radiative flow of ternary hybrid nanofluid over a porous stretching surface","authors":"Shital Sobale , Jagadish V. Tawade , Pooja Bagane , Vediyappn Govindan , Barno Abdullaeva , Hawzhen Fateh M. Ameen , Manish Gupta , Nadia Batool","doi":"10.1016/j.padiff.2025.101267","DOIUrl":"10.1016/j.padiff.2025.101267","url":null,"abstract":"<div><div>The present work focuses on the exploration of MHD ternary hybrid nanofluid (THNF) flow of boundary layer past a porous stretching surface. In this investigation, we have analysed how various sources such as magnetic field, porosity, heat generation, radiation affect the flow dynamics. The novelty of the work is to understand the heat transfer phenomenon of <span><math><mrow><mi>A</mi><msub><mi>l</mi><mn>2</mn></msub><msub><mi>O</mi><mn>3</mn></msub><mo>,</mo><mo>−</mo><mi>T</mi><mi>i</mi><msub><mi>O</mi><mn>2</mn></msub><mo>−</mo><mi>A</mi><mi>g</mi><mo>/</mo><mi>w</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>r</mi></mrow></math></span> hybrid nanofluid subjected to magnetic field, viscous dissipation, radiation and porosity effects. of To understand the flow behaviour better associated partial differential equations were transformed to ordinary differential equations via similarity transformations. We have explored this resulting system through MATLAB bvp4c. The results showed that thermal radiation, solid volume fraction improved heat transfer in THNFs as compared to HNFs. By varying the values of various parameters of flow like solid volume fraction, magnetic field parameter, radiation parameter, permeability parameter we have thoroughly studied and compared the flow dynamics with the previously established results. The study has real world applications involving solar plants, applications demanding improved heat transfer and energy saving applications such as air coolers etc.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101267"},"PeriodicalIF":0.0,"publicationDate":"2025-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144724517","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 : 2025-07-22DOI: 10.1016/j.padiff.2025.101262
Sangamesh , K.R. Raghunatha , Ali J. Chamkha , Vinod Y
The research examines the behaviour of nanofluid flow, incorporating Casson fluid properties and a heat source, as it moves over a sheet that stretches exponentially at the stagnation point. The interplay of Brownian motion and thermophoretic properties adds to the complexity, creating a coupled nonlinear boundary-value problem (BVP). The original partial differential equations (PDEs) are converted into ordinary forms by applying proper similarity conversions. Initially formulated for an infinite domain [0, ∞), the problem was then converted to a finite domain [0, 1] using wavelet transformations. The Bernoulli wavelet method (BWM) was employed to numerically solve the transformed equations within the MATHEMATICA 12 platform. The obtained findings are extremely compared with earlier research that examined various specific scenarios within the problem. A detailed investigation of the physical limitations is conducted and the numerical results are visually presented to provide clear illustrations. A higher Prandtl number leads to reduced thermal diffusivity, resulting in a thinner thermal boundary layer and steeper temperature gradients concentrated near the surface. Similarly, an increase in the Lewis number lowers molecular diffusivity, producing a more confined solutal boundary layer. The presence of an internal heat source further elevates fluid temperature near the stretching sheet, expanding the thermal boundary layer due to added thermal energy.
{"title":"Influence of heat source on Casson nanofluid flow over an exponentially stretching sheet","authors":"Sangamesh , K.R. Raghunatha , Ali J. Chamkha , Vinod Y","doi":"10.1016/j.padiff.2025.101262","DOIUrl":"10.1016/j.padiff.2025.101262","url":null,"abstract":"<div><div>The research examines the behaviour of nanofluid flow, incorporating Casson fluid properties and a heat source, as it moves over a sheet that stretches exponentially at the stagnation point. The interplay of Brownian motion and thermophoretic properties adds to the complexity, creating a coupled nonlinear boundary-value problem (BVP). The original partial differential equations (PDEs) are converted into ordinary forms by applying proper similarity conversions. Initially formulated for an infinite domain [0, ∞), the problem was then converted to a finite domain [0, 1] using wavelet transformations. The Bernoulli wavelet method (BWM) was employed to numerically solve the transformed equations within the MATHEMATICA 12 platform. The obtained findings are extremely compared with earlier research that examined various specific scenarios within the problem. A detailed investigation of the physical limitations is conducted and the numerical results are visually presented to provide clear illustrations. A higher Prandtl number leads to reduced thermal diffusivity, resulting in a thinner thermal boundary layer and steeper temperature gradients concentrated near the surface. Similarly, an increase in the Lewis number lowers molecular diffusivity, producing a more confined solutal boundary layer. The presence of an internal heat source further elevates fluid temperature near the stretching sheet, expanding the thermal boundary layer due to added thermal energy.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101262"},"PeriodicalIF":0.0,"publicationDate":"2025-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144704591","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 : 2025-07-17DOI: 10.1016/j.padiff.2025.101260
Mostafa Mohamed Okasha , Mohammed Qader Gubari , Hawzhen Fateh M. Ameen , Munawar Abbas , Muyassar Norberdiyeva , Wei Sin Koh , Ilyas Khan
This study examines the effects of velocity slip and local thermal non-equilibrium on the non-Darcy chemical convective flow of a Boger hybrid nanofluid across a sheet. The energy equation-based on local thermal non-equilibrium model provides outstanding heat transmission for solid and liquid phases. The two thermal distributions for the liquid and solid phases are basically used in this method. The hybrid nanoliquid (SiC − Co3O4/DO) flow model consist of nanoparticles of silicon carbide (SiC) and Cobalt oxide (Co3O4) dissolved in diathermic oil. This model can be used in sectors of the economy where improved heat transfer is essential, like electronic cooling systems, automotive thermal systems, and energy-efficient heat exchangers. The concept is also applicable to the design of materials for use in aerospace applications, where it is necessary to precisely regulate the mechanical and thermal properties under conditions of high stress and temperature gradients. The Bvp4c method is used to numerically solve the model equation system once all relevant similarity variables have been decreased. Outcomes display that Boger hybrid nanofluid shows increase flow and decline the thermal and concentration distributions as increasing the solvent percent and Stefan blowing parameters values.
{"title":"Computational assessment of local thermal non-equilibrium effects on non-darcy chemical reactive flow of boger hybrid nanofluid with elastic deformation","authors":"Mostafa Mohamed Okasha , Mohammed Qader Gubari , Hawzhen Fateh M. Ameen , Munawar Abbas , Muyassar Norberdiyeva , Wei Sin Koh , Ilyas Khan","doi":"10.1016/j.padiff.2025.101260","DOIUrl":"10.1016/j.padiff.2025.101260","url":null,"abstract":"<div><div>This study examines the effects of velocity slip and local thermal non-equilibrium on the non-Darcy chemical convective flow of a Boger hybrid nanofluid across a sheet. The energy equation-based on local thermal non-equilibrium model provides outstanding heat transmission for solid and liquid phases. The two thermal distributions for the liquid and solid phases are basically used in this method. The hybrid nanoliquid (<em>SiC</em> − <em>C</em>o<sub>3</sub>O<sub>4</sub>/<em>DO</em>) flow model consist of nanoparticles of silicon carbide (<em>SiC</em>) and Cobalt oxide (Co<sub>3</sub>O<sub>4</sub>) dissolved in diathermic oil. This model can be used in sectors of the economy where improved heat transfer is essential, like electronic cooling systems, automotive thermal systems, and energy-efficient heat exchangers. The concept is also applicable to the design of materials for use in aerospace applications, where it is necessary to precisely regulate the mechanical and thermal properties under conditions of high stress and temperature gradients. The Bvp4c method is used to numerically solve the model equation system once all relevant similarity variables have been decreased. Outcomes display that Boger hybrid nanofluid shows increase flow and decline the thermal and concentration distributions as increasing the solvent percent and Stefan blowing parameters values.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101260"},"PeriodicalIF":0.0,"publicationDate":"2025-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144757968","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 : 2025-07-16DOI: 10.1016/j.padiff.2025.101259
Adedapo Chris Loyinmi , Alani Lateef Ijaola
In this study, we presented a fractional order transmission model to investigate the dynamics and potential controls for measles, in order to accurately represent the dynamics of its transmission. We propose a modified S, V, E, I and R (Susceptible, Vaccinated, Exposed, Infectious and Recovered individuals), a workable human population model with an incident rate equipped with a saturation factor to investigate the combined impact of three prophylactic techniques, which are public awareness, second dose vaccination and proper treatment in case of severity.. Here, we assumed there is a vaccinated population that has taken first dose in the proposed model. We established among other things, the parameter responsible for invasion, the reproductive number,R0 is less than unity through the stability analysis and the numerical solution of the fractional order model was done using the Adams Bashforth predictor-corrector method. In addition, the effects of the prophylactic measures and the fractional order (α) were simulated and findings from the graphical solutions depict that these measures aid in flattening out the trajectory of the disease if measure are properly implemented.
{"title":"Fractional order modeling of prophylactic measures on the transmission dynamics of measles: An optimal control analysis","authors":"Adedapo Chris Loyinmi , Alani Lateef Ijaola","doi":"10.1016/j.padiff.2025.101259","DOIUrl":"10.1016/j.padiff.2025.101259","url":null,"abstract":"<div><div>In this study, we presented a fractional order transmission model to investigate the dynamics and potential controls for measles, in order to accurately represent the dynamics of its transmission. We propose a modified S, V, E, I and R (Susceptible, Vaccinated, Exposed, Infectious and Recovered individuals), a workable human population model with an incident rate equipped with a saturation factor to investigate the combined impact of three prophylactic techniques, which are public awareness, second dose vaccination and proper treatment in case of severity.. Here, we assumed there is a vaccinated population that has taken first dose in the proposed model. We established among other things, the parameter responsible for invasion, the reproductive number,<em>R</em><sub>0</sub> is less than unity through the stability analysis and the numerical solution of the fractional order model was done using the Adams Bashforth predictor-corrector method. In addition, the effects of the prophylactic measures and the fractional order (α) were simulated and findings from the graphical solutions depict that these measures aid in flattening out the trajectory of the disease if measure are properly implemented.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101259"},"PeriodicalIF":0.0,"publicationDate":"2025-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144680601","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 : 2025-07-14DOI: 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":"2025-07-14","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}
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