The present analysis is aimed at examining MHD micropolar nanofluid flow past a radially stretchable rotating disk with the Cattaneo-Christov non-Fourier heat and non-Fick mass flux model. To begin with, the model is developed in the form of nonlinear partial differential equations (PDEs) for momentum, microrotation, thermal, and concentration with their boundary conditions. Employing suitable similarity transformation, the boundary layer micropolar nanofluid flows governing these PDEs are transformed into large systems of dimensionless coupled nonlinear ordinary differential equations (ODEs). These dimensionless ODEs are solved numerically by means of the spectral local linearization method (SLLM). The consequences of more noticeable involved parameters on different flow fields and engineering quantities of interest are thoroughly inspected, and the results are presented via graph plots and tables. The obtained results confirm that SLLM is a stable, accurate, convergent, and computationally very efficient method to solve a large coupled system of equations. The radial velocity grows while the tangential velocity, temperature, and concentration distributions turn down as the value of the radial stretching parameter improves, and hence, in practical applications, radial stretching of the disk is helpful to advance the cooling process of the rotating disk. The occurrence of microrotation viscosity in microrotation parameters ( A 1 − A 6 ) declines the radial velocity profile, and the kinetic energy of the fluid is reduced to some extent far away from the surface of the disk. The novelty of the study is the consideration of microscopic effects occurring from the micropolar fluid elements such as micromotion and couple stress, the effects of non-Fourier’s heat and non-Fick’s mass flux, and the effect of radial stretching disk on micropolar nanofluid flow, heat, and mass transfer.
{"title":"Analysis of Magnetohydrodynamic Micropolar Nanofluid Flow due to Radially Stretchable Rotating Disk Employing Spectral Method","authors":"Ayele Tulu","doi":"10.1155/2023/5283475","DOIUrl":"https://doi.org/10.1155/2023/5283475","url":null,"abstract":"The present analysis is aimed at examining MHD micropolar nanofluid flow past a radially stretchable rotating disk with the Cattaneo-Christov non-Fourier heat and non-Fick mass flux model. To begin with, the model is developed in the form of nonlinear partial differential equations (PDEs) for momentum, microrotation, thermal, and concentration with their boundary conditions. Employing suitable similarity transformation, the boundary layer micropolar nanofluid flows governing these PDEs are transformed into large systems of dimensionless coupled nonlinear ordinary differential equations (ODEs). These dimensionless ODEs are solved numerically by means of the spectral local linearization method (SLLM). The consequences of more noticeable involved parameters on different flow fields and engineering quantities of interest are thoroughly inspected, and the results are presented via graph plots and tables. The obtained results confirm that SLLM is a stable, accurate, convergent, and computationally very efficient method to solve a large coupled system of equations. The radial velocity grows while the tangential velocity, temperature, and concentration distributions turn down as the value of the radial stretching parameter improves, and hence, in practical applications, radial stretching of the disk is helpful to advance the cooling process of the rotating disk. The occurrence of microrotation viscosity in microrotation parameters (\u0000 \u0000 \u0000 \u0000 A\u0000 \u0000 \u0000 1\u0000 \u0000 \u0000 −\u0000 \u0000 \u0000 A\u0000 \u0000 \u0000 6\u0000 \u0000 \u0000 \u0000 ) declines the radial velocity profile, and the kinetic energy of the fluid is reduced to some extent far away from the surface of the disk. The novelty of the study is the consideration of microscopic effects occurring from the micropolar fluid elements such as micromotion and couple stress, the effects of non-Fourier’s heat and non-Fick’s mass flux, and the effect of radial stretching disk on micropolar nanofluid flow, heat, and mass transfer.","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42749863","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The current study examined the effects of magnetohydrodynamics (MHD) on time-dependent mixed convection flow of an exothermic fluid in a vertical channel. Convective heating and Navier’s slip conditions are considered. The dimensional nonlinear flow equations are transformed into dimensionless form with suitable transformation. For steady-state flow formations, we apply homotopy perturbation approach. However, for the unsteady-state governing equation, we use numerical technique known as the implicit finite difference approach. Flow is influenced by several factors, including the Hartmann number, Newtonian heating, Navier slip parameter, Frank-Kamenetskii parameter, and mixed convection parameter. Shear stress and heat transfer rates were also investigated and reported. The steady-state and unsteady-state solutions are visually expressed in terms of velocity and temperature profiles. Due to the presence of opposing force factors such as the Lorentz force, the research found that the Hartmann number reduces the momentum profile. Fluid temperature and velocity increase as the thermal Biot number and Frank-Kamenetskii parameter increase. There are several scientific and infrastructure capabilities that use this type of flow, such flow including solar communication systems exposed to airflow, electronic devices cooled at room temperature by airflow, nuclear units maintained during unscheduled shutoffs, and cooling systems occurring in low circumstances. The current findings and the literature are very consistent, which recommend the application of the current study.
{"title":"Time-Dependent Magnetohydrodynamic (MHD) Flow of an Exothermic Arrhenius Fluid in a Vertical Channel with Convective Boundary Condition","authors":"M. Hamza, S. Abdulsalam, S. Ahmad","doi":"10.1155/2023/7173925","DOIUrl":"https://doi.org/10.1155/2023/7173925","url":null,"abstract":"The current study examined the effects of magnetohydrodynamics (MHD) on time-dependent mixed convection flow of an exothermic fluid in a vertical channel. Convective heating and Navier’s slip conditions are considered. The dimensional nonlinear flow equations are transformed into dimensionless form with suitable transformation. For steady-state flow formations, we apply homotopy perturbation approach. However, for the unsteady-state governing equation, we use numerical technique known as the implicit finite difference approach. Flow is influenced by several factors, including the Hartmann number, Newtonian heating, Navier slip parameter, Frank-Kamenetskii parameter, and mixed convection parameter. Shear stress and heat transfer rates were also investigated and reported. The steady-state and unsteady-state solutions are visually expressed in terms of velocity and temperature profiles. Due to the presence of opposing force factors such as the Lorentz force, the research found that the Hartmann number reduces the momentum profile. Fluid temperature and velocity increase as the thermal Biot number and Frank-Kamenetskii parameter increase. There are several scientific and infrastructure capabilities that use this type of flow, such flow including solar communication systems exposed to airflow, electronic devices cooled at room temperature by airflow, nuclear units maintained during unscheduled shutoffs, and cooling systems occurring in low circumstances. The current findings and the literature are very consistent, which recommend the application of the current study.","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46140263","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This study examines the flow of hyperbolic nanofluid over a stretching sheet in three dimensions. The influence of velocity slip on the flow and heat transfer properties of a hyperbolic nanofluid has been investigated. The partial differential equations for nanoparticle solid concentration, energy, and motion were turned into ordinary differential equations. Nanoparticle mass fluxes at boundaries are assumed to be zero, unlike surface concentrations. The influence of the main parameters on flow characteristics, surface friction coefficients, and the Nusselt number has been visualized. The results suggest that Brownian motion has a negligible impact on the heat transfer rate. The ratio of the elastic force to the viscosity force was found to decrease the fluid velocity. The resulting thermophysical properties of nanofluids are in agreement with previous research. The present findings can be used to expand the potential for using nanofluids as a coolant in critical thermophysical and industrial installations.
{"title":"Quasilinear Hyperbolic Systems Applied to Describe the Magnetohydrodynamic Nanofluid Flow","authors":"Dayong Nie","doi":"10.1155/2023/4349646","DOIUrl":"https://doi.org/10.1155/2023/4349646","url":null,"abstract":"This study examines the flow of hyperbolic nanofluid over a stretching sheet in three dimensions. The influence of velocity slip on the flow and heat transfer properties of a hyperbolic nanofluid has been investigated. The partial differential equations for nanoparticle solid concentration, energy, and motion were turned into ordinary differential equations. Nanoparticle mass fluxes at boundaries are assumed to be zero, unlike surface concentrations. The influence of the main parameters on flow characteristics, surface friction coefficients, and the Nusselt number has been visualized. The results suggest that Brownian motion has a negligible impact on the heat transfer rate. The ratio of the elastic force to the viscosity force was found to decrease the fluid velocity. The resulting thermophysical properties of nanofluids are in agreement with previous research. The present findings can be used to expand the potential for using nanofluids as a coolant in critical thermophysical and industrial installations.","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46726402","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The combined quasineutral and zero-viscosity limits of the bipolar Navier-Stokes-Poisson system with boundary are rigorously proved by establishing the nonlinear stability of the approximate solutions. Based on the conormal energy estimates, we showed that the solutions for the original system converge strongly in H 3 space towards the solutions of the one-fluid compressible Euler system as long as the amplitude of the boundary layers is small enough.
{"title":"Nonlinear Stability of the Bipolar Navier-Stokes-Poisson System with Boundary","authors":"Tiantian Yu, Yong Li","doi":"10.1155/2023/2461834","DOIUrl":"https://doi.org/10.1155/2023/2461834","url":null,"abstract":"The combined quasineutral and zero-viscosity limits of the bipolar Navier-Stokes-Poisson system with boundary are rigorously proved by establishing the nonlinear stability of the approximate solutions. Based on the conormal energy estimates, we showed that the solutions for the original system converge strongly in \u0000 \u0000 \u0000 \u0000 H\u0000 \u0000 \u0000 3\u0000 \u0000 \u0000 \u0000 space towards the solutions of the one-fluid compressible Euler system as long as the amplitude of the boundary layers is small enough.","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44051514","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we aim to investigate the ( 2 + 1 )-dimensional Heisenberg ferromagnetic spin chain equation that is used to describe the nonlinear dynamics of magnets. Two recent effective technologies, namely, the variational method and subequation method, are employed to construct the abundant soliton solutions. By these two methods, diverse solutions such as the bright soliton, dark soliton, bright-dark soliton, perfect periodic soliton, and singular periodic soliton are successfully extracted. The numerical results are illustrated in the form of 3-D plots and 2-D curves by choosing proper parametric values to interpret the dynamics of wave profiles. Finally, the physical interpretation of the acquired results is elaborated in detail. The results obtained in this study are helpful to explain some physical meanings of some nonlinear physical models in electromagnetic waves.
{"title":"Abundant Soliton Structures to the (\u0000 2\u0000 +\u0000 1\u0000 )-Dimensional Heisenberg Ferromagnetic Spin Chain Dynamical Model","authors":"Kangkang Wang, Feng Shi, Guo‐Dong Wang","doi":"10.1155/2023/4348758","DOIUrl":"https://doi.org/10.1155/2023/4348758","url":null,"abstract":"In this paper, we aim to investigate the (\u0000 \u0000 2\u0000 +\u0000 1\u0000 \u0000 )-dimensional Heisenberg ferromagnetic spin chain equation that is used to describe the nonlinear dynamics of magnets. Two recent effective technologies, namely, the variational method and subequation method, are employed to construct the abundant soliton solutions. By these two methods, diverse solutions such as the bright soliton, dark soliton, bright-dark soliton, perfect periodic soliton, and singular periodic soliton are successfully extracted. The numerical results are illustrated in the form of 3-D plots and 2-D curves by choosing proper parametric values to interpret the dynamics of wave profiles. Finally, the physical interpretation of the acquired results is elaborated in detail. The results obtained in this study are helpful to explain some physical meanings of some nonlinear physical models in electromagnetic waves.","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47763033","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Based on the Hirota bilinear method, using the heuristic function method and mathematical symbolic computation system, various exact solutions of the ( 4 + 1 )-dimensional Boiti–Leon–Manna–Pempinelli equation including the block kink wave solution, block soliton solution, periodic block solution, and new composite solution are obtained. Upon selection of the appropriate parameters, three-dimensional and contour diagrams of the exact solution were generated to illustrate their properties.
{"title":"Exact Solution of (<math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\">\u0000 <mn>4</mn>\u0000 <mo>+</mo>\u0000 <mn>1</mn>\u0000 </math>)-Dimensional Boiti–Leon–Manna–Pempinelli Equation","authors":"Qili Hao","doi":"10.1155/2023/1448953","DOIUrl":"https://doi.org/10.1155/2023/1448953","url":null,"abstract":"Based on the Hirota bilinear method, using the heuristic function method and mathematical symbolic computation system, various exact solutions of the (\u0000 \u0000 4\u0000 +\u0000 1\u0000 \u0000 )-dimensional Boiti–Leon–Manna–Pempinelli equation including the block kink wave solution, block soliton solution, periodic block solution, and new composite solution are obtained. Upon selection of the appropriate parameters, three-dimensional and contour diagrams of the exact solution were generated to illustrate their properties.","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49249220","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Fangfang Wu, Duoduo Xu, Ming-Feng Tian, Yingying Wang
In this paper, an efficient lattice Boltzmann model for the generalized Black-Scholes equation governing option pricing is proposed. The Black-Scholes equation is firstly equivalently transformed into an initial value problem for a partial differential equation with a source term using the variable substitution and the derivative rules, respectively. Then, applying the multiscale Chapman-Enskog expansion, the amending function is expanded to second order to recover the convective and source terms of the macroscopic equation. The D1Q3 lattice Boltzmann model with spatial second-order accuracy is constructed, and the accuracy of the established D1Q5 model is greater than second order. The numerical simulation results demonstrate the effectiveness and numerical accuracy of the proposed models and indicate that our proposed models are suitable for solving the Black-Scholes equation. The proposed lattice Boltzmann model can also be applied to a class of partial differential equations with variable coefficients and source terms.
{"title":"Lattice Boltzmann Method for the Generalized Black-Scholes Equation","authors":"Fangfang Wu, Duoduo Xu, Ming-Feng Tian, Yingying Wang","doi":"10.1155/2023/1812518","DOIUrl":"https://doi.org/10.1155/2023/1812518","url":null,"abstract":"In this paper, an efficient lattice Boltzmann model for the generalized Black-Scholes equation governing option pricing is proposed. The Black-Scholes equation is firstly equivalently transformed into an initial value problem for a partial differential equation with a source term using the variable substitution and the derivative rules, respectively. Then, applying the multiscale Chapman-Enskog expansion, the amending function is expanded to second order to recover the convective and source terms of the macroscopic equation. The D1Q3 lattice Boltzmann model with spatial second-order accuracy is constructed, and the accuracy of the established D1Q5 model is greater than second order. The numerical simulation results demonstrate the effectiveness and numerical accuracy of the proposed models and indicate that our proposed models are suitable for solving the Black-Scholes equation. The proposed lattice Boltzmann model can also be applied to a class of partial differential equations with variable coefficients and source terms.","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46466669","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The N-soliton solution of the (2+1)-dimensional Sawada-Kotera equation is given by using the Hirota bilinear method, and then, the conjugate parameter method and the long-wave limit method are used to get the breather solution and the lump solution, as well as the interaction solution of the elastic collision properties between them. In addition, according to the expression of the lump-type soliton solution and the striped soliton solution, the completely inelastic collision, rebound, absorption, splitting, and other particle characteristics of the two solitons in the interaction process are directly studied with the simulation method, which reveals the laws of physics reflected behind the phenomenon.
{"title":"Interaction Solutions of the (2+1)-Dimensional Sawada-Kotera Equation","authors":"Yong Meng","doi":"10.1155/2023/9472715","DOIUrl":"https://doi.org/10.1155/2023/9472715","url":null,"abstract":"The N-soliton solution of the (2+1)-dimensional Sawada-Kotera equation is given by using the Hirota bilinear method, and then, the conjugate parameter method and the long-wave limit method are used to get the breather solution and the lump solution, as well as the interaction solution of the elastic collision properties between them. In addition, according to the expression of the lump-type soliton solution and the striped soliton solution, the completely inelastic collision, rebound, absorption, splitting, and other particle characteristics of the two solitons in the interaction process are directly studied with the simulation method, which reveals the laws of physics reflected behind the phenomenon.","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44428399","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, a family of the weakly dissipative periodic Camassa-Holm type equation cubic and quartic nonlinearities is considered. The precise blow-up scenarios of strong solutions and several conditions on the initial data to guarantee blow-up of the induced solutions are described in detail. Finally, we establish a sufficient condition for global solutions.
{"title":"Wave Breaking and Global Existence for the Generalized Periodic Camassa-Holm Equation with the Weak Dissipation","authors":"Ying Zhang, Congming Peng","doi":"10.1155/2022/6955014","DOIUrl":"https://doi.org/10.1155/2022/6955014","url":null,"abstract":"In this paper, a family of the weakly dissipative periodic Camassa-Holm type equation cubic and quartic nonlinearities is considered. The precise blow-up scenarios of strong solutions and several conditions on the initial data to guarantee blow-up of the induced solutions are described in detail. Finally, we establish a sufficient condition for global solutions.","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2022-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46268928","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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