Mashiyat Khan, Amzad Hossain, Afroja Parvin, M. Molla
A numerical analysis of magnetohydrodynamic natural convection along a thin vertical cylinder with a sinusoidal heat flux at the wall immersed in copper (Cu) and aluminum-oxide (Al2O3) hybrid nanofluids has been studied. A 2D vertical thin cylinder shape geometry has been considered with a radius of R. The fluid flow is considered laminar and incompressible with the Prandtl number of Pr = 6.2 and 10% concentration of hybrid nanoparticles. The nondimensional governing equations have been solved numerically by using the implicit finite difference method. An in-house FORTRAN 90 code is used for solving this problem and the code is validated with the available benchmark results. Numerical simulations have been performed for a wide range of governing parameters, Hartmann number from Ha = 0 to Ha = 4, nanoparticles volume fractions ϕ = 0.0 to ϕ = 0.1, and the amplitude of the wall heat flux ε = 0.0–0.3. The findings have been illustrated in terms of streamlines, isotherms, local skin friction coefficients, local Nusselt numbers, velocity, and temperature distributions. The flow field and temperature distribution within the boundary layer are deceased by the effects of the wall heat flux amplitudes. It is also noted that the rate of heat transfer increases with particle volume fraction and the amplitude of the wall heat flux. According to the findings, Nu increases by 24.72% as ϕ increases from 0 to 0.1 while ε = 0.3, and 27.66% while ε increases from 0.0 to 0.3 at 5% hybrid nanoparticles. The local skin frictions and Nusselt number diminish with the increment of the Hartman number due to the effects of the Lorenz force. The findings of this study can lead to a better understanding of the fundamental principles regarding the behavior of hybrid nanofluids under complex conditions, such as a vertical thin cylinder with a sinusoidal wall heat flux. Understanding the behavior of hybrid nanofluids in the presence of a magnetic field and a nonuniform wall heat flow can also lead to the development of innovative heat transfer enhancement strategies.
{"title":"Implicit Finite Difference Simulation of Hybrid Nanofluid along a Vertical Thin Cylinder with Sinusoidal Wall Heat Flux under the Effects of Magnetic Field","authors":"Mashiyat Khan, Amzad Hossain, Afroja Parvin, M. Molla","doi":"10.1155/2023/6699888","DOIUrl":"https://doi.org/10.1155/2023/6699888","url":null,"abstract":"A numerical analysis of magnetohydrodynamic natural convection along a thin vertical cylinder with a sinusoidal heat flux at the wall immersed in copper (Cu) and aluminum-oxide (Al2O3) hybrid nanofluids has been studied. A 2D vertical thin cylinder shape geometry has been considered with a radius of R. The fluid flow is considered laminar and incompressible with the Prandtl number of Pr = 6.2 and 10% concentration of hybrid nanoparticles. The nondimensional governing equations have been solved numerically by using the implicit finite difference method. An in-house FORTRAN 90 code is used for solving this problem and the code is validated with the available benchmark results. Numerical simulations have been performed for a wide range of governing parameters, Hartmann number from Ha = 0 to Ha = 4, nanoparticles volume fractions ϕ = 0.0 to ϕ = 0.1, and the amplitude of the wall heat flux ε = 0.0–0.3. The findings have been illustrated in terms of streamlines, isotherms, local skin friction coefficients, local Nusselt numbers, velocity, and temperature distributions. The flow field and temperature distribution within the boundary layer are deceased by the effects of the wall heat flux amplitudes. It is also noted that the rate of heat transfer increases with particle volume fraction and the amplitude of the wall heat flux. According to the findings, Nu increases by 24.72% as ϕ increases from 0 to 0.1 while ε = 0.3, and 27.66% while ε increases from 0.0 to 0.3 at 5% hybrid nanoparticles. The local skin frictions and Nusselt number diminish with the increment of the Hartman number due to the effects of the Lorenz force. The findings of this study can lead to a better understanding of the fundamental principles regarding the behavior of hybrid nanofluids under complex conditions, such as a vertical thin cylinder with a sinusoidal wall heat flux. Understanding the behavior of hybrid nanofluids in the presence of a magnetic field and a nonuniform wall heat flow can also lead to the development of innovative heat transfer enhancement strategies.","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":"46 13","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138945807","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}
{"title":"Retracted: Research on Spectrum Feature Identification of Indoor Multimodal Communication Signal","authors":"Advances in Mathematical Physics","doi":"10.1155/2023/9848035","DOIUrl":"https://doi.org/10.1155/2023/9848035","url":null,"abstract":"<jats:p />","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":"43 2","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139169274","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}
{"title":"Retracted: Study on Announcement Effect of Stock Repurchase from the Perspective of Configuration Analysis","authors":"Advances in Mathematical Physics","doi":"10.1155/2023/9836215","DOIUrl":"https://doi.org/10.1155/2023/9836215","url":null,"abstract":"<jats:p />","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":"258 12","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139170765","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}
{"title":"Retracted: Asymptotic Behavior of Solution for Functional Evolution Equations with Stepanov Forcing Terms","authors":"Advances in Mathematical Physics","doi":"10.1155/2023/9816201","DOIUrl":"https://doi.org/10.1155/2023/9816201","url":null,"abstract":"<jats:p />","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":"77 14","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138957859","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 section, the dynamic propagation behavior of a penny-shaped interface crack in piezoelectric bimaterials is analyzed. The objective of this paper is to use the boundary conditions of the penny-shaped interface crack to study the dynamic propagation of the crack under the action of load, so as to provide some valuable implications for the fracture mechanics of the piezoelectric bimaterials and simulate the interface crack between piezoelectric bimaterials, it is necessary to establish a suitable model and give appropriate boundary conditions according to the actual situation. The elastic displacement and potential equations are constructed according to the structural characteristics of the circular crack. In the case of a given displacement or stress, the Laplace transform and Hankel transform are used to simplify the problem into an integral equation with unknown functions. According to the boundary conditions, the corresponding unknowns are obtained, and the closed solution is derived. The results show that the fracture toughness of a penny-shaped interface crack in piezoelectric bimaterials is related to the thickness of the material, the impact time, the material characteristics, and the electric field. At the same time, it can be found that different materials have different roles in the crack propagation, so it is very important to study the crack opening displacement (COD) intensity factor of the crack for safety design.
{"title":"Modelling and Investigation of the Dynamic Behavior of a Penny-Shaped Interface Crack in Piezoelectric Bimaterials","authors":"Yani Zhang, Junlin Li, Di Liu, Xiufeng Xie","doi":"10.1155/2023/6660484","DOIUrl":"https://doi.org/10.1155/2023/6660484","url":null,"abstract":"In this section, the dynamic propagation behavior of a penny-shaped interface crack in piezoelectric bimaterials is analyzed. The objective of this paper is to use the boundary conditions of the penny-shaped interface crack to study the dynamic propagation of the crack under the action of load, so as to provide some valuable implications for the fracture mechanics of the piezoelectric bimaterials and simulate the interface crack between piezoelectric bimaterials, it is necessary to establish a suitable model and give appropriate boundary conditions according to the actual situation. The elastic displacement and potential equations are constructed according to the structural characteristics of the circular crack. In the case of a given displacement or stress, the Laplace transform and Hankel transform are used to simplify the problem into an integral equation with unknown functions. According to the boundary conditions, the corresponding unknowns are obtained, and the closed solution is derived. The results show that the fracture toughness of a penny-shaped interface crack in piezoelectric bimaterials is related to the thickness of the material, the impact time, the material characteristics, and the electric field. At the same time, it can be found that different materials have different roles in the crack propagation, so it is very important to study the crack opening displacement (COD) intensity factor of the crack for safety design.","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":"34 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138741350","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 focus of this paper is on utilizing the spectral element method to find the numerical solution of the fractional Klein–Gordon equation. The algorithm employs interpolating scaling functions (ISFs) that meet specific properties and satisfy the multiresolution analysis. Using an orthonormal projection, the equation is mapped to the scaling spaces in this method. A matrix representation of the Caputo fractional derivative of ISFs is presented using matrices representing the fractional integral and derivative operators. Using this matrix, the spectral element method reduces the desired equation to a system of algebraic equations. To find the solution, the generalized minimal residual method (GMRES method) and Newton’s method are used in linear and nonlinear forms of this system, respectively. The method’s convergence is proven, and some illustrative examples confirm it. The method is characterized by its simplicity in implementation, high efficiency, and significant accuracy.
{"title":"Spectral Element Method for Fractional Klein–Gordon Equations Using Interpolating Scaling Functions","authors":"Haifa Bin Jebreen","doi":"10.1155/2023/8453459","DOIUrl":"https://doi.org/10.1155/2023/8453459","url":null,"abstract":"The focus of this paper is on utilizing the spectral element method to find the numerical solution of the fractional Klein–Gordon equation. The algorithm employs interpolating scaling functions (ISFs) that meet specific properties and satisfy the multiresolution analysis. Using an orthonormal projection, the equation is mapped to the scaling spaces in this method. A matrix representation of the Caputo fractional derivative of ISFs is presented using matrices representing the fractional integral and derivative operators. Using this matrix, the spectral element method reduces the desired equation to a system of algebraic equations. To find the solution, the generalized minimal residual method (GMRES method) and Newton’s method are used in linear and nonlinear forms of this system, respectively. The method’s convergence is proven, and some illustrative examples confirm it. The method is characterized by its simplicity in implementation, high efficiency, and significant accuracy.","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":"11 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138573440","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 work conducts a numerical investigation of convection heat transfer within two composite enclosures. These enclosures consist of porous and nanofluidic layers, where the porous layers are saturated with the same nanofluid. The first enclosure has two porous layers of different sizes and permeabilities, while the second is separated by a single porous layer. As the porous layer thickness approaches zero, both enclosures transition to clear nanofluid enclosures. The study uses the Navier–Stokes equations to govern fluid flow in the nanofluid domain and the Brinkman–Forchheimer extended Darcy model to describe flow within the saturated porous layer. Numerical solutions are obtained using an iterative finite difference method. Key parameters studied include the porous thickness (<span><svg height="9.75571pt" style="vertical-align:-1.11981pt" version="1.1" viewbox="-0.0498162 -8.6359 26.707 9.75571" width="26.707pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"></path></g><g transform="matrix(.013,0,0,-0.013,6.24,0)"></path></g><g transform="matrix(.013,0,0,-0.013,9.204,0)"><use xlink:href="#g113-49"></use></g><g transform="matrix(.013,0,0,-0.013,19.076,0)"></path></g></svg><span></span><svg height="9.75571pt" style="vertical-align:-1.11981pt" version="1.1" viewbox="30.2891838 -8.6359 17.399 9.75571" width="17.399pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,30.339,0)"></path></g><g transform="matrix(.013,0,0,-0.013,40.107,0)"><use xlink:href="#g117-93"></use></g></svg><span></span><span><svg height="9.75571pt" style="vertical-align:-1.11981pt" version="1.1" viewbox="51.320183799999995 -8.6359 15.739 9.75571" width="15.739pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,51.37,0)"></path></g><g transform="matrix(.013,0,0,-0.013,57.61,0)"><use xlink:href="#g113-47"></use></g><g transform="matrix(.013,0,0,-0.013,60.574,0)"><use xlink:href="#g113-49"></use></g></svg>),</span></span> the nanoparticle volume fraction (<span><svg height="12.3916pt" style="vertical-align:-3.42948pt" version="1.1" viewbox="-0.0498162 -8.96212 26.707 12.3916" width="26.707pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><use xlink:href="#g113-49"></use></g><g transform="matrix(.013,0,0,-0.013,6.24,0)"><use xlink:href="#g113-47"></use></g><g transform="matrix(.013,0,0,-0.013,9.204,0)"><use xlink:href="#g113-49"></use></g><g transform="matrix(.013,0,0,-0.013,19.076,0)"><use xlink:href="#g117-93"></use></g></svg><span></span><svg height="12.3916pt" style="vertical-align:-3.42948pt" version="1.1" viewbox="30.2891838 -8.96212 18.609 12.3916" width="18.609pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,30.339,0)"></path>
{"title":"Free Convection Heat Transfer in Composite Enclosures with Porous and Nanofluid Layers","authors":"Abeer Alhashash","doi":"10.1155/2023/2088607","DOIUrl":"https://doi.org/10.1155/2023/2088607","url":null,"abstract":"This work conducts a numerical investigation of convection heat transfer within two composite enclosures. These enclosures consist of porous and nanofluidic layers, where the porous layers are saturated with the same nanofluid. The first enclosure has two porous layers of different sizes and permeabilities, while the second is separated by a single porous layer. As the porous layer thickness approaches zero, both enclosures transition to clear nanofluid enclosures. The study uses the Navier–Stokes equations to govern fluid flow in the nanofluid domain and the Brinkman–Forchheimer extended Darcy model to describe flow within the saturated porous layer. Numerical solutions are obtained using an iterative finite difference method. Key parameters studied include the porous thickness (<span><svg height=\"9.75571pt\" style=\"vertical-align:-1.11981pt\" version=\"1.1\" viewbox=\"-0.0498162 -8.6359 26.707 9.75571\" width=\"26.707pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,6.24,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,9.204,0)\"><use xlink:href=\"#g113-49\"></use></g><g transform=\"matrix(.013,0,0,-0.013,19.076,0)\"></path></g></svg><span></span><svg height=\"9.75571pt\" style=\"vertical-align:-1.11981pt\" version=\"1.1\" viewbox=\"30.2891838 -8.6359 17.399 9.75571\" width=\"17.399pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,30.339,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,40.107,0)\"><use xlink:href=\"#g117-93\"></use></g></svg><span></span><span><svg height=\"9.75571pt\" style=\"vertical-align:-1.11981pt\" version=\"1.1\" viewbox=\"51.320183799999995 -8.6359 15.739 9.75571\" width=\"15.739pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,51.37,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,57.61,0)\"><use xlink:href=\"#g113-47\"></use></g><g transform=\"matrix(.013,0,0,-0.013,60.574,0)\"><use xlink:href=\"#g113-49\"></use></g></svg>),</span></span> the nanoparticle volume fraction (<span><svg height=\"12.3916pt\" style=\"vertical-align:-3.42948pt\" version=\"1.1\" viewbox=\"-0.0498162 -8.96212 26.707 12.3916\" width=\"26.707pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"><use xlink:href=\"#g113-49\"></use></g><g transform=\"matrix(.013,0,0,-0.013,6.24,0)\"><use xlink:href=\"#g113-47\"></use></g><g transform=\"matrix(.013,0,0,-0.013,9.204,0)\"><use xlink:href=\"#g113-49\"></use></g><g transform=\"matrix(.013,0,0,-0.013,19.076,0)\"><use xlink:href=\"#g117-93\"></use></g></svg><span></span><svg height=\"12.3916pt\" style=\"vertical-align:-3.42948pt\" version=\"1.1\" viewbox=\"30.2891838 -8.96212 18.609 12.3916\" width=\"18.609pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,30.339,0)\"></path>","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":"1 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138569867","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 recent years, with the rapid development of nanotechnology, a new type of electromechanical coupling effect similar to the piezoelectric effect, the flexoelectric effect, has gradually come into the public’s view. The flexoelectric beam that is the main structural unit of the flexoelectric signal output has broad application prospects in the next generation of micro- and nanoelectromechanical systems. Therefore, the investigation of flexoelectric materials and structures has important scientific and engineering application significances for the design of flexoelectric devices. In this paper, a model of flexoelectric Timoshenko beam is established, the deflection, rotation angle, and dynamic electrical signal output of the forced vibration are taken as the system response, and the density , shear correction factor , and frequency ratio are selected as the key performance parameters of the system. The combination of available data and engineers’ experience suggests that there are random and cognitive uncertainties in the parameters. Therefore, the probability distribution of the system performance response is expressed by the likelihood function and belief function through the quantification of margins and uncertainties (QMUs) analysis methodology under the framework of evidence theory, and the system reliability or performance evaluation is measured by the calculated confidence factors. These results provide a theoretical basis for accurate analysis of flexoelectric components and provide guidance for the design of flexoelectric components with excellent performance.
{"title":"QMU Analysis of Flexoelectric Timoshenko Beam by Evidence Theory","authors":"Feng Zhang, Jiajia Zhang, Weiyue Wang, Ruijie Du, Cheng Han, Zijie Qiao","doi":"10.1155/2023/2967408","DOIUrl":"https://doi.org/10.1155/2023/2967408","url":null,"abstract":"In recent years, with the rapid development of nanotechnology, a new type of electromechanical coupling effect similar to the piezoelectric effect, the flexoelectric effect, has gradually come into the public’s view. The flexoelectric beam that is the main structural unit of the flexoelectric signal output has broad application prospects in the next generation of micro- and nanoelectromechanical systems. Therefore, the investigation of flexoelectric materials and structures has important scientific and engineering application significances for the design of flexoelectric devices. In this paper, a model of flexoelectric Timoshenko beam is established, the deflection, rotation angle, and dynamic electrical signal output of the forced vibration are taken as the system response, and the density <span><svg height=\"9.39034pt\" style=\"vertical-align:-3.42943pt\" version=\"1.1\" viewbox=\"-0.0498162 -5.96091 7.13289 9.39034\" width=\"7.13289pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"></path></g></svg>,</span> shear correction factor <span><svg height=\"6.1673pt\" style=\"vertical-align:-0.2063904pt\" version=\"1.1\" viewbox=\"-0.0498162 -5.96091 6.71534 6.1673\" width=\"6.71534pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"></path></g></svg>,</span> and frequency ratio <svg height=\"9.49473pt\" style=\"vertical-align:-0.2063999pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.28833 7.30254 9.49473\" width=\"7.30254pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"></path></g></svg> are selected as the key performance parameters of the system. The combination of available data and engineers’ experience suggests that there are random and cognitive uncertainties in the parameters. Therefore, the probability distribution of the system performance response is expressed by the likelihood function and belief function through the quantification of margins and uncertainties (QMUs) analysis methodology under the framework of evidence theory, and the system reliability or performance evaluation is measured by the calculated confidence factors. These results provide a theoretical basis for accurate analysis of flexoelectric components and provide guidance for the design of flexoelectric components with excellent performance.","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":"16 10","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138508743","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}
Md. Mosharrof Hossain, Md. Hasanuzzaman, A. Rahim Laskar, Ashish Barmon
An investigation of the effects of Soret and Dufour on an unsteady MHD convective transmission over a vertical porous sheet with chemical reaction was introduced throughout this study. The model that formed nonlinear governing equations is transformed by applying the similarity analysis with the help of the finite difference method. The numerical resolutions of the fluid characteristics like velocity, concentration, and temperature are explained graphically. This research also presented the mass transmission rate, heat transmission rate, and the local skin friction coefficient, which are explained in tabular form. The results give the fluid motion and temperature improvement for growing values of the Dofour effect. Also, the fluid velocity and concentration improve for elevated amounts of the Soret effect. The local skin friction improves by around 66% whereas the mass transmission rate lessens by around 247% with the growing Soret number (0.5–2.0).
{"title":"Effects of Soret and Dufour on Unsteady Magneto-Convective Transport through a Vertical Perforated Sheet with Chemical Reaction","authors":"Md. Mosharrof Hossain, Md. Hasanuzzaman, A. Rahim Laskar, Ashish Barmon","doi":"10.1155/2023/6648797","DOIUrl":"https://doi.org/10.1155/2023/6648797","url":null,"abstract":"An investigation of the effects of Soret and Dufour on an unsteady MHD convective transmission over a vertical porous sheet with chemical reaction was introduced throughout this study. The model that formed nonlinear governing equations is transformed by applying the similarity analysis with the help of the finite difference method. The numerical resolutions of the fluid characteristics like velocity, concentration, and temperature are explained graphically. This research also presented the mass transmission rate, heat transmission rate, and the local skin friction coefficient, which are explained in tabular form. The results give the fluid motion and temperature improvement for growing values of the Dofour effect. Also, the fluid velocity and concentration improve for elevated amounts of the Soret effect. The local skin friction improves by around 66% whereas the mass transmission rate lessens by around 247% with the growing Soret number (0.5–2.0).","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":"15 5","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138508737","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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