The boundary element method is widely used in practical engineering problems, especially in the field of acoustics. For flow-induced noise, the main target of acoustic calculations is to solve the wave equation with the flow field information. However, the sound field distribution of noncompact structures in half-space is especially complex because of the strong scattering effect, while the object surface boundary integration often brings a large workload and generates numerical singularities. In this paper, an improved boundary element method for predicting the aeroacoustic noise of noncompact structures is proposed, which can consider the characteristic distribution of sound field induced by complex structures in half-space. The smooth permeable boundary surrounding the object is used as the integration boundary, while the scattering effect of the ground boundary is investigated by combining the mirror Green’s function method, and the numerical prediction of aeroacoustic noise is carried out for the dipole source and NACA0012 airfoil in half-space. Numerical results show that the far-field noise obtained by using the permeable surface is consistent with that obtained by integrating the direct object boundary under the influence of ground boundary scattering. The mirror image Green’s function method is able to finely capture the ground scattering effect, which has a significant effect on the sound field as the frequency increases.
{"title":"An Improved Boundary Element Method for Predicting Half-Space Scattered Noise Combined with Permeable Boundaries","authors":"Wensi Zheng, Fang Wang","doi":"10.1155/2024/7979078","DOIUrl":"https://doi.org/10.1155/2024/7979078","url":null,"abstract":"The boundary element method is widely used in practical engineering problems, especially in the field of acoustics. For flow-induced noise, the main target of acoustic calculations is to solve the wave equation with the flow field information. However, the sound field distribution of noncompact structures in half-space is especially complex because of the strong scattering effect, while the object surface boundary integration often brings a large workload and generates numerical singularities. In this paper, an improved boundary element method for predicting the aeroacoustic noise of noncompact structures is proposed, which can consider the characteristic distribution of sound field induced by complex structures in half-space. The smooth permeable boundary surrounding the object is used as the integration boundary, while the scattering effect of the ground boundary is investigated by combining the mirror Green’s function method, and the numerical prediction of aeroacoustic noise is carried out for the dipole source and NACA0012 airfoil in half-space. Numerical results show that the far-field noise obtained by using the permeable surface is consistent with that obtained by integrating the direct object boundary under the influence of ground boundary scattering. The mirror image Green’s function method is able to finely capture the ground scattering effect, which has a significant effect on the sound field as the frequency increases.","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":"9 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141170377","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}
Wei Zhu, Jian-Yong Wang, Kai Zhou, Shoufeng Shen, Bo Ren
The multilinear variable separation (MLVS) approach has been proven to be very useful in solving (2 + 1)-dimensional integrable systems. Taking the (3 + 1)-dimensional Burgers hierarchy as an example, we extend the MLVS approach to a whole family of (3 + 1)-dimensional Burgers hierarchy. New exact solutions and universal formulas are obtained, which lead to abundant (3 + 1)-dimensional coherent structures. In particular, two ring-type soliton molecules and their interactions are shown in detail. We also generalize the MLVS results of the (3 + 1)-dimensional Jimbo–Miwa (JM) equation and modified JM equation.
{"title":"New Multilinear Variable Separation Solutions of the (3 + 1)-Dimensional Burgers Hierarchy","authors":"Wei Zhu, Jian-Yong Wang, Kai Zhou, Shoufeng Shen, Bo Ren","doi":"10.1155/2024/5533472","DOIUrl":"https://doi.org/10.1155/2024/5533472","url":null,"abstract":"The multilinear variable separation (MLVS) approach has been proven to be very useful in solving (2 + 1)-dimensional integrable systems. Taking the (3 + 1)-dimensional Burgers hierarchy as an example, we extend the MLVS approach to a whole family of (3 + 1)-dimensional Burgers hierarchy. New exact solutions and universal formulas are obtained, which lead to abundant (3 + 1)-dimensional coherent structures. In particular, two ring-type soliton molecules and their interactions are shown in detail. We also generalize the MLVS results of the (3 + 1)-dimensional Jimbo–Miwa (JM) equation and modified JM equation.","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":"17 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140826686","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}
To improve the complexity of the chaotic system and achieve the effective transmission of image information, in this paper, a five-dimensional memristive chaotic system with cubic nonlinear terms is constructed, which has four pairs of symmetric coordinates. First, the cubic nonlinear memristive chaotic system is analyzed using the Lyapunov exponential map, bifurcation map, and attractor phase diagram. The experimental results show that under four pairs of symmetric coordinates, the system exists not only parameter-dependent symmetric rotational coexisting attractor and transient chaotic phenomena but also exists super-multistationary with alternating chaotic cycles dependent on the initial value of the memristor. Then, it is proposed to add a constant term to the linear state variable to explore the effect of the offset increment of the linear state variable on the system in four pairs of symmetric coordinates, while circuit simulation of the five-dimensional chaotic system is carried out using Simulink to verify its existence and realisability. Finally, the synchronization of the dimensionality reduction system and the confidential transmission of the image are achieved, using the control voltage of the system to replace the internal state variables of the memristor to achieve the one-dimensional reduction process, and an adaptive synchronization controller is designed to synchronize the system before and after the dimensionality reduction. Based on the above, an image to be transmitted is modulated into a one-dimensional array and then subjected to the fractional and cyclic operations and combined with the linear encryption and decryption functions and the chaotic masking technique, the simple encryption and decryption of the image processes are realized.
{"title":"Analysis of the Dynamics of a Cubic Nonlinear Five-Dimensional Memristive Chaotic System and the Study of Reduced-Dimensional Synchronous Masking","authors":"Lina Ding, Pan Wang","doi":"10.1155/2024/9363431","DOIUrl":"https://doi.org/10.1155/2024/9363431","url":null,"abstract":"To improve the complexity of the chaotic system and achieve the effective transmission of image information, in this paper, a five-dimensional memristive chaotic system with cubic nonlinear terms is constructed, which has four pairs of symmetric coordinates. First, the cubic nonlinear memristive chaotic system is analyzed using the Lyapunov exponential map, bifurcation map, and attractor phase diagram. The experimental results show that under four pairs of symmetric coordinates, the system exists not only parameter-dependent symmetric rotational coexisting attractor and transient chaotic phenomena but also exists super-multistationary with alternating chaotic cycles dependent on the initial value of the memristor. Then, it is proposed to add a constant term to the linear state variable to explore the effect of the offset increment of the linear state variable on the system in four pairs of symmetric coordinates, while circuit simulation of the five-dimensional chaotic system is carried out using Simulink to verify its existence and realisability. Finally, the synchronization of the dimensionality reduction system and the confidential transmission of the image are achieved, using the control voltage of the system to replace the internal state variables of the memristor to achieve the one-dimensional reduction process, and an adaptive synchronization controller is designed to synchronize the system before and after the dimensionality reduction. Based on the above, an image to be transmitted is modulated into a one-dimensional array and then subjected to the fractional and cyclic operations and combined with the linear encryption and decryption functions and the chaotic masking technique, the simple encryption and decryption of the image processes are realized.","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":"34 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140803967","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 mechanical behavior of the fine-grained piezoelectric/substrate structure with multiple interface cracks under the electromechanical impact loading is investigated. Using the Laplace and Fourier integral transforms, the double-coupled singular integral equations and single-valued conditions of the problems are formulated. Both the singular integral equation and single-valued conditions are simplified into an algebraic equation through the Chebyshev point placement method and solved by numerical calculation. Then, the expression of the dynamic energy release rate is given with the help of the dynamic intensity factors of electric displacement and stress obtained. Finally, numerical results of the dynamic energy release rate with material parameters are demonstrated. The results show that the dynamic energy release rate depends on the size of the interface cracks, coating thickness, and the mechanical–electrical loading. Meanwhile, the fine-grained piezoelectric structures exhibit safer structural performance compared to normal one.
{"title":"Transient Response of Multiple Interface Cracks in Fine-Grained Coating Composite Structures under Impact Loading","authors":"Shuaishuai Hu, Junlin Li","doi":"10.1155/2024/3931231","DOIUrl":"https://doi.org/10.1155/2024/3931231","url":null,"abstract":"The mechanical behavior of the fine-grained piezoelectric/substrate structure with multiple interface cracks under the electromechanical impact loading is investigated. Using the Laplace and Fourier integral transforms, the double-coupled singular integral equations and single-valued conditions of the problems are formulated. Both the singular integral equation and single-valued conditions are simplified into an algebraic equation through the Chebyshev point placement method and solved by numerical calculation. Then, the expression of the dynamic energy release rate is given with the help of the dynamic intensity factors of electric displacement and stress obtained. Finally, numerical results of the dynamic energy release rate with material parameters are demonstrated. The results show that the dynamic energy release rate depends on the size of the interface cracks, coating thickness, and the mechanical–electrical loading. Meanwhile, the fine-grained piezoelectric structures exhibit safer structural performance compared to normal one.","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":"13 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140615678","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}
Maham Abdul Qayyum, Aya Mohammed Dhiaa, Abid Mahboob, Muhammad Waheed Rasheed, Abdu Alameri
The extended conformable k-hypergeometric function finds various applications in physics due to its ability to describe complex mathematical relationships arising in different physical scenarios. Here are a few instances of its uses in physics, including nuclear physics, fluid dynamics, quantum mechanics, and astronomy. The main objectives of this paper are to introduce the extended conformable k-hypergeometric and confluent hypergeometric functions by utilizing the new definition of the -beta function and studying its important properties, like integral representation, summation formula, derivative formula, transform formula, and generating function. Also, introduce the extension of the Riemann–Liouville fractional derivative and establish some results related to the newly defined fractional operator, such as the Mellin transform and relations to extended -hypergeometric functions.
{"title":"Extended Conformable K-Hypergeometric Function and Its Application","authors":"Maham Abdul Qayyum, Aya Mohammed Dhiaa, Abid Mahboob, Muhammad Waheed Rasheed, Abdu Alameri","doi":"10.1155/2024/5709319","DOIUrl":"https://doi.org/10.1155/2024/5709319","url":null,"abstract":"The extended conformable <i>k</i>-hypergeometric function finds various applications in physics due to its ability to describe complex mathematical relationships arising in different physical scenarios. Here are a few instances of its uses in physics, including nuclear physics, fluid dynamics, quantum mechanics, and astronomy. The main objectives of this paper are to introduce the extended conformable <i>k</i>-hypergeometric and confluent hypergeometric functions by utilizing the new definition of the <span><svg height=\"11.5564pt\" style=\"vertical-align:-2.26807pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.28833 14.847 11.5564\" width=\"14.847pt\" 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,-0.013,4.498,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,11.883,0)\"></path></g></svg><span></span><span><svg height=\"11.5564pt\" style=\"vertical-align:-2.26807pt\" version=\"1.1\" viewbox=\"16.9761838 -9.28833 11.233 11.5564\" width=\"11.233pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,17.026,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,23.566,0)\"></path></g></svg>-</span></span>beta function and studying its important properties, like integral representation, summation formula, derivative formula, transform formula, and generating function. Also, introduce the extension of the Riemann–Liouville fractional derivative and establish some results related to the newly defined fractional operator, such as the Mellin transform and relations to extended <span><svg height=\"11.5564pt\" style=\"vertical-align:-2.26807pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.28833 14.847 11.5564\" width=\"14.847pt\" 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=\"#g113-41\"></use></g><g transform=\"matrix(.013,0,0,-0.013,4.498,0)\"><use xlink:href=\"#g113-223\"></use></g><g transform=\"matrix(.013,0,0,-0.013,11.883,0)\"><use xlink:href=\"#g113-45\"></use></g></svg><span></span><span><svg height=\"11.5564pt\" style=\"vertical-align:-2.26807pt\" version=\"1.1\" viewbox=\"16.9761838 -9.28833 11.233 11.5564\" width=\"11.233pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,17.026,0)\"><use xlink:href=\"#g113-108\"></use></g><g transform=\"matrix(.013,0,0,-0.013,23.566,0)\"><use xlink:href=\"#g113-42\"></use></g></svg>-</span></span>hypergeometric functions.","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":"12 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140115043","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 paper addresses the unsteady hydrodynamic convective heat and mass transfer of three fluids namely air, water, and electrolyte solution past an impulsively started vertical surface with Newtonian heating in a porous medium under the influences of magnetic field and chemical reaction. Suitable dimensionless parameters are used to transform the flow equations and the approximate analytic method employed to solve the flow problem. The results are illustrated graphically for the velocity, temperature, and concentration profiles. Though, low Prandtl numbers produce high-thermal boundary layer thickness, however, as a novelty, the presence of the magnetic field delayed the convection motion hence, the thermal boundary layer thickness is greater for water with high Pr = 7.0 as compared to air with low Pr = 0.71 and electrolyte solution with low Pr = 1.0. Practically, water with a high-Prandtl number can effectively absorb and release heat. This makes water useful in applications such as geothermal heat pumps and solar thermal collectors, industrial processes such as chemical reactions, distillation, and drying, and in oceanography in predicting the movement and behavior of ocean currents, which in turn can impact weather patterns and climate. Another major observation from the study is that the rate of cooling associated with air, water, or electrolyte impacts differently on the product being cooled.
{"title":"Approximate Analytical Solution of the Influences of Magnetic Field and Chemical Reaction on Unsteady Convective Heat and Mass Transfer of Air, Water, and Electrolyte Fluids Subject to Newtonian Heating in a Porous Medium","authors":"M. Sulemana, Y. I. Seini, O. D. Makinde","doi":"10.1155/2024/4519487","DOIUrl":"https://doi.org/10.1155/2024/4519487","url":null,"abstract":"This paper addresses the unsteady hydrodynamic convective heat and mass transfer of three fluids namely air, water, and electrolyte solution past an impulsively started vertical surface with Newtonian heating in a porous medium under the influences of magnetic field and chemical reaction. Suitable dimensionless parameters are used to transform the flow equations and the approximate analytic method employed to solve the flow problem. The results are illustrated graphically for the velocity, temperature, and concentration profiles. Though, low Prandtl numbers produce high-thermal boundary layer thickness, however, as a novelty, the presence of the magnetic field delayed the convection motion hence, the thermal boundary layer thickness is greater for water with high <i>P</i><sub><i>r</i></sub> = 7.0 as compared to air with low <i>P</i><sub><i>r</i></sub> = 0.71 and electrolyte solution with low <i>P</i><sub><i>r</i></sub> = 1.0. Practically, water with a high-Prandtl number can effectively absorb and release heat. This makes water useful in applications such as geothermal heat pumps and solar thermal collectors, industrial processes such as chemical reactions, distillation, and drying, and in oceanography in predicting the movement and behavior of ocean currents, which in turn can impact weather patterns and climate. Another major observation from the study is that the rate of cooling associated with air, water, or electrolyte impacts differently on the product being cooled.","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":"20 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139587323","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}
Adnan Ahmad, M. Nazar, M. Ahmad, Sayed M. Eldin, Zaib Un Nisa, Hassan Waqas, M. Imran
Thermal diffusion is a phenomenon where the concentration gradient or diffusive flux is created due to the temperature gradient. Thermal diffusion is induced because of the higher temperature and uneven distribution of the mixture. Formally, thermal diffusion is called the Soret effect, and it is a crucial factor in a number of natural occurrences like the separation of isotopes technique of purification. In this research paper, Maxwell fluid’s flow in the vicinage of a flat plate is discussed by considering the effect of the thermodiffusion subject to the first-order slip at the boundary with the application of a constant proportional Caputo (CPC) fractional derivative. The effect of heat generation and radiation is also taken into consideration, as well as the effect of a magnetic field of constant magnitude. The generalized heat and mass fluxes are considered, and this generalization of heat and mass fluxes is done by utilizing the CPC fractional derivative. After converting the current model’s governing equations into a dimensionless form, the temperature, concentration, and velocity fields’ analytical solutions are found. By drawing graphs of the temperature, concentration, and velocity fields for the parametric modifications, the results are graphically illustrated. It becomes clear from the results discussion that the outcomes produced by the constant proportional derivative are more decaying than those obtained with the classical differential operator of order one.
{"title":"Application of Constant Proportional Caputo Fractional Derivative to Thermodiffusion Flow of MHD Radiative Maxwell Fluid under Slip Effect over a Moving Flat Surface with Heat and Mass Diffusion","authors":"Adnan Ahmad, M. Nazar, M. Ahmad, Sayed M. Eldin, Zaib Un Nisa, Hassan Waqas, M. Imran","doi":"10.1155/2024/9306915","DOIUrl":"https://doi.org/10.1155/2024/9306915","url":null,"abstract":"Thermal diffusion is a phenomenon where the concentration gradient or diffusive flux is created due to the temperature gradient. Thermal diffusion is induced because of the higher temperature and uneven distribution of the mixture. Formally, thermal diffusion is called the Soret effect, and it is a crucial factor in a number of natural occurrences like the separation of isotopes technique of purification. In this research paper, Maxwell fluid’s flow in the vicinage of a flat plate is discussed by considering the effect of the thermodiffusion subject to the first-order slip at the boundary with the application of a constant proportional Caputo (CPC) fractional derivative. The effect of heat generation and radiation is also taken into consideration, as well as the effect of a magnetic field of constant magnitude. The generalized heat and mass fluxes are considered, and this generalization of heat and mass fluxes is done by utilizing the CPC fractional derivative. After converting the current model’s governing equations into a dimensionless form, the temperature, concentration, and velocity fields’ analytical solutions are found. By drawing graphs of the temperature, concentration, and velocity fields for the parametric modifications, the results are graphically illustrated. It becomes clear from the results discussion that the outcomes produced by the constant proportional derivative are more decaying than those obtained with the classical differential operator of order one.","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":"1 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139514778","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}
Farah Nadzirah Jamrus, Anuar Ishak, Iskandar Waini, Umair Khan, Md Irfanul Haque Siddiqui, J. K. Madhukesh
This study is carried out to scrutinize the Hiemenz flow for ternary hybrid nanofluid flow across a stretching/shrinking sheet. This study aims to inspect the impacts of variations in the stretching/shrinking parameter and the volume fraction of nanoparticles on key aspects of the ternary hybrid nanofluid flow, specifically the skin friction, Nusselt number (which relates to heat transfer), velocity profiles, and the temperature profiles. The flow equations transform into a system of ordinary differential equations (ODEs) using a similarity transformation. Subsequently, the system is numerically solved using the MATLAB software’s 4th-order accuracy boundary value problem solver, known as “bvp4c”. Numeric findings reveal that skin friction values exhibit variations based on the magnitude of the stretching/shrinking parameter. Moreover, in the specific context of the flow problem being studied, the heat conduction efficiency of the hybrid (ternary) nanofluid surpasses that of the hybrid nanofluid. The system yields two distinct solutions within a specific shrinking/stretching parameter interval. Through an examination of the temporal stability of the solutions, it was determined that only one remained stable over an extended period. Remember that these current findings hold solely for the combination of copper, alumina, and titania.
{"title":"Aspects of Non-unique Solutions for Hiemenz Flow Filled with Ternary Hybrid Nanofluid over a Stretching/Shrinking Sheet","authors":"Farah Nadzirah Jamrus, Anuar Ishak, Iskandar Waini, Umair Khan, Md Irfanul Haque Siddiqui, J. K. Madhukesh","doi":"10.1155/2024/7253630","DOIUrl":"https://doi.org/10.1155/2024/7253630","url":null,"abstract":"This study is carried out to scrutinize the Hiemenz flow for ternary hybrid nanofluid flow across a stretching/shrinking sheet. This study aims to inspect the impacts of variations in the stretching/shrinking parameter and the volume fraction of nanoparticles on key aspects of the ternary hybrid nanofluid flow, specifically the skin friction, Nusselt number (which relates to heat transfer), velocity profiles, and the temperature profiles. The flow equations transform into a system of ordinary differential equations (ODEs) using a similarity transformation. Subsequently, the system is numerically solved using the MATLAB software’s 4th-order accuracy boundary value problem solver, known as “bvp4c”. Numeric findings reveal that skin friction values exhibit variations based on the magnitude of the stretching/shrinking parameter. Moreover, in the specific context of the flow problem being studied, the heat conduction efficiency of the hybrid (ternary) nanofluid surpasses that of the hybrid nanofluid. The system yields two distinct solutions within a specific shrinking/stretching parameter interval. Through an examination of the temporal stability of the solutions, it was determined that only one remained stable over an extended period. Remember that these current findings hold solely for the combination of copper, alumina, and titania.","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":"298 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139420544","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}
Yin Zhang, Menglong Zhang, Jianwu Xiong, Gang Mao, Yicong Qi
Natural convection in cavity plays a significant role in energy-related field, including the indoor heat transfer analysis in greenhouse with integrated PV roof. In this study, mathematical model is established for two-dimensional heat transfer analysis in greenhouse air cavity, with numerical simulation through computational fluid dynamics (CFD). Main natural convection impact factors, such as system configuration parameters (tilting angle and PV panel unit number) and fluid thermal–physical properties, are investigated with indoor temperature distribution and streamline comparison by finite-volume method (FVD). Preliminary results show that with rising Rayleigh number (Ra), natural convection is enhanced with growing Nusselt number (Nu). Moreover, panel slope tilting angle (θ) highly determines inside heat transfer subregions in terms of the vertical temperature gradient declines with rising θ, improving the temperature distribution uniformity inside. The solar greenhouse example illustrates that with the increasing numbers of panel group numbers (n), the air temperature gradient differences decrease, improving the temperature distribution uniformity inside, which is preferable to built environment accurate control for greenhouse in the practical engineering. This work can provide modeling method support and reference for natural heat convection applications.
{"title":"Computational Fluid Dynamics for Cavity Natural Heat Convection: Numerical Analysis and Optimization in Greenhouse Application","authors":"Yin Zhang, Menglong Zhang, Jianwu Xiong, Gang Mao, Yicong Qi","doi":"10.1155/2023/1074719","DOIUrl":"https://doi.org/10.1155/2023/1074719","url":null,"abstract":"Natural convection in cavity plays a significant role in energy-related field, including the indoor heat transfer analysis in greenhouse with integrated PV roof. In this study, mathematical model is established for two-dimensional heat transfer analysis in greenhouse air cavity, with numerical simulation through computational fluid dynamics (CFD). Main natural convection impact factors, such as system configuration parameters (tilting angle and PV panel unit number) and fluid thermal–physical properties, are investigated with indoor temperature distribution and streamline comparison by finite-volume method (FVD). Preliminary results show that with rising Rayleigh number (<i>Ra</i>), natural convection is enhanced with growing Nusselt number (<i>Nu</i>). Moreover, panel slope tilting angle (<i>θ</i>) highly determines inside heat transfer subregions in terms of the vertical temperature gradient declines with rising <i>θ</i>, improving the temperature distribution uniformity inside. The solar greenhouse example illustrates that with the increasing numbers of panel group numbers (<i>n</i>), the air temperature gradient differences decrease, improving the temperature distribution uniformity inside, which is preferable to built environment accurate control for greenhouse in the practical engineering. This work can provide modeling method support and reference for natural heat convection applications.","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":"5 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139066142","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}
Wen-Hui Zhu, Jian-Guo Liu, Mohammad Asif Arefin, M. Hafiz Uddin, Ya-Kui Wu
In this work, a (2 + 1)-dimensional Ito equation is investigated, which represents the generalization of the bilinear KdV equation. Abundant double-periodic soliton solutions to the (2 + 1)-dimensional Ito equation are presented by the Hirota bilinear form and a mixture of exponentials and trigonometric functions. The dynamic properties are described through some 3D graphics and contour graphics.
{"title":"Double-Periodic Soliton Solutions of the (2+1)-Dimensional Ito Equation","authors":"Wen-Hui Zhu, Jian-Guo Liu, Mohammad Asif Arefin, M. Hafiz Uddin, Ya-Kui Wu","doi":"10.1155/2023/9321673","DOIUrl":"https://doi.org/10.1155/2023/9321673","url":null,"abstract":"In this work, a (2 + 1)-dimensional Ito equation is investigated, which represents the generalization of the bilinear KdV equation. Abundant double-periodic soliton solutions to the (2 + 1)-dimensional Ito equation are presented by the Hirota bilinear form and a mixture of exponentials and trigonometric functions. The dynamic properties are described through some 3D graphics and contour graphics.","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":"19 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139052760","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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