Migration of pollutant particles into subsurface water reservoirs through point sources is largely involved mixing processes within the system of water flow. Possible potential sources of pollution to these point sources include municipal wastes, septic loads, landfills, uncontrolled hazardous wastes, and sewage storage tanks. The mixing processes of pollutant significantly alter their predictive rate of flow in the water reservoirs, and therefore the time inherent in mixing processes need to be accounted for. In this study, pollution of subsurface water reservoirs mainly rivers and streams through contaminated water point sources (CWPS) was studied through a conceptual perspective of mixing problem processes in water tanks. The objective was to formulate a discrete time delay mathematical model which describes the dynamics of water reservoir pollution that involve single species contaminants such as nitrates, phosphorous, and detergents injecting from a point source. The concentration x t of pollutants was expressed as a function of the inflow and outflow rates using the principle for the conservation of mass. The major assumption made in modeling of mixing problems using tanks is that mixing is instantaneous. Practical realities dictate that mixing cannot occur instantaneously throughout the tank. So as to accommodate these realities, the study refined the systems of ordinary differential equations (ODEs) generated from principles of mixing problems in cascading tanks, into a system of delayed differential equations (DDEs) so that the concentration of pollutant leaving the reservoir at time t would be equal to the average concentration at some earlier instant, t − τ for the delay τ > 0 . The formulated model is a mathematical discrete time delay model which can be used to describe the dynamics of subsurface water reservoir pollution through a point source. The model was simulated on municipal River Nyakomisaro in Kisii County, Kenya. Physical and kinematic parameters of the river (cross-sectional lengths, depths, flow velocities) at three river sectional reservoirs were measured and the obtained parameter values were then used to evaluate coefficients of the formulated model equation. The system of DDEs from this simulation was solved numerically on MATLAB using dde23 software. From the graphical views generated for concentration of pollutant x t versus time t , it was established that the developed DDEs cover longer time series solutions (characteristic curves) than that from the corresponding ODEs in the same reservoir indicating that time necessary for particle flow through water reservoirs is underestimated if ODEs are used to describe particle flow. Also, the graphical views indicated similar tendencies (characteristics) in particle flow with time elapse even though initial values of concentration x t were different for every potentially recog
{"title":"Formulated Mathematical Model for Delayed Particle Flow in Cascaded Subsurface Water Reservoirs with Validation on River Flow","authors":"Richard Ombaki, J. Kerongo","doi":"10.1155/2022/3438200","DOIUrl":"https://doi.org/10.1155/2022/3438200","url":null,"abstract":"Migration of pollutant particles into subsurface water reservoirs through point sources is largely involved mixing processes within the system of water flow. Possible potential sources of pollution to these point sources include municipal wastes, septic loads, landfills, uncontrolled hazardous wastes, and sewage storage tanks. The mixing processes of pollutant significantly alter their predictive rate of flow in the water reservoirs, and therefore the time inherent in mixing processes need to be accounted for. In this study, pollution of subsurface water reservoirs mainly rivers and streams through contaminated water point sources (CWPS) was studied through a conceptual perspective of mixing problem processes in water tanks. The objective was to formulate a discrete time delay mathematical model which describes the dynamics of water reservoir pollution that involve single species contaminants such as nitrates, phosphorous, and detergents injecting from a point source. The concentration \u0000 \u0000 x\u0000 \u0000 \u0000 t\u0000 \u0000 \u0000 \u0000 of pollutants was expressed as a function of the inflow and outflow rates using the principle for the conservation of mass. The major assumption made in modeling of mixing problems using tanks is that mixing is instantaneous. Practical realities dictate that mixing cannot occur instantaneously throughout the tank. So as to accommodate these realities, the study refined the systems of ordinary differential equations (ODEs) generated from principles of mixing problems in cascading tanks, into a system of delayed differential equations (DDEs) so that the concentration of pollutant leaving the reservoir at time \u0000 \u0000 t\u0000 \u0000 would be equal to the average concentration at some earlier instant, \u0000 \u0000 \u0000 \u0000 t\u0000 −\u0000 τ\u0000 \u0000 \u0000 \u0000 for the delay \u0000 \u0000 τ\u0000 >\u0000 0\u0000 .\u0000 \u0000 The formulated model is a mathematical discrete time delay model which can be used to describe the dynamics of subsurface water reservoir pollution through a point source. The model was simulated on municipal River Nyakomisaro in Kisii County, Kenya. Physical and kinematic parameters of the river (cross-sectional lengths, depths, flow velocities) at three river sectional reservoirs were measured and the obtained parameter values were then used to evaluate coefficients of the formulated model equation. The system of DDEs from this simulation was solved numerically on MATLAB using dde23 software. From the graphical views generated for concentration of pollutant \u0000 \u0000 x\u0000 \u0000 \u0000 t\u0000 \u0000 \u0000 \u0000 versus time \u0000 \u0000 \u0000 \u0000 t\u0000 \u0000 \u0000 ,\u0000 \u0000 it was established that the developed DDEs cover longer time series solutions (characteristic curves) than that from the corresponding ODEs in the same reservoir indicating that time necessary for particle flow through water reservoirs is underestimated if ODEs are used to describe particle flow. Also, the graphical views indicated similar tendencies (characteristics) in particle flow with time elapse even though initial values of concentration \u0000 \u0000 x\u0000 \u0000 \u0000 t\u0000 \u0000 \u0000 \u0000 were different for every potentially recog","PeriodicalId":14766,"journal":{"name":"J. Appl. Math.","volume":"32 1","pages":"3438200:1-3438200:11"},"PeriodicalIF":0.0,"publicationDate":"2022-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80595395","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}
To improve the quality of local feature filtering for dynamic multiframe video sequence images, this study is aimed at designing an improved nontexture class noise filtering algorithm based on noise construction denoising algorithm and gray histogram of pixel points, and then designs a texture noise denoising algorithm based on texture smoothing processing and circular gradient values. The two algorithms are combined to propose a comprehensive filtering and denoising algorithm for horizontal dynamic video images. The experimental test results show that the normalized correlation coefficient, mutual information quantity, peak signal-to-noise ratio, and information entropy of the integrated filter denoising algorithm are 0.950, 0.935, 0.816, and 0.933 after convergence of the training effect, which are significantly higher than those of the commonly used median denoising algorithm and Kalman denoising algorithm. However, the computational time consumption of the proposed integrated filtering and denoising algorithm is higher than that of the comparison algorithms. The experimental results show that the integrated filtering algorithm for dynamic video images designed in this study can achieve better filtering and image reconstruction results in application scenarios with lower requirements for the timeliness of processing results.
{"title":"Local Feature Filtering Method for Dynamic Multiframe Video Sequence Images","authors":"Dawei Zhang, D. Huang","doi":"10.1155/2022/8417499","DOIUrl":"https://doi.org/10.1155/2022/8417499","url":null,"abstract":"To improve the quality of local feature filtering for dynamic multiframe video sequence images, this study is aimed at designing an improved nontexture class noise filtering algorithm based on noise construction denoising algorithm and gray histogram of pixel points, and then designs a texture noise denoising algorithm based on texture smoothing processing and circular gradient values. The two algorithms are combined to propose a comprehensive filtering and denoising algorithm for horizontal dynamic video images. The experimental test results show that the normalized correlation coefficient, mutual information quantity, peak signal-to-noise ratio, and information entropy of the integrated filter denoising algorithm are 0.950, 0.935, 0.816, and 0.933 after convergence of the training effect, which are significantly higher than those of the commonly used median denoising algorithm and Kalman denoising algorithm. However, the computational time consumption of the proposed integrated filtering and denoising algorithm is higher than that of the comparison algorithms. The experimental results show that the integrated filtering algorithm for dynamic video images designed in this study can achieve better filtering and image reconstruction results in application scenarios with lower requirements for the timeliness of processing results.","PeriodicalId":14766,"journal":{"name":"J. Appl. Math.","volume":"130 1","pages":"8417499:1-8417499:10"},"PeriodicalIF":0.0,"publicationDate":"2022-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80554400","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}
In this study, two-phase non-Newtonian turbulent fluid flow in an inclined geothermal pipe with chemical reaction was considered. The governing nonlinear partial differential equations derived were solved numerically using Finite Difference Method. Influence of flow parameters on the temperature, concentration and velocity profiles were analyzed graphically. From the mathematical analysis of the model, it was established that the chemical reaction parameter significantly influenced the concentration distribution in both gaseous and liquid phases. Findings further revealed that decreasing the chemical reaction parameter resulted in decreased concentration of the geothermal fluid, which causes corrosion of geothermal pipes. These findings provide important information to engineers and researchers in making better decisions in terms of design, sizing and maintenance of flow systems in geothermal pipes.
{"title":"Two-Phase Turbulent Fluid Flow in a Geothermal Pipe with Chemical Reaction","authors":"Nyariki M. Eric, M. Kinyanjui, J. Abonyo","doi":"10.1155/2022/7617017","DOIUrl":"https://doi.org/10.1155/2022/7617017","url":null,"abstract":"In this study, two-phase non-Newtonian turbulent fluid flow in an inclined geothermal pipe with chemical reaction was considered. The governing nonlinear partial differential equations derived were solved numerically using Finite Difference Method. Influence of flow parameters on the temperature, concentration and velocity profiles were analyzed graphically. From the mathematical analysis of the model, it was established that the chemical reaction parameter significantly influenced the concentration distribution in both gaseous and liquid phases. Findings further revealed that decreasing the chemical reaction parameter resulted in decreased concentration of the geothermal fluid, which causes corrosion of geothermal pipes. These findings provide important information to engineers and researchers in making better decisions in terms of design, sizing and maintenance of flow systems in geothermal pipes.","PeriodicalId":14766,"journal":{"name":"J. Appl. Math.","volume":"9 1","pages":"7617017:1-7617017:19"},"PeriodicalIF":0.0,"publicationDate":"2022-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84787437","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 precision of the traditional satellite remote sensing image denoising model cannot deal well with some precise production scenes. To solve this problem, this research proposes an improved remote sensing image processing model, in which the dual tree complex wavelet transform (DTCWT) method is used to conduct multiscale decomposition of the impact, and the fourth-order differential equation is used to denoise the decomposed complex high-frequency subband information, and then the denoised subbands are reconstructed into the denoised image. Through these two advanced signal-processing methods, the quality of reconstructed signals is improved and the noise content of various types is greatly reduced. The experimental results show that the normalized root mean square error of the denoising model designed in this study after training convergence is 0.02. When the noise variance is 0.030, the structure similarity, peak signal to noise ratio, and normalized signal to noise ratio are 0.74, 25.3, and 0.76, respectively, which are better than all other comparison models. The experimental data prove that the satellite remote sensing image data denoising model designed in this study has better denoising performance, and has certain application potential in high-precision satellite remote sensing image big data processing.
{"title":"Application of DTCWT Decomposition and Partial Differential Equation Denoising Methods in Remote Sensing Image Big Data Denoising and Reconstruction","authors":"W. Zeng","doi":"10.1155/2022/8553330","DOIUrl":"https://doi.org/10.1155/2022/8553330","url":null,"abstract":"The precision of the traditional satellite remote sensing image denoising model cannot deal well with some precise production scenes. To solve this problem, this research proposes an improved remote sensing image processing model, in which the dual tree complex wavelet transform (DTCWT) method is used to conduct multiscale decomposition of the impact, and the fourth-order differential equation is used to denoise the decomposed complex high-frequency subband information, and then the denoised subbands are reconstructed into the denoised image. Through these two advanced signal-processing methods, the quality of reconstructed signals is improved and the noise content of various types is greatly reduced. The experimental results show that the normalized root mean square error of the denoising model designed in this study after training convergence is 0.02. When the noise variance is 0.030, the structure similarity, peak signal to noise ratio, and normalized signal to noise ratio are 0.74, 25.3, and 0.76, respectively, which are better than all other comparison models. The experimental data prove that the satellite remote sensing image data denoising model designed in this study has better denoising performance, and has certain application potential in high-precision satellite remote sensing image big data processing.","PeriodicalId":14766,"journal":{"name":"J. Appl. Math.","volume":"52 3","pages":"8553330:1-8553330:13"},"PeriodicalIF":0.0,"publicationDate":"2022-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72558538","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}
Numerical computation of maximum likelihood estimates (MLE) is one of the most common problems encountered in applied statistics. Even if there exist many algorithms considered as performing, they can suffer in some cases for one or many of the following criteria: global convergence (capacity of an algorithm to converge to the true unknown solution from all starting guesses), numerical stability (ascent property), implementation feasibility (for example, algorithms requiring matrix inversion cannot be implemented when the involved matrices are not invertible), low computation time, low computational complexity, and capacity to handle high dimensional problems. The reality is that, in practice, no algorithm is perfect, and for each problem, it is necessary to find the most performing of all existing algorithms or even develop new ones. In this paper, we consider the computing of the maximum likelihood estimate of the vector parameter of a statistical model of crash frequencies. We split the parameter vector, and we develop a new estimation algorithm using the profile likelihood principle. We provide an automatic starting guess for which convergence and numerical stability are guaranteed. We study the performance of our new algorithm on simulated data by comparing it to some of the most famous and modern optimization algorithms. The results suggest that our proposed algorithm outperforms these algorithms.
{"title":"An Automated Profile-Likelihood-Based Algorithm for Fast Computation of the Maximum Likelihood Estimate in a Statistical Model for Crash Data","authors":"Issa Cherif Geraldo","doi":"10.1155/2022/6974166","DOIUrl":"https://doi.org/10.1155/2022/6974166","url":null,"abstract":"Numerical computation of maximum likelihood estimates (MLE) is one of the most common problems encountered in applied statistics. Even if there exist many algorithms considered as performing, they can suffer in some cases for one or many of the following criteria: global convergence (capacity of an algorithm to converge to the true unknown solution from all starting guesses), numerical stability (ascent property), implementation feasibility (for example, algorithms requiring matrix inversion cannot be implemented when the involved matrices are not invertible), low computation time, low computational complexity, and capacity to handle high dimensional problems. The reality is that, in practice, no algorithm is perfect, and for each problem, it is necessary to find the most performing of all existing algorithms or even develop new ones. In this paper, we consider the computing of the maximum likelihood estimate of the vector parameter of a statistical model of crash frequencies. We split the parameter vector, and we develop a new estimation algorithm using the profile likelihood principle. We provide an automatic starting guess for which convergence and numerical stability are guaranteed. We study the performance of our new algorithm on simulated data by comparing it to some of the most famous and modern optimization algorithms. The results suggest that our proposed algorithm outperforms these algorithms.","PeriodicalId":14766,"journal":{"name":"J. Appl. Math.","volume":"20 1","pages":"6974166:1-6974166:11"},"PeriodicalIF":0.0,"publicationDate":"2022-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82714239","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 classification is one of the main tasks in the current data mining field, and the existing network data triage algorithms have problems such as too small a proportion of labeled samples, a large amount of noise, and redundant data, which lead to low classification accuracy of data stream implementation. Network embedding can effectively improve these problems, but the network embedding itself has problems such as capturing relational honor and ambiguity. This study proposes a SNN-RODE based LapRLS heterogeneous network data classification algorithm to achieve deep embedding of structure and semantics among nodes by constructing a multitask SNN and selecting dead song datasets to perform mining tasks to train the neural network. Then a semisupervised learning classifier based on Laplace regular least squares regression model is designed to use the relative support difference function as the decision method and optimize the function. The simulation experimental results show that the SNN-RODE-LapRLS algorithm improves the performance by 14%-51% over the mainstream classification algorithms, and the consumption time meets the demand of real-time classification.
{"title":"Classification Algorithm for Heterogeneous Network Data Streams Based on Big Data Active Learning","authors":"Li Zhan","doi":"10.1155/2022/2996725","DOIUrl":"https://doi.org/10.1155/2022/2996725","url":null,"abstract":"Data classification is one of the main tasks in the current data mining field, and the existing network data triage algorithms have problems such as too small a proportion of labeled samples, a large amount of noise, and redundant data, which lead to low classification accuracy of data stream implementation. Network embedding can effectively improve these problems, but the network embedding itself has problems such as capturing relational honor and ambiguity. This study proposes a SNN-RODE based LapRLS heterogeneous network data classification algorithm to achieve deep embedding of structure and semantics among nodes by constructing a multitask SNN and selecting dead song datasets to perform mining tasks to train the neural network. Then a semisupervised learning classifier based on Laplace regular least squares regression model is designed to use the relative support difference function as the decision method and optimize the function. The simulation experimental results show that the SNN-RODE-LapRLS algorithm improves the performance by 14%-51% over the mainstream classification algorithms, and the consumption time meets the demand of real-time classification.","PeriodicalId":14766,"journal":{"name":"J. Appl. Math.","volume":"53 1","pages":"2996725:1-2996725:10"},"PeriodicalIF":0.0,"publicationDate":"2022-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82831766","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}
In this paper, a mathematical model based on a system of nonlinear parabolic partial differential equations is developed to investigate the effect of human mobility on the dynamics of coronavirus 2019 (COVID-19) disease. Positivity and boundedness of the model solutions are shown. The existence of the disease-free, the endemic equilibria, and the travelling wave solutions of the model are shown. From the numerical analysis, it is shown that human mobility plays a crucial role in the disease transmission. Therefore, interventions that affect diffusion (human mobility), such as lock-down, travel restrictions, and cessation of movement, may play a significant role in controlling and preventing the spread of COVID-19.
{"title":"Travelling Wave Analysis of a Diffusive COVID-19 Model","authors":"Charles M. Wachira, G. O. Lawi, L. Omondi","doi":"10.1155/2022/6052274","DOIUrl":"https://doi.org/10.1155/2022/6052274","url":null,"abstract":"In this paper, a mathematical model based on a system of nonlinear parabolic partial differential equations is developed to investigate the effect of human mobility on the dynamics of coronavirus 2019 (COVID-19) disease. Positivity and boundedness of the model solutions are shown. The existence of the disease-free, the endemic equilibria, and the travelling wave solutions of the model are shown. From the numerical analysis, it is shown that human mobility plays a crucial role in the disease transmission. Therefore, interventions that affect diffusion (human mobility), such as lock-down, travel restrictions, and cessation of movement, may play a significant role in controlling and preventing the spread of COVID-19.","PeriodicalId":14766,"journal":{"name":"J. Appl. Math.","volume":"48 1","pages":"6052274:1-6052274:7"},"PeriodicalIF":0.0,"publicationDate":"2022-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87893915","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}
Demsis Dejene Hailemichael, G. K. Edessa, Koya Purnachandra Rao
In this paper, the population dynamics of rabies-infected dogs are studied. The mathematical model is constructed by dividing the dog population into two categories: stray dogs and domestic dogs. On the other hand, the rabies virus is likely to spread in both populations. In the current model, disease-controlling strategies such as vaccination and culling are applied, and their impact is studied. Both subpopulations of susceptible individuals are vaccinated to control disease spread. The current study assumes that stray dogs can transmit rabies to domestic dogs but not the other way around. Because domestic dogs are under the control of their owners, they are well vaccinated. The model is medically and analytically correct because the findings are idealistic and limited. The next-generation matrix technique is used to compute the effective reproductive amount, and also, each parameter is subjected to sensitivity analysis. The equilibrium point free from disease is discovered, demonstrating that it was asymptotically steady locally and globally. A conditionally global asymptotically stable point of endemic equilibrium is also discovered using the Lyapunov function method. The numerical simulation, which makes use of approximations for parameter values, shows that the most efficient method for avoiding rabies transmission is a combination of vaccination and the culling of infected stray dogs. Using MATLAB’s ode45, this numerical simulation investigation was carried out. Our early findings indicated that the annual dog birth rate is a critical factor in influencing the occurrence of rabies. In the body of the paper, the findings and discussion are organized logically.
{"title":"Effect of Vaccination and Culling on the Dynamics of Rabies Transmission from Stray Dogs to Domestic Dogs","authors":"Demsis Dejene Hailemichael, G. K. Edessa, Koya Purnachandra Rao","doi":"10.1155/2022/2769494","DOIUrl":"https://doi.org/10.1155/2022/2769494","url":null,"abstract":"In this paper, the population dynamics of rabies-infected dogs are studied. The mathematical model is constructed by dividing the dog population into two categories: stray dogs and domestic dogs. On the other hand, the rabies virus is likely to spread in both populations. In the current model, disease-controlling strategies such as vaccination and culling are applied, and their impact is studied. Both subpopulations of susceptible individuals are vaccinated to control disease spread. The current study assumes that stray dogs can transmit rabies to domestic dogs but not the other way around. Because domestic dogs are under the control of their owners, they are well vaccinated. The model is medically and analytically correct because the findings are idealistic and limited. The next-generation matrix technique is used to compute the effective reproductive amount, and also, each parameter is subjected to sensitivity analysis. The equilibrium point free from disease is discovered, demonstrating that it was asymptotically steady locally and globally. A conditionally global asymptotically stable point of endemic equilibrium is also discovered using the Lyapunov function method. The numerical simulation, which makes use of approximations for parameter values, shows that the most efficient method for avoiding rabies transmission is a combination of vaccination and the culling of infected stray dogs. Using MATLAB’s ode45, this numerical simulation investigation was carried out. Our early findings indicated that the annual dog birth rate is a critical factor in influencing the occurrence of rabies. In the body of the paper, the findings and discussion are organized logically.","PeriodicalId":14766,"journal":{"name":"J. Appl. Math.","volume":"14 1","pages":"2769494:1-2769494:14"},"PeriodicalIF":0.0,"publicationDate":"2022-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86685073","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}
In this paper, we study the flow of two immiscible fluids namely, couple stress fluid and Jeffrey fluid in a porous channel. Instead of the classical no-slip conditions on the boundaries, we used slip boundary conditions, which are more realistic and meaningful. In addition, we used inclined magnetic field effects on the fluid flow. The couple stress fluid and Jeffrey fluid are flowing adjacent to each other in the region I and in the region II, respectively, of the horizontal porous channel. The nondimensionalized governing equations are solved analytically by using slip conditions at the lower and upper boundaries and interface conditions at the fluid-fluid interface. The analytical expressions for the velocity components in both regions are obtained in closed form. The effects of slip parameter, Hartmann number, couple stress parameter, Jeffrey parameter, angle of inclination, and Darcy number on velocity components in both regions are investigated. In the absence of slip, couple stress parameter, and Jeffrey parameters, limiting cases are obtained and discussed.
{"title":"Effects of Slip and Inclined Magnetic Field on the Flow of Immiscible Fluids (Couple Stress Fluid and Jeffrey Fluid) in a Porous Channel","authors":"Punnamchandar Bitla, Fekadu Yemataw Sitotaw","doi":"10.1155/2022/2799773","DOIUrl":"https://doi.org/10.1155/2022/2799773","url":null,"abstract":"In this paper, we study the flow of two immiscible fluids namely, couple stress fluid and Jeffrey fluid in a porous channel. Instead of the classical no-slip conditions on the boundaries, we used slip boundary conditions, which are more realistic and meaningful. In addition, we used inclined magnetic field effects on the fluid flow. The couple stress fluid and Jeffrey fluid are flowing adjacent to each other in the region I and in the region II, respectively, of the horizontal porous channel. The nondimensionalized governing equations are solved analytically by using slip conditions at the lower and upper boundaries and interface conditions at the fluid-fluid interface. The analytical expressions for the velocity components in both regions are obtained in closed form. The effects of slip parameter, Hartmann number, couple stress parameter, Jeffrey parameter, angle of inclination, and Darcy number on velocity components in both regions are investigated. In the absence of slip, couple stress parameter, and Jeffrey parameters, limiting cases are obtained and discussed.","PeriodicalId":14766,"journal":{"name":"J. Appl. Math.","volume":"22 1","pages":"2799773:1-2799773:11"},"PeriodicalIF":0.0,"publicationDate":"2022-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72968541","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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