In the present study,we concentrate on finding the dual solutions of biomagnetic fluid namely blood flow and heat transfer along with magnetic particles over a two dimensional shrinking cylinder in the presence of a m...In the present study,we concentrate on finding the dual solutions of biomagnetic fluid namely blood flow and heat transfer along with magnetic particles over a two dimensional shrinking cylinder in the presence of a magnetic dipole.To make the results physically realistic,stability analysis is also carried out in this study so that we realized which solution is stable and which is not.The governing partial equations are converted into ordinary differential equations by using similarity transformations and the numerical solution is calculated by applying bvp4c function technique in MATLAB software.The effects of different physical parameters are plotted graphically and discussed according to the outcomes of results.From the present study we observe that ferromagnetic interaction parameter had a great influenced on fluid velocity and temperature distributions.It is also found from the current analysis that the first and second solutions of shrinking cylinder obtained only when we applied particular ranges values of suction parameter.The most important characteristics part of study is to analyze the skin friction coefficient and rate of heat transfer which also covered in this analysis.It reveals that both skin friction coefficient and rate of heat transfer are reduced with rising values of ferromagnetic number.A comparison has also been made to make the solution feasible.展开更多
This paper discusses the model of the boundary layer(BL)flow and the heat transfer characteristics of hybrid nanofluid(HNF)over shrinking/stretching disks.In addition,the thermal radiation and the impact of velocity a...This paper discusses the model of the boundary layer(BL)flow and the heat transfer characteristics of hybrid nanofluid(HNF)over shrinking/stretching disks.In addition,the thermal radiation and the impact of velocity and thermal slip boundary conditions are also examined.The considered hybrid nano-fluid contains silver(Ag)and iron oxide(Fe_(3)O_(4))nanoparticles dispersed in the water to prepare the Ag-Fe_(3)O_(4)/water-based hybrid nanofluid.The requisite posited partial differential equations model is converted to ordinary differential equations using similarity transformations.For a numerical solution,the shooting method in Maple is employed.Moreover,the duality in solutions is achieved for both cases of the disk(stretching(λ>0)and shrinking(λ<0)).At the same time,a unique solution is observed for λ=0.No solution is found for them at λ<λ_(c),whereas the solutions are split at the λ=λ_(c).Besides,the value of the λ_(c) is dependent on the φ_(hnf).Meanwhile,the values of f″(0)and -θ′(0)intensified with increasing φ_(hnf).Stability analysis has been applied using bvp4c in MATLAB software due to a dual solution.Furthermore,analysis shows that the first solution is stable and feasible physically.For the slip parameters,an increase in the velocity slip parameter increases the velocity and shear stress profiles while increasing the temperature profile in the first solutions.While the rise in thermal slip parameter reduces the temperature profile nanoparticle volume fractions increase it.展开更多
Urban vitality is one of the key indicators of sustainable urban development and an important factor for shrinking cities to achieve internal optimization.The relationship between the built environment and urban vital...Urban vitality is one of the key indicators of sustainable urban development and an important factor for shrinking cities to achieve internal optimization.The relationship between the built environment and urban vitality has been extensively discussed.However,the moderating effect of housing vacancy on the built environment’s effect on urban vitality in shrinking cities has not been explored in detail.This paper selected Yichun District in Yichun City of Heilongjiang Province,a typical shrinking city in Northeast China,as the study area,focusing on the effect of the built environment on urban vitality in shrinking cities based on residential and commercial electricity consumption data for 2013 and 2018.Moreover,this study also explored the moderating mechanisms of residential and commercial housing vacancies on the built environment’s effect on urban vitality.The results demonstrate that the spatial pattern of urban vitality in the Yichun District is‘high in the center and low in the periphery’.Population density,building age,road density,and catering facilities are recognized as the main built environment factors affecting the vitality of shrinking cities.Residential and commercial housing vacancies have a significant moderating effect on the built environment’s effect on urban vitality.Residential housing vacancies enhance the positive effect of road density and the negative effect of greening rate.In addition,commercial housing vacancies suppress the positive effect of building density and enhance the positive effect of accessibility to urban service facilities.The study indicates that built environment factors exhibit heterogeneous effects on vitality in the context of urban shrinkage,as moderated by housing vacancies.Targeted regulation of built environment factors is of practical significance in realizing the internal development and vitality enhancement of shrinking cities.展开更多
An analysis of unsteady boundary layer flow and heat transfer over an exponentially shrinking porous sheet filled with a copper-water nanofluid is presented.Water is treated as a base fluid.In the investigation,non-un...An analysis of unsteady boundary layer flow and heat transfer over an exponentially shrinking porous sheet filled with a copper-water nanofluid is presented.Water is treated as a base fluid.In the investigation,non-uniform mass suction through the porous sheet is considered.Using Keller-box method the transformed equations are solved numerically.The results of skin friction coefficient,the local Nusselt number as well as the velocity and temperature profiles are presented for different flow parameters.The results showed that the dual non-similar solutions exist only when certain amount of mass suction is applied through the porous sheet for various unsteady parameters and nanoparticle volume fractions.The ranges of suction where dual non-similar solution exists,become larger when values of unsteady parameter as well as nanoparticle volume fraction increase.So,due to unsteadiness of flow dynamics and the presence of nanoparticles in flow field,the requirement of mass suction for existence of solution of boundary layer flow past an exponentially shrinking sheet is less.Furthermore,the velocity boundary layer thickness decreases and thermal boundary layer thickness increases with increasing of nanoparticle volume fraction in both non-similar solutions.Whereas,for stronger mass suction,the velocity boundary layer thickness becomes thinner for the first solution and the effect is opposite in the case of second solution.The temperature inside the boundary layer increases with nanoparticle volume fraction and decreases with mass suction.So,for the unsteadiness and for the presence of nanoparticles,the flow separation is delayed to some extent.展开更多
Most of the current evolutionary algorithms for constrained optimization algorithm are low computational efficiency. In order to improve efficiency, an improved differential evolution with shrinking space technique an...Most of the current evolutionary algorithms for constrained optimization algorithm are low computational efficiency. In order to improve efficiency, an improved differential evolution with shrinking space technique and adaptive trade-off model, named ATMDE, is proposed to solve constrained optimization problems. The proposed ATMDE algorithm employs an improved differential evolution as the search optimizer to generate new offspring individuals into evolutionary population. For the con- straints, the adaptive trade-off model as one of the most important constraint-handling techniques is employed to select better individuals to retain into the next population, which could effectively handle multiple constraints. Then the shrinking space technique is designed to shrink the search region according to feedback information in order to improve computational efficiency without losing accuracy. The improved DE algorithm introduces three different mutant strategies to generate different offspring into evo- lutionary population. Moreover, a new mutant strategy called ＂DE/rand/best/l＂ is constructed to generate new individuals according to the feasibility proportion ofcurrent population. Finally, the effectiveness of the pro- posed method is verified by a suite of benchmark functions and practical engineering problems. This research presents a constrained evolutionary algorithm with high efficiency and accuracy for constrained optimization problems.展开更多
The steady flow and heat transfer of a hybrid nanofluid past a permeable stretching/shrinking wedge with magnetic field and radiation effects are studied. The governing equations of the hybrid nanofluid are converted ...The steady flow and heat transfer of a hybrid nanofluid past a permeable stretching/shrinking wedge with magnetic field and radiation effects are studied. The governing equations of the hybrid nanofluid are converted to the similarity equations by techniques of the similarity transformation. The bvp4c function that is available in MATLAB software is utilized for solving the similarity equations numerically. The numerical results are obtained for selected different values of parameters. The results discover that two solutions exist, up to a certain value of the stretching/shrinking and suction strengths. The critical value in which the solution is in existence decreases as nanoparticle volume fractions for copper and wedge angle parameter increase. It is also found that the hybrid nanofluid enhances the heat transfer rate compared with the regular nanofluid. The reduction of the heat transfer rate is observed with the increase in radiation parameter. The temporal stability analysis is performed to analyze the stability of the dual solutions, and it is revealed that only one of them is stable and physically reliable.展开更多
The kinetics of H<sub>2</sub>S removal by zinc oxide desulfurizer was studied through thermogravimetricanalysis.The experimental results show that desulfurization rate was controlled,at high temperatureand...The kinetics of H<sub>2</sub>S removal by zinc oxide desulfurizer was studied through thermogravimetricanalysis.The experimental results show that desulfurization rate was controlled,at high temperatureand low conversion,by the chemical reaction rate,and at low temperature and high conversion by thegrain diffusion rate.The reaction is first order with respect to H<sub>2</sub>S concentration in the differentcontrolled stages.The kinetic behavior can be modeled through the employment of the shrinking coremodel.The values of the model parameters were determined.The variation tendencies with temperatureand concentration of H<sub>2</sub>S at the controlled stages were discussed.展开更多
Model of Casson nanofluid flow over a nonlinear shrinking surface is considered.Model of Tiwari and Das is applied to nanofluid comprising of sodium alginate with copper and silver.The governing nonlinear equations in...Model of Casson nanofluid flow over a nonlinear shrinking surface is considered.Model of Tiwari and Das is applied to nanofluid comprising of sodium alginate with copper and silver.The governing nonlinear equations incorporating the effects of the viscous dissipation are transformed into boundary value problems (BVPs) of ordinary differential equations (ODEs) by using appropriate similarity transformations.The resulting equations are converted into initial value problems (IVPs) using the shooting method which are then solved by Runge-Kutta method of fourth order.In order to determine the stability of the dual solutions obtained,stability analysis is performed and discovered that the first (second) solution is stable (unstable) and physically realizable (unrealizable).Both the thickness of the thermal boundary layer as well as temperature increase when the Casson parameter (β) is increased in the second solution.展开更多
We show that closed shrinking gradient Ricci solitons with positive Ricci curvature and sufficiently pinched Weyl tensor are Einstein. When Weyl tensor vanishes, this has been proved before but our proof here is much ...We show that closed shrinking gradient Ricci solitons with positive Ricci curvature and sufficiently pinched Weyl tensor are Einstein. When Weyl tensor vanishes, this has been proved before but our proof here is much simpler.展开更多
This work is concerned with Magnetohydrodynamic viscous flow due to a shrinking sheet in the presence of suction. The cases of two dimensional and axisymmetric shrinking are discussed. The governing boundary layer equ...This work is concerned with Magnetohydrodynamic viscous flow due to a shrinking sheet in the presence of suction. The cases of two dimensional and axisymmetric shrinking are discussed. The governing boundary layer equations are written into a dimensionless form by similarity transformations. The transformed coupled nonlinear ordinary differential equations are numerically solved by using an advanced numeric technique. Favorability comparisons with previously published work are presented. Numerical results for the dimensionless velocity, temperature and concentration profiles as well as for the skin friction, heat and mass transfer and deposition rate are obtained and displayed graphically for pertinent parameters to show interesting aspects of the solution.展开更多
The present article investigates the dual nature of the solution of the magneto- hydrodynamic （MHD） stagnation-point flow of a Prandtl fluid model towards a shrinking surface. The self-similar nonlinear ordinary dif...The present article investigates the dual nature of the solution of the magneto- hydrodynamic （MHD） stagnation-point flow of a Prandtl fluid model towards a shrinking surface. The self-similar nonlinear ordinary differential equations are solved numerically by the shooting： method. It is found that the dual solutions of the flow exist for cer- tain values of tile velocity ratio parameter. The special case of the first branch solutions （the classical Newtonian fluid model） is compared with the present numerical results of stretching flow. The results are found to be in good agreement. It is also shown that the boundary layer thickness for the second solution is thicker than that for the first solution.展开更多
The boundary layer flow of a nanofluid past a stretching/shrinking sheet with hydrodynamic and thermal slip boundary conditions is studied. Numerical solutions to the governing equations are obtained using a shooting ...The boundary layer flow of a nanofluid past a stretching/shrinking sheet with hydrodynamic and thermal slip boundary conditions is studied. Numerical solutions to the governing equations are obtained using a shooting method. The results are found for the skin friction coefficient, the local Nusselt number, and the local Sherwood number as well as the velocity, temperature, and concentration profiles for some values of the velocity slip parameter, thermal slip parameter, stretching/shrinking parameter, thermophoresis parameter, and Brownian motion parameter. The results show that the local Nusselt number, which represents the heat transfer rate, is lower for higher values of thermal slip parameter, thermophoresis parameter, and Brownian motion parameter.展开更多
Studying the impact of urbanization on agricultural development in shrinking areas is important for maintaining food security and promoted agricultural development in China.Based on the measurement results of the shri...Studying the impact of urbanization on agricultural development in shrinking areas is important for maintaining food security and promoted agricultural development in China.Based on the measurement results of the shrinking cities in the three provinces of Northeast China,this paper selects 15 shrinking cities as the research object,and constructs a multi-dimensional index system to explore the impact of the urbanization level of the shrinking areas on the agricultural development in the region since 2007–2019,analyzes the influencing factors and their differences by using the geographically-weighted regression model and Geodetector,and proposes a targeted regulation strategy.The results show that:1)overall,there is a negative correlation between the urbanization level and the agricultural development level in the contracted areas of the three northeastern provinces.The urbanization level in these areas has a certain negative impact on the overall level of agricultural development;2)regarding the time dimension,the impact of urbanization level on the agricultural development level in the contracted areas of the three northeastern provinces gradually increases over time;3)regarding the spatial pattern,the overall impact of shrinking urbanization levels in the three provinces of Northeast China on the agricultural development shows a significant distribution pattern of high in the east and low in the west;4)the total population and natural population growth rate at the end of the year were the main factors influencing a certain level of urbanization on agricultural development in the shrinking cities while population density and the urban fixed asset investment rate were the secondary factors;and 5)the main reasons why the level of agricultural development in different cities was affected by the level of urbanization were different.However,they can be categorized into areas of population loss and spatial construction,which can be further divided into area of population loss in the northeast,areas of negative population growth in the west,and areas of urban spatial change in the south.According to the causes of the impact,this paper adopted targeted regulation strategies and formulated relevant policies and solutions that cater to local conditions.展开更多
In this study, a reliable algorithm to develop approximate solutions for the problem of fluid flow over a stretching or shrinking sheet is proposed. It is depicted that the differential transform method (DTM) solution...In this study, a reliable algorithm to develop approximate solutions for the problem of fluid flow over a stretching or shrinking sheet is proposed. It is depicted that the differential transform method (DTM) solutions are only valid for small values of the independent variable. The DTM solutions diverge for some differential equations that extremely have nonlinear behaviors or have boundary-conditions at infinity. For this reason the governing boundary-layer equations are solved by the Multi-step Differential Transform Method (MDTM). The main advantage of this method is that it can be applied directly to nonlinear differential equations without requiring linearization, discretization, or perturbation. It is a semi analytical-numerical technique that formulizes Taylor series in a very different manner. By applying the MDTM the interval of convergence for the series solution is increased. The MDTM is treated as an algorithm in a sequence of intervals for finding accurate approximate solutions for systems of differential equations. It is predicted that the MDTM can be applied to a wide range of engineering applications.展开更多
The magnetohydrodynamic （MHD） stagnation point flow of micropolar flu- ids towards a heated shrinking surface is analyzed. The effects of viscous dissipation and internal heat generation/absorption are taken into ac...The magnetohydrodynamic （MHD） stagnation point flow of micropolar flu- ids towards a heated shrinking surface is analyzed. The effects of viscous dissipation and internal heat generation/absorption are taken into account. Two explicit cases, i.e., the prescribed surface temperature （PST） and the prescribed heat flux （PHF）, are discussed. The boundary layer flow and energy equations are solved by employing the homotopy analysis method. The quantities of physical interest are examined through the presenta- tion of plots/tabulated values. It is noticed that the existence of the solutions for high shrinking parameters is associated closely with the applied magnetic field.展开更多
This paper investigates the effects of thermal radiation on the magnetohy- drodynamic （MHD） flow and heat transfer over a nonlinear shrinking porous sheet. The surface velocity of the shrinking sheet and the transve...This paper investigates the effects of thermal radiation on the magnetohy- drodynamic （MHD） flow and heat transfer over a nonlinear shrinking porous sheet. The surface velocity of the shrinking sheet and the transverse magnetic field are assumed to vary as a power function of the distance from the origin. The temperature dependent viscosity and the thermal conductivity are also assumed to vary as an inverse function and a linear function of the temperature, respectively. A generalized similarity transfor- mation is used to reduce the governing partial differential equations to their nonlinear coupled ordinary differential equations, and is solved numerically by using a finite difference scheme. The numerical results concern with the velocity and temperature profiles as well as the local skin-friction coefficient and the rate of the heat transfer at the porous sheet for different values of several physical parameters of interest.展开更多
In this analysis,the magnetohydrodynamic boundary layer flow of Casson fluid over a permeable stretching/shrinking sheet in the presence of wall mass transfer is studied.Using similarity transformations,the governing ...In this analysis,the magnetohydrodynamic boundary layer flow of Casson fluid over a permeable stretching/shrinking sheet in the presence of wall mass transfer is studied.Using similarity transformations,the governing equations are converted to an ordinary differential equation and then solved analytically.The introduction of a magnetic field changes the behavior of the entire flow dynamics in the shrinking sheet case and also has a major impact in the stretching sheet case.The similarity solution is always unique in the stretching case,and in the shrinking case the solution shows dual nature for certain values of the parameters.For stronger magnetic field,the similarity solution for the shrinking sheet case becomes unique.展开更多
文摘In the present study,we concentrate on finding the dual solutions of biomagnetic fluid namely blood flow and heat transfer along with magnetic particles over a two dimensional shrinking cylinder in the presence of a magnetic dipole.To make the results physically realistic,stability analysis is also carried out in this study so that we realized which solution is stable and which is not.The governing partial equations are converted into ordinary differential equations by using similarity transformations and the numerical solution is calculated by applying bvp4c function technique in MATLAB software.The effects of different physical parameters are plotted graphically and discussed according to the outcomes of results.From the present study we observe that ferromagnetic interaction parameter had a great influenced on fluid velocity and temperature distributions.It is also found from the current analysis that the first and second solutions of shrinking cylinder obtained only when we applied particular ranges values of suction parameter.The most important characteristics part of study is to analyze the skin friction coefficient and rate of heat transfer which also covered in this analysis.It reveals that both skin friction coefficient and rate of heat transfer are reduced with rising values of ferromagnetic number.A comparison has also been made to make the solution feasible.
基金the Researchers Supporting Project number(RSPD2025R997),King Saud University,Riyadh,Saudi Arabia.
文摘This paper discusses the model of the boundary layer(BL)flow and the heat transfer characteristics of hybrid nanofluid(HNF)over shrinking/stretching disks.In addition,the thermal radiation and the impact of velocity and thermal slip boundary conditions are also examined.The considered hybrid nano-fluid contains silver(Ag)and iron oxide(Fe_(3)O_(4))nanoparticles dispersed in the water to prepare the Ag-Fe_(3)O_(4)/water-based hybrid nanofluid.The requisite posited partial differential equations model is converted to ordinary differential equations using similarity transformations.For a numerical solution,the shooting method in Maple is employed.Moreover,the duality in solutions is achieved for both cases of the disk(stretching(λ>0)and shrinking(λ<0)).At the same time,a unique solution is observed for λ=0.No solution is found for them at λ<λ_(c),whereas the solutions are split at the λ=λ_(c).Besides,the value of the λ_(c) is dependent on the φ_(hnf).Meanwhile,the values of f″(0)and -θ′(0)intensified with increasing φ_(hnf).Stability analysis has been applied using bvp4c in MATLAB software due to a dual solution.Furthermore,analysis shows that the first solution is stable and feasible physically.For the slip parameters,an increase in the velocity slip parameter increases the velocity and shear stress profiles while increasing the temperature profile in the first solutions.While the rise in thermal slip parameter reduces the temperature profile nanoparticle volume fractions increase it.
基金Under the auspices of the National Natural Science Foundation of China(No.42171191,41771172,42201211,42401249)Science and Technology Development Plan Project of Jilin Province,China(No.20220508025RC)Young Scientist Group Project of Northeast Institute of Geography and Agroecology,Chinese Academy of Sciences(No.2022QNXZ02)。
文摘Urban vitality is one of the key indicators of sustainable urban development and an important factor for shrinking cities to achieve internal optimization.The relationship between the built environment and urban vitality has been extensively discussed.However,the moderating effect of housing vacancy on the built environment’s effect on urban vitality in shrinking cities has not been explored in detail.This paper selected Yichun District in Yichun City of Heilongjiang Province,a typical shrinking city in Northeast China,as the study area,focusing on the effect of the built environment on urban vitality in shrinking cities based on residential and commercial electricity consumption data for 2013 and 2018.Moreover,this study also explored the moderating mechanisms of residential and commercial housing vacancies on the built environment’s effect on urban vitality.The results demonstrate that the spatial pattern of urban vitality in the Yichun District is‘high in the center and low in the periphery’.Population density,building age,road density,and catering facilities are recognized as the main built environment factors affecting the vitality of shrinking cities.Residential and commercial housing vacancies have a significant moderating effect on the built environment’s effect on urban vitality.Residential housing vacancies enhance the positive effect of road density and the negative effect of greening rate.In addition,commercial housing vacancies suppress the positive effect of building density and enhance the positive effect of accessibility to urban service facilities.The study indicates that built environment factors exhibit heterogeneous effects on vitality in the context of urban shrinkage,as moderated by housing vacancies.Targeted regulation of built environment factors is of practical significance in realizing the internal development and vitality enhancement of shrinking cities.
基金the National Board for Higher Mathematics(NBHM),Department of Atomic Energy,Government of India for the financial support in pursuing this workthe financial support from MOHE and the Research Management Center-UTM through FRGS and RUG vote number 4F109 and 02H80 for this research
文摘An analysis of unsteady boundary layer flow and heat transfer over an exponentially shrinking porous sheet filled with a copper-water nanofluid is presented.Water is treated as a base fluid.In the investigation,non-uniform mass suction through the porous sheet is considered.Using Keller-box method the transformed equations are solved numerically.The results of skin friction coefficient,the local Nusselt number as well as the velocity and temperature profiles are presented for different flow parameters.The results showed that the dual non-similar solutions exist only when certain amount of mass suction is applied through the porous sheet for various unsteady parameters and nanoparticle volume fractions.The ranges of suction where dual non-similar solution exists,become larger when values of unsteady parameter as well as nanoparticle volume fraction increase.So,due to unsteadiness of flow dynamics and the presence of nanoparticles in flow field,the requirement of mass suction for existence of solution of boundary layer flow past an exponentially shrinking sheet is less.Furthermore,the velocity boundary layer thickness decreases and thermal boundary layer thickness increases with increasing of nanoparticle volume fraction in both non-similar solutions.Whereas,for stronger mass suction,the velocity boundary layer thickness becomes thinner for the first solution and the effect is opposite in the case of second solution.The temperature inside the boundary layer increases with nanoparticle volume fraction and decreases with mass suction.So,for the unsteadiness and for the presence of nanoparticles,the flow separation is delayed to some extent.
基金Supported by National Science Foundation for Excellent Young Scholars,China(Grant No.51222502)Funds for Distinguished Young Scientists of Hunan Province,China(Grant No.14JJ1016)Major Program of National Natural Science Foundation of China(Grant No.51490662)
文摘Most of the current evolutionary algorithms for constrained optimization algorithm are low computational efficiency. In order to improve efficiency, an improved differential evolution with shrinking space technique and adaptive trade-off model, named ATMDE, is proposed to solve constrained optimization problems. The proposed ATMDE algorithm employs an improved differential evolution as the search optimizer to generate new offspring individuals into evolutionary population. For the con- straints, the adaptive trade-off model as one of the most important constraint-handling techniques is employed to select better individuals to retain into the next population, which could effectively handle multiple constraints. Then the shrinking space technique is designed to shrink the search region according to feedback information in order to improve computational efficiency without losing accuracy. The improved DE algorithm introduces three different mutant strategies to generate different offspring into evo- lutionary population. Moreover, a new mutant strategy called ＂DE/rand/best/l＂ is constructed to generate new individuals according to the feasibility proportion ofcurrent population. Finally, the effectiveness of the pro- posed method is verified by a suite of benchmark functions and practical engineering problems. This research presents a constrained evolutionary algorithm with high efficiency and accuracy for constrained optimization problems.
基金the Ministry of Education of Malaysia(No.FRGS/1/2019/STG06/UKM/01/4)Ministry of Science of Romania(No.PN-III-P4-ID-PCE-2016-0036)。
文摘The steady flow and heat transfer of a hybrid nanofluid past a permeable stretching/shrinking wedge with magnetic field and radiation effects are studied. The governing equations of the hybrid nanofluid are converted to the similarity equations by techniques of the similarity transformation. The bvp4c function that is available in MATLAB software is utilized for solving the similarity equations numerically. The numerical results are obtained for selected different values of parameters. The results discover that two solutions exist, up to a certain value of the stretching/shrinking and suction strengths. The critical value in which the solution is in existence decreases as nanoparticle volume fractions for copper and wedge angle parameter increase. It is also found that the hybrid nanofluid enhances the heat transfer rate compared with the regular nanofluid. The reduction of the heat transfer rate is observed with the increase in radiation parameter. The temporal stability analysis is performed to analyze the stability of the dual solutions, and it is revealed that only one of them is stable and physically reliable.
基金Supported by the National Natural Science Foundation of China.
文摘The kinetics of H<sub>2</sub>S removal by zinc oxide desulfurizer was studied through thermogravimetricanalysis.The experimental results show that desulfurization rate was controlled,at high temperatureand low conversion,by the chemical reaction rate,and at low temperature and high conversion by thegrain diffusion rate.The reaction is first order with respect to H<sub>2</sub>S concentration in the differentcontrolled stages.The kinetic behavior can be modeled through the employment of the shrinking coremodel.The values of the model parameters were determined.The variation tendencies with temperatureand concentration of H<sub>2</sub>S at the controlled stages were discussed.
基金Universiti Utara Malaysia (UUM) for the moral and financial support in conducting this research
文摘Model of Casson nanofluid flow over a nonlinear shrinking surface is considered.Model of Tiwari and Das is applied to nanofluid comprising of sodium alginate with copper and silver.The governing nonlinear equations incorporating the effects of the viscous dissipation are transformed into boundary value problems (BVPs) of ordinary differential equations (ODEs) by using appropriate similarity transformations.The resulting equations are converted into initial value problems (IVPs) using the shooting method which are then solved by Runge-Kutta method of fourth order.In order to determine the stability of the dual solutions obtained,stability analysis is performed and discovered that the first (second) solution is stable (unstable) and physically realizable (unrealizable).Both the thickness of the thermal boundary layer as well as temperature increase when the Casson parameter (β) is increased in the second solution.
基金supported by National Natural Science Foundation of China(11301191)supported by MOST(MOST107-2115-M-110-007-MY2)
文摘We show that closed shrinking gradient Ricci solitons with positive Ricci curvature and sufficiently pinched Weyl tensor are Einstein. When Weyl tensor vanishes, this has been proved before but our proof here is much simpler.
文摘This work is concerned with Magnetohydrodynamic viscous flow due to a shrinking sheet in the presence of suction. The cases of two dimensional and axisymmetric shrinking are discussed. The governing boundary layer equations are written into a dimensionless form by similarity transformations. The transformed coupled nonlinear ordinary differential equations are numerically solved by using an advanced numeric technique. Favorability comparisons with previously published work are presented. Numerical results for the dimensionless velocity, temperature and concentration profiles as well as for the skin friction, heat and mass transfer and deposition rate are obtained and displayed graphically for pertinent parameters to show interesting aspects of the solution.
文摘The present article investigates the dual nature of the solution of the magneto- hydrodynamic （MHD） stagnation-point flow of a Prandtl fluid model towards a shrinking surface. The self-similar nonlinear ordinary differential equations are solved numerically by the shooting： method. It is found that the dual solutions of the flow exist for cer- tain values of tile velocity ratio parameter. The special case of the first branch solutions （the classical Newtonian fluid model） is compared with the present numerical results of stretching flow. The results are found to be in good agreement. It is also shown that the boundary layer thickness for the second solution is thicker than that for the first solution.
基金Project supported by the Ministry of Higher Education in Malaysia(No.FRGS/1/2012/SG04/UKM/2001/1)the Universiti Kebangsaan Malaysia(No.DIP-2012-31)
文摘The boundary layer flow of a nanofluid past a stretching/shrinking sheet with hydrodynamic and thermal slip boundary conditions is studied. Numerical solutions to the governing equations are obtained using a shooting method. The results are found for the skin friction coefficient, the local Nusselt number, and the local Sherwood number as well as the velocity, temperature, and concentration profiles for some values of the velocity slip parameter, thermal slip parameter, stretching/shrinking parameter, thermophoresis parameter, and Brownian motion parameter. The results show that the local Nusselt number, which represents the heat transfer rate, is lower for higher values of thermal slip parameter, thermophoresis parameter, and Brownian motion parameter.
基金Under the auspices of Natural Science Foundation of Heilongjiang(No.JJ2023LH0720)Philosophy and Social Sciences Research Program of Heilongjiang(No.21JLE323)Social Service Capacity Improvement Project of Harbin Normal University in 2022(No.1305123124)。
文摘Studying the impact of urbanization on agricultural development in shrinking areas is important for maintaining food security and promoted agricultural development in China.Based on the measurement results of the shrinking cities in the three provinces of Northeast China,this paper selects 15 shrinking cities as the research object,and constructs a multi-dimensional index system to explore the impact of the urbanization level of the shrinking areas on the agricultural development in the region since 2007–2019,analyzes the influencing factors and their differences by using the geographically-weighted regression model and Geodetector,and proposes a targeted regulation strategy.The results show that:1)overall,there is a negative correlation between the urbanization level and the agricultural development level in the contracted areas of the three northeastern provinces.The urbanization level in these areas has a certain negative impact on the overall level of agricultural development;2)regarding the time dimension,the impact of urbanization level on the agricultural development level in the contracted areas of the three northeastern provinces gradually increases over time;3)regarding the spatial pattern,the overall impact of shrinking urbanization levels in the three provinces of Northeast China on the agricultural development shows a significant distribution pattern of high in the east and low in the west;4)the total population and natural population growth rate at the end of the year were the main factors influencing a certain level of urbanization on agricultural development in the shrinking cities while population density and the urban fixed asset investment rate were the secondary factors;and 5)the main reasons why the level of agricultural development in different cities was affected by the level of urbanization were different.However,they can be categorized into areas of population loss and spatial construction,which can be further divided into area of population loss in the northeast,areas of negative population growth in the west,and areas of urban spatial change in the south.According to the causes of the impact,this paper adopted targeted regulation strategies and formulated relevant policies and solutions that cater to local conditions.
文摘In this study, a reliable algorithm to develop approximate solutions for the problem of fluid flow over a stretching or shrinking sheet is proposed. It is depicted that the differential transform method (DTM) solutions are only valid for small values of the independent variable. The DTM solutions diverge for some differential equations that extremely have nonlinear behaviors or have boundary-conditions at infinity. For this reason the governing boundary-layer equations are solved by the Multi-step Differential Transform Method (MDTM). The main advantage of this method is that it can be applied directly to nonlinear differential equations without requiring linearization, discretization, or perturbation. It is a semi analytical-numerical technique that formulizes Taylor series in a very different manner. By applying the MDTM the interval of convergence for the series solution is increased. The MDTM is treated as an algorithm in a sequence of intervals for finding accurate approximate solutions for systems of differential equations. It is predicted that the MDTM can be applied to a wide range of engineering applications.
基金Project supported by the Higher Education Commission (HEC) of Pakistan (No. 106-1396-Ps6-004)
文摘The magnetohydrodynamic （MHD） stagnation point flow of micropolar flu- ids towards a heated shrinking surface is analyzed. The effects of viscous dissipation and internal heat generation/absorption are taken into account. Two explicit cases, i.e., the prescribed surface temperature （PST） and the prescribed heat flux （PHF）, are discussed. The boundary layer flow and energy equations are solved by employing the homotopy analysis method. The quantities of physical interest are examined through the presenta- tion of plots/tabulated values. It is noticed that the existence of the solutions for high shrinking parameters is associated closely with the applied magnetic field.
基金Project supported by the Department of Science and Technology, Government of India (DST-GOI)Funded Promotion of University Research and Scientific Excellence (PURSE) Programme of Jadavpur University (No. SR/S9/Z-23/2008/5)
文摘This paper investigates the effects of thermal radiation on the magnetohy- drodynamic （MHD） flow and heat transfer over a nonlinear shrinking porous sheet. The surface velocity of the shrinking sheet and the transverse magnetic field are assumed to vary as a power function of the distance from the origin. The temperature dependent viscosity and the thermal conductivity are also assumed to vary as an inverse function and a linear function of the temperature, respectively. A generalized similarity transfor- mation is used to reduce the governing partial differential equations to their nonlinear coupled ordinary differential equations, and is solved numerically by using a finite difference scheme. The numerical results concern with the velocity and temperature profiles as well as the local skin-friction coefficient and the rate of the heat transfer at the porous sheet for different values of several physical parameters of interest.
基金the financial support of National Board forHigher Mathematics (NBHM),DAE,Mumbai,India for pursuing this workThe research of A. Alsaedi is partially supported by the Deanship of Scientific Research (DSR),King Abdulaziz University,Jeddah,Saudi Arabia
文摘In this analysis,the magnetohydrodynamic boundary layer flow of Casson fluid over a permeable stretching/shrinking sheet in the presence of wall mass transfer is studied.Using similarity transformations,the governing equations are converted to an ordinary differential equation and then solved analytically.The introduction of a magnetic field changes the behavior of the entire flow dynamics in the shrinking sheet case and also has a major impact in the stretching sheet case.The similarity solution is always unique in the stretching case,and in the shrinking case the solution shows dual nature for certain values of the parameters.For stronger magnetic field,the similarity solution for the shrinking sheet case becomes unique.
