Cell behaviors are regulated by the physical cues in their microenvironment,where extracellular fluid(ECF)viscosity is an important yet relatively underexplored cue.Recent evidence indicates that ECF viscosity plays a...Cell behaviors are regulated by the physical cues in their microenvironment,where extracellular fluid(ECF)viscosity is an important yet relatively underexplored cue.Recent evidence indicates that ECF viscosity plays a critical role in regulating cellular processes with pathological relevance to various diseases,such as cardiovascular related diseases,inflammatory diseases,and cancer.展开更多
Ultrasonic velocities of a set of saturated sandstone samples were measured at simulated in-situ pressures in the laboratory.The samples were obtained from the W formation of the WXS Depression and covered low to near...Ultrasonic velocities of a set of saturated sandstone samples were measured at simulated in-situ pressures in the laboratory.The samples were obtained from the W formation of the WXS Depression and covered low to nearly high porosity and permeability ranges.The brine and four different density oils were used as pore fluids,which provided a good chance to investigate fluid viscosity-induced velocity dispersion.The analysis of experimental observations of velocity dispersion indicates that（1）the Biot model can explain most of the small discrepancy（about 2–3%）between ultrasonic measurements and zero frequency Gassmann predictions for high porosity and permeability samples saturated by all the fluids used in this experiment and is also valid for medium porosity and permeability samples saturated with low viscosity fluids（less than approximately 3 mP·S）and（2）the squirt flow mechanism dominates the low to medium porosity and permeability samples when fluid viscosity increases and produces large velocity dispersions as high as about 8%. The microfracture aspect ratios were also estimated for the reservoir sandstones and applied to calculate the characteristic frequency of the squirt flow model,above which the Gassmann’ s assumptions are violated and the measured high frequency velocities cannot be directly used for Gassmann’s fluid replacement at the exploration seismic frequency band for W formation sandstones.展开更多
This paper examines a steady two-dimensional flow of incompressible fluid over a vertical stretching sheet. The fluid viscosity is assumed to vary as a linear function of temperature. A scaling group of transformation...This paper examines a steady two-dimensional flow of incompressible fluid over a vertical stretching sheet. The fluid viscosity is assumed to vary as a linear function of temperature. A scaling group of transformations is applied to the governing equa- tions. The system remains invariant due to some relations among the transformation parameters. After finding three absolute invariants, a third-order ordinary differential equation corresponding to the momentum equation and two second-order ordinary differential equations corresponding to energy and diffusion equations are derived. The equations along with the boundary conditions are solved numerically. It is found that the decrease in the temperature-dependent fluid viscosity makes the velocity decrease with the increasing distance of the stretching sheet. At a particular point of the sheet, the fluid velocity decreases but the temperature increases with the decreasing viscosity. The impact of the thermophoresis particle deposition plays an important role in the concentration boundary layer. The obtained results are presented graphically and discussed.展开更多
Fractal time-dependent issues in fluid dynamics provide a distinct difficulty in numerical analysis due to their complex characteristics,necessitating specialized computing techniques for precise and economical soluti...Fractal time-dependent issues in fluid dynamics provide a distinct difficulty in numerical analysis due to their complex characteristics,necessitating specialized computing techniques for precise and economical solutions.This study presents an innovative computational approach to tackle these difficulties.The main focus is applying the Fractal Runge-Kutta Method to model the time-dependent magnetohydrodynamic(MHD)Newtonian fluid with rescaled viscosity flow on Riga plates.An efficient computational scheme is proposed for handling fractal time-dependent problems in flow phenomena.The scheme is comprised of three stages and constructed using three different time levels.The stability of the scheme is shown by employing the Fourier series analysis to solve scalar problems.The scheme’s convergence is guaranteed for a time fractal partial differential equations system.The scheme is applied to the dimensionless fractal heat and mass transfer model of incompressible,unsteady,laminar,Newtonian fluid with rescaled viscosity flow over the flat and oscillatory Riga plates under the effects of space-and temperature-dependent heat sources.The first-order back differences discretize the continuity equation.The results show that skin friction local Nusselt number declines by raising the coefficient of the temperature-dependent term of heat source and Eckert number.The numerical simulations provide valuable insights into fluid dynamics,explicitly highlighting the influence of the temperature-dependent coefficient of the heat source and the Eckert number on skin friction and local Nusselt number.展开更多
In this paper, using Navier-Stokes equations and Reynolds time-averaged rules, the turbulent motional differential equations of variable density and variable viscosity Newtonian fluid have been presented, and the turb...In this paper, using Navier-Stokes equations and Reynolds time-averaged rules, the turbulent motional differential equations of variable density and variable viscosity Newtonian fluid have been presented, and the turbulent motional differential equations of variable density and variable viscosity Newtonian fluid in open channel have been further proposed. The concepts of the density turbulence stress and the viscosity turbulence stress have been firstly presented in the paper.展开更多
This paper studies the viscid and inviscid fluid resonance in gaps of bottom mounted caissons onthe basis of the plane wave hypothesis and full wave model, The theoretical analysis and the numerical results demonstrat...This paper studies the viscid and inviscid fluid resonance in gaps of bottom mounted caissons onthe basis of the plane wave hypothesis and full wave model, The theoretical analysis and the numerical results demonstrate that the condition for the appearance of fluid resonance in narrow gaps is kh=（2n＋1）π （n=0, 1, 2, 3 ）, rather than kh=nn （n=0, 1, 2, 3, ...）; the transmission peaks in viscid fluid are related to the resonance peaks in the gaps. k and h stand for the wave number and the gap length. The combination of the plane wave hypothesis or the full wave model with the local viscosity model can accurately determine the heights and the locations of the resonance peaks. The upper bound for the appearance of fluid resonance in gaps is 2b/L〈l （2b, grating constant; L, wave length） and the lower bound is h/b〈~ l. The main reason for the phase shift of the resonance peaks is the inductive factors. The number of resonance peaks in the spectrum curve is dependent on the ratio of the gap length to the grating constant. The heights and the positions of the resonance peaks predicted by the present models agree well with the experimental data.展开更多
Based on analyzing the limit of Ziolkowski＇s bubble oscillation formulation,a new model with various physical factors is established to simulate air gun signatures fo marine seismic exploration.The practical effects ...Based on analyzing the limit of Ziolkowski＇s bubble oscillation formulation,a new model with various physical factors is established to simulate air gun signatures fo marine seismic exploration.The practical effects of physical factors,such as heat transfe across the bubble wall,air gun port throttling,vertical rise of the bubble,fluid viscosity,and the existence of the air gun body were all taken into account in the new model.Compared with Ziolkowski＇s model,the signatures simulated by the new model,with small peak amplitude and rapid decay of bubble oscillation,are more consistent with actual signatures The experiment analysis indicates：（1）gun port throttling controls the peak amplitude of ai gun pulse;（2）since the hydrostatic pressure decreases when the bubble rises,the bubble oscillation period changes;（3）heat transfer and fluid viscosity are the main factors tha explain the bubble oscillation damping.展开更多
In this context, recent developments in the coupled three-dimensional(3 D) hydro-mechanical(HM)simulation tool TOUGH-RBSN are presented. This tool is used to model hydraulic fracture in geological media, as observed i...In this context, recent developments in the coupled three-dimensional(3 D) hydro-mechanical(HM)simulation tool TOUGH-RBSN are presented. This tool is used to model hydraulic fracture in geological media, as observed in laboratory-scale tests. The TOUGH-RBSN simulator is based on the effective linking of two numerical methods: TOUGH2, a finite volume method for simulating mass transport within a permeable medium; and a lattice model based on the rigid-body-spring network(RBSN) concept. The method relies on a Voronoi-based discretization technique that can represent fracture development within a permeable rock matrix. The simulator provides two-way coupling of HM processes, including fluid pressure-induced fracture and fracture-assisted flow. We first present the basic capabilities of the modeling approach using two example applications, i.e. permeability evolution under compression deformation, and analyses of a static fracturing simulation. Thereafter, the model is used to simulate laboratory tests of hydraulic fracturing in granite. In most respects, the simulation results meet expectations with respect to permeability evolution and fracturing patterns. It can be seen that the evolution of injection pressure associated with the simulated fracture developments is strongly affected by fluid viscosity.展开更多
With a clear understanding of the drilling fluid techniques and the cutting taking mechanism, a new advanced model is set up for analyzing field data and quantitative forecast of cutting taking mechanism. Therefore,...With a clear understanding of the drilling fluid techniques and the cutting taking mechanism, a new advanced model is set up for analyzing field data and quantitative forecast of cutting taking mechanism. Therefore, a number of values affecting the drilling rate and the hole cleaning are studied over a wide range of parameters. Drilling data obtained under high borehole pressure conditions are analyzed to determine the causes of the reduction in rate of penetration (ROP) as the borehole pressure increases, which in some cases is caused by the buildup of rock debris under the bit. The theoretical achievement and testing conclusions can be very instructional for horizontal well drilling. Much higher annular velocities are required for effective hole cleaning in directional wells than in vertical wells. High viscosity muds are observed to provide better transport than low viscosity muds.展开更多
Based on a quasi-adiabatic model, the parameters of the bubble interior for a moving single bubble sonoluminescence （m-SBSL） in water are calculated. By using a complete form of the hydrodynamic force, a unique circ...Based on a quasi-adiabatic model, the parameters of the bubble interior for a moving single bubble sonoluminescence （m-SBSL） in water are calculated. By using a complete form of the hydrodynamic force, a unique circular path for the m-SBSL in water is obtained. The effect of the ambient pressure variation on the bubble trajectory is also investigated. It is concluded that as the ambient pressure increases, the bubble moves along a circular path with a larger radius and all bubble parameters, such as gas pressure, interior temperature and light intensity, increase. A comparison is made between the parameters of the moving bubble in water and those in N-methylformamide. With fluid viscosity increasing, the circular path changes into an elliptic form and the light intensity increases.展开更多
A lift distribution based section design method has been proposed. Through Newton-Raphson iterations, the section geometry is efficiently designed to meet the requirements for total lift and lift distribution. The eff...A lift distribution based section design method has been proposed. Through Newton-Raphson iterations, the section geometry is efficiently designed to meet the requirements for total lift and lift distribution. The effect of fluid viscosity on total lift is taken into account by coupling Reynolds-averaged Navier-Stokes(RANS)simulation with the potential-flow based design procedure. The present method avoids the difficulty of assigning velocity or pressure distributions on section surfaces. As the loading and thickness distributions are expressed in parametric forms, it is easy to ensure that the designed geometry is continuous and smooth. The effects of lift and thickness distributions on cavitation bucket are numerically investigated. A shift of lift loading towards the aft part of section tends to decrease the margin of back cavitation, while the width of cavitation bucket can be kept almost unchanged. To have a wider cavitation bucket, one can increase the leading edge radius, move properly the location of maximum thickness towards the leading edge, or decrease the curvature at the location of maximum thickness.展开更多
Hyaluronic acid (HA) preparations have emerged as pivotal components in contemporary dentistry, gaining widespread recognition for their multifaceted roles in various biological functions. Extensive literature undersc...Hyaluronic acid (HA) preparations have emerged as pivotal components in contemporary dentistry, gaining widespread recognition for their multifaceted roles in various biological functions. Extensive literature underscores the significance of HA in maintaining tissue water balance, fostering cell proliferation, promoting rapid cell migration, influencing cell differentiation during organism development, and facilitating tissue regeneration. Notably, HA’s interactions with cell surface receptors contribute to the viscosity of synovial fluid, activate the immune system, and enhance cartilage elasticity. Beyond these established functions, HA has also been investigated for its potential involvement in determining and studying the hormetic effects of radon water, adding a novel dimension to its applications in dental research. A thorough exploration of existing studies reveals a nuanced understanding of how HA interventions impact the outcomes of dental procedures. The comprehensive scope of these investigations allows for a more accurate assessment of the potential effectiveness of specific interventions and provides valuable insights into post-procedural prognoses for individual patients. This synthesis of literature serves as the foundation for elucidating the intricate interplay between HA, radon exposure, and their relevance in modern dental practices.展开更多
Neglecting the consumption of the material, a steady incompressible flow of an exothermic reacting third-grade fluid with viscous heating in a circular cylindrical pipe is numerically studied for both cases of constan...Neglecting the consumption of the material, a steady incompressible flow of an exothermic reacting third-grade fluid with viscous heating in a circular cylindrical pipe is numerically studied for both cases of constant viscosity and Reynolds＇ viscosity model. The coupled ordinary differential equations governing the flow in cylindrical coordinates, are transformed into dimensionless forms using appropriate transformations, and then solved numerically. Solutions using Maple are presented in tabular form and given in terms of dimensionless central fluid velocity and temperature, skin friction and heat transfer rate for three parametric values in the Reynolds＇ case. The numerical results for the velocity and temperature fields are also presented through graphs. Bifurcations are discussed using shooting method. Comparisons are also made between the present results and those of previous work, and thus verify the validity of the provided numerical solutions. Important properties of thermal criticality are provided for variable viscosity parameter and reaction order. Further numerical results are presented in the form of tables and graphs for transition of physical parameters, while varying certain flow and fluid material parameters. Also, the flow behaviour of the reactive fluid of third-grade is compared with those of the Newtonian reactive fluid.展开更多
In this paper,we investigate the initial value problem for the two-dimensiona magneto-micropolar fluid equations with partial viscosity.We prove that global existence of smooth large solutions by the energy method.Fur...In this paper,we investigate the initial value problem for the two-dimensiona magneto-micropolar fluid equations with partial viscosity.We prove that global existence of smooth large solutions by the energy method.Furthermore,with aid of the Fourier splitting methods,optimal time-decay rates of global smooth large solutions are also established.展开更多
基金This work was supported by the National Natural Science Foundation of China(Grant No.82303812)。
文摘Cell behaviors are regulated by the physical cues in their microenvironment,where extracellular fluid(ECF)viscosity is an important yet relatively underexplored cue.Recent evidence indicates that ECF viscosity plays a critical role in regulating cellular processes with pathological relevance to various diseases,such as cardiovascular related diseases,inflammatory diseases,and cancer.
基金sponsored by the National Natural Science Foundation of China(Grant Nos.40830423and40904029)CNOOC Zhanjiang Research Project(Contract No.Z2008SLZJ-FN0158)the Scientific Research Foundation for the Returned Overseas Chinese Scholars,State Education Ministry
文摘Ultrasonic velocities of a set of saturated sandstone samples were measured at simulated in-situ pressures in the laboratory.The samples were obtained from the W formation of the WXS Depression and covered low to nearly high porosity and permeability ranges.The brine and four different density oils were used as pore fluids,which provided a good chance to investigate fluid viscosity-induced velocity dispersion.The analysis of experimental observations of velocity dispersion indicates that（1）the Biot model can explain most of the small discrepancy（about 2–3%）between ultrasonic measurements and zero frequency Gassmann predictions for high porosity and permeability samples saturated by all the fluids used in this experiment and is also valid for medium porosity and permeability samples saturated with low viscosity fluids（less than approximately 3 mP·S）and（2）the squirt flow mechanism dominates the low to medium porosity and permeability samples when fluid viscosity increases and produces large velocity dispersions as high as about 8%. The microfracture aspect ratios were also estimated for the reservoir sandstones and applied to calculate the characteristic frequency of the squirt flow model,above which the Gassmann’ s assumptions are violated and the measured high frequency velocities cannot be directly used for Gassmann’s fluid replacement at the exploration seismic frequency band for W formation sandstones.
文摘This paper examines a steady two-dimensional flow of incompressible fluid over a vertical stretching sheet. The fluid viscosity is assumed to vary as a linear function of temperature. A scaling group of transformations is applied to the governing equa- tions. The system remains invariant due to some relations among the transformation parameters. After finding three absolute invariants, a third-order ordinary differential equation corresponding to the momentum equation and two second-order ordinary differential equations corresponding to energy and diffusion equations are derived. The equations along with the boundary conditions are solved numerically. It is found that the decrease in the temperature-dependent fluid viscosity makes the velocity decrease with the increasing distance of the stretching sheet. At a particular point of the sheet, the fluid velocity decreases but the temperature increases with the decreasing viscosity. The impact of the thermophoresis particle deposition plays an important role in the concentration boundary layer. The obtained results are presented graphically and discussed.
基金support of Prince Sultan University in paying the article processing charges(APC)for this publication.
文摘Fractal time-dependent issues in fluid dynamics provide a distinct difficulty in numerical analysis due to their complex characteristics,necessitating specialized computing techniques for precise and economical solutions.This study presents an innovative computational approach to tackle these difficulties.The main focus is applying the Fractal Runge-Kutta Method to model the time-dependent magnetohydrodynamic(MHD)Newtonian fluid with rescaled viscosity flow on Riga plates.An efficient computational scheme is proposed for handling fractal time-dependent problems in flow phenomena.The scheme is comprised of three stages and constructed using three different time levels.The stability of the scheme is shown by employing the Fourier series analysis to solve scalar problems.The scheme’s convergence is guaranteed for a time fractal partial differential equations system.The scheme is applied to the dimensionless fractal heat and mass transfer model of incompressible,unsteady,laminar,Newtonian fluid with rescaled viscosity flow over the flat and oscillatory Riga plates under the effects of space-and temperature-dependent heat sources.The first-order back differences discretize the continuity equation.The results show that skin friction local Nusselt number declines by raising the coefficient of the temperature-dependent term of heat source and Eckert number.The numerical simulations provide valuable insights into fluid dynamics,explicitly highlighting the influence of the temperature-dependent coefficient of the heat source and the Eckert number on skin friction and local Nusselt number.
文摘In this paper, using Navier-Stokes equations and Reynolds time-averaged rules, the turbulent motional differential equations of variable density and variable viscosity Newtonian fluid have been presented, and the turbulent motional differential equations of variable density and variable viscosity Newtonian fluid in open channel have been further proposed. The concepts of the density turbulence stress and the viscosity turbulence stress have been firstly presented in the paper.
基金financially supported by the National Key R&D Program of China(Grant No.2017YFC0405402)
文摘This paper studies the viscid and inviscid fluid resonance in gaps of bottom mounted caissons onthe basis of the plane wave hypothesis and full wave model, The theoretical analysis and the numerical results demonstrate that the condition for the appearance of fluid resonance in narrow gaps is kh=（2n＋1）π （n=0, 1, 2, 3 ）, rather than kh=nn （n=0, 1, 2, 3, ...）; the transmission peaks in viscid fluid are related to the resonance peaks in the gaps. k and h stand for the wave number and the gap length. The combination of the plane wave hypothesis or the full wave model with the local viscosity model can accurately determine the heights and the locations of the resonance peaks. The upper bound for the appearance of fluid resonance in gaps is 2b/L〈l （2b, grating constant; L, wave length） and the lower bound is h/b〈~ l. The main reason for the phase shift of the resonance peaks is the inductive factors. The number of resonance peaks in the spectrum curve is dependent on the ratio of the gap length to the grating constant. The heights and the positions of the resonance peaks predicted by the present models agree well with the experimental data.
基金supported by the National 973 Program(Grant No.2007CB209608)National 863 Program(Grant No.2007AA06Z218)
文摘Based on analyzing the limit of Ziolkowski＇s bubble oscillation formulation,a new model with various physical factors is established to simulate air gun signatures fo marine seismic exploration.The practical effects of physical factors,such as heat transfe across the bubble wall,air gun port throttling,vertical rise of the bubble,fluid viscosity,and the existence of the air gun body were all taken into account in the new model.Compared with Ziolkowski＇s model,the signatures simulated by the new model,with small peak amplitude and rapid decay of bubble oscillation,are more consistent with actual signatures The experiment analysis indicates：（1）gun port throttling controls the peak amplitude of ai gun pulse;（2）since the hydrostatic pressure decreases when the bubble rises,the bubble oscillation period changes;（3）heat transfer and fluid viscosity are the main factors tha explain the bubble oscillation damping.
基金partially supported by the National Key Research&Development Plan of China(Grant No.2017YFC0804203)International Cooperation Project of Chinese Academy of Sciences(Grant No.115242KYSB20160024)the Open Fund of State Key Laboratory of Geomechanics and Geotechnical Engineering,Institute of Rock and Soil Mechanics,Chinese Academy of Sciences(Grant No.Z016003)
文摘In this context, recent developments in the coupled three-dimensional(3 D) hydro-mechanical(HM)simulation tool TOUGH-RBSN are presented. This tool is used to model hydraulic fracture in geological media, as observed in laboratory-scale tests. The TOUGH-RBSN simulator is based on the effective linking of two numerical methods: TOUGH2, a finite volume method for simulating mass transport within a permeable medium; and a lattice model based on the rigid-body-spring network(RBSN) concept. The method relies on a Voronoi-based discretization technique that can represent fracture development within a permeable rock matrix. The simulator provides two-way coupling of HM processes, including fluid pressure-induced fracture and fracture-assisted flow. We first present the basic capabilities of the modeling approach using two example applications, i.e. permeability evolution under compression deformation, and analyses of a static fracturing simulation. Thereafter, the model is used to simulate laboratory tests of hydraulic fracturing in granite. In most respects, the simulation results meet expectations with respect to permeability evolution and fracturing patterns. It can be seen that the evolution of injection pressure associated with the simulated fracture developments is strongly affected by fluid viscosity.
文摘With a clear understanding of the drilling fluid techniques and the cutting taking mechanism, a new advanced model is set up for analyzing field data and quantitative forecast of cutting taking mechanism. Therefore, a number of values affecting the drilling rate and the hole cleaning are studied over a wide range of parameters. Drilling data obtained under high borehole pressure conditions are analyzed to determine the causes of the reduction in rate of penetration (ROP) as the borehole pressure increases, which in some cases is caused by the buildup of rock debris under the bit. The theoretical achievement and testing conclusions can be very instructional for horizontal well drilling. Much higher annular velocities are required for effective hole cleaning in directional wells than in vertical wells. High viscosity muds are observed to provide better transport than low viscosity muds.
基金Project supported by the Research Deputy of Sharif University of technology,Iran
文摘Based on a quasi-adiabatic model, the parameters of the bubble interior for a moving single bubble sonoluminescence （m-SBSL） in water are calculated. By using a complete form of the hydrodynamic force, a unique circular path for the m-SBSL in water is obtained. The effect of the ambient pressure variation on the bubble trajectory is also investigated. It is concluded that as the ambient pressure increases, the bubble moves along a circular path with a larger radius and all bubble parameters, such as gas pressure, interior temperature and light intensity, increase. A comparison is made between the parameters of the moving bubble in water and those in N-methylformamide. With fluid viscosity increasing, the circular path changes into an elliptic form and the light intensity increases.
文摘A lift distribution based section design method has been proposed. Through Newton-Raphson iterations, the section geometry is efficiently designed to meet the requirements for total lift and lift distribution. The effect of fluid viscosity on total lift is taken into account by coupling Reynolds-averaged Navier-Stokes(RANS)simulation with the potential-flow based design procedure. The present method avoids the difficulty of assigning velocity or pressure distributions on section surfaces. As the loading and thickness distributions are expressed in parametric forms, it is easy to ensure that the designed geometry is continuous and smooth. The effects of lift and thickness distributions on cavitation bucket are numerically investigated. A shift of lift loading towards the aft part of section tends to decrease the margin of back cavitation, while the width of cavitation bucket can be kept almost unchanged. To have a wider cavitation bucket, one can increase the leading edge radius, move properly the location of maximum thickness towards the leading edge, or decrease the curvature at the location of maximum thickness.
文摘Hyaluronic acid (HA) preparations have emerged as pivotal components in contemporary dentistry, gaining widespread recognition for their multifaceted roles in various biological functions. Extensive literature underscores the significance of HA in maintaining tissue water balance, fostering cell proliferation, promoting rapid cell migration, influencing cell differentiation during organism development, and facilitating tissue regeneration. Notably, HA’s interactions with cell surface receptors contribute to the viscosity of synovial fluid, activate the immune system, and enhance cartilage elasticity. Beyond these established functions, HA has also been investigated for its potential involvement in determining and studying the hormetic effects of radon water, adding a novel dimension to its applications in dental research. A thorough exploration of existing studies reveals a nuanced understanding of how HA interventions impact the outcomes of dental procedures. The comprehensive scope of these investigations allows for a more accurate assessment of the potential effectiveness of specific interventions and provides valuable insights into post-procedural prognoses for individual patients. This synthesis of literature serves as the foundation for elucidating the intricate interplay between HA, radon exposure, and their relevance in modern dental practices.
基金supported by Pastor E. A. Adeboye endowed Professorial Chair and conducted at the Department of Mathematics, University of Lagos, Lagos, Nigeria while on leave from
文摘Neglecting the consumption of the material, a steady incompressible flow of an exothermic reacting third-grade fluid with viscous heating in a circular cylindrical pipe is numerically studied for both cases of constant viscosity and Reynolds＇ viscosity model. The coupled ordinary differential equations governing the flow in cylindrical coordinates, are transformed into dimensionless forms using appropriate transformations, and then solved numerically. Solutions using Maple are presented in tabular form and given in terms of dimensionless central fluid velocity and temperature, skin friction and heat transfer rate for three parametric values in the Reynolds＇ case. The numerical results for the velocity and temperature fields are also presented through graphs. Bifurcations are discussed using shooting method. Comparisons are also made between the present results and those of previous work, and thus verify the validity of the provided numerical solutions. Important properties of thermal criticality are provided for variable viscosity parameter and reaction order. Further numerical results are presented in the form of tables and graphs for transition of physical parameters, while varying certain flow and fluid material parameters. Also, the flow behaviour of the reactive fluid of third-grade is compared with those of the Newtonian reactive fluid.
基金supported in part by the NNSF of China(Grant No.11871212)the Basic Research Project of Key Scientific Research Project Plan of Universities in Henan Province(Grant No.20ZX002).
文摘In this paper,we investigate the initial value problem for the two-dimensiona magneto-micropolar fluid equations with partial viscosity.We prove that global existence of smooth large solutions by the energy method.Furthermore,with aid of the Fourier splitting methods,optimal time-decay rates of global smooth large solutions are also established.
