＂ Analysis is performed to study the slip effects on the peristaltic flow of non-Newtonian fluid in a curved channel with wall properties. The resulting nonlinear partial differential equations are transformed to a s...＂ Analysis is performed to study the slip effects on the peristaltic flow of non-Newtonian fluid in a curved channel with wall properties. The resulting nonlinear partial differential equations are transformed to a single ordinary differential equation in a stream function by using the assumptions of long wavelength and low Reynolds number. This differential equation is solved numerically by employing the built-in routine for solving nonlinear boundary value problems （BVPs） through the software Mathematica. In addition, the analytic solutions for small Deborah number are computed with a regular perturbation technique. It is noticed that the symmetry of bolus is destroyed in a curved channel. An intensification in the slip effect results in a larger magnitude of axial velocity. Further, the size and circulation of the trapped boluses increase with an increase in the slip parameter. Different from the case of planar channel, the axial velocity profiles are tilted towards the lower part of the channel. A comparative study between analytic and numerical solutions shows excellent agreement.展开更多
This article addresses the magnetohydrodynamics(MHD) flow of a third grade fluid over an exponentially stretching sheet. Analysis is carried out in the presence of first order chemical reaction. Both cases of construc...This article addresses the magnetohydrodynamics(MHD) flow of a third grade fluid over an exponentially stretching sheet. Analysis is carried out in the presence of first order chemical reaction. Both cases of constructive and destructive chemical reactions are reported. Convergent solutions of the resulting differential systems are presented in series forms. Characteristics of various sundry parameters on the velocity, concentration, skin friction and local Sherwood number are analyzed and discussed.展开更多
Two-dimensional boundary layer flow of an incompressible third grade nanofluid over a stretching surface is investigated.Influence of thermophoresis and Brownian motion is considered in the presence of Newtonian heati...Two-dimensional boundary layer flow of an incompressible third grade nanofluid over a stretching surface is investigated.Influence of thermophoresis and Brownian motion is considered in the presence of Newtonian heating and viscous dissipation.Governing nonlinear problems of velocity, temperature and nanoparticle concentration are solved via homotopic procedure.Convergence is examined graphically and numerically. Results of temperature and nanoparticle concentration are plotted and discussed for various values of material parameters, Prandtl number, Lewis number, Newtonian heating parameter, Eckert number and thermophoresis and Brownian motion parameters. Numerical computations are performed. The results show that the change in temperature and nanoparticle concentration distribution functions is similar when we use higher values of material parameters β1 andβ2. It is seen that the temperature and thermal boundary layer thickness are increasing functions of Newtonian heating parameter γ.An increase in thermophoresis and Brownian motion parameters tends to an enhancement in the temperature.展开更多
This work investigates the flow of a third grade fluid in a rotating frame of reference. The fluid is incompressible and magnetohydrodynamic （MHD）. The flow is bounded between two porous plates, the lower of which i...This work investigates the flow of a third grade fluid in a rotating frame of reference. The fluid is incompressible and magnetohydrodynamic （MHD）. The flow is bounded between two porous plates, the lower of which is shrinking linearly. Mathematical modelling of the considered flow leads to a nonlinear problem. The solution of this nonlinear problem is computed by the homotopy analysis method （HAM）. Graphs are presented to demonstrate the effect of several emerging parameters, which clearly describe the flow characteristics.展开更多
Here thermal dependence conductivity and nonlinear convection features in third-grade liquid flow bounded by moving surface having varying thickness are formulated. Stagnation point flow is considered. Revised Fourier...Here thermal dependence conductivity and nonlinear convection features in third-grade liquid flow bounded by moving surface having varying thickness are formulated. Stagnation point flow is considered. Revised FourierFick relations and double stratification phenomena are utilized for modeling energy and concentration expressions.Mathematical model of considered physical problem is achieved by implementing the idea of boundary layer theory. The acquired partial differential system is transformed into ordinary ones by employing relevant variables. The homotopic scheme yield convergent solutions of governing nonlinear expressions. Graphs are constructed for distinct values of physical constraints to elaborate the heat/mass transportation mechanisms.展开更多
The magnetohydrodynamic （MHD） flow of the third grade fluid between two permeable disks with heat transfer is investigated. The governing partial differential equa- tions are converted into the ordinary differential...The magnetohydrodynamic （MHD） flow of the third grade fluid between two permeable disks with heat transfer is investigated. The governing partial differential equa- tions are converted into the ordinary differential equations by suitable transformations. The transformed equations are solved by the homotopy analysis method （HAM）. The expressions for square residual errors are defined, and the optimal values of convergence- control parameters are selected. The dimensionless velocity and temperature fields are examined for various dimensionless parameters. The skin friction coefficient and the Nus- selt number are tabulated to analyze the effects of dimensionless parameters.展开更多
We consider the large time behavior of a non-autonomous third grade fluid sys- tem, which could be viewed as a perturbation of the classical Navier-Stokes system. Under proper assumptions, we firstly prove that the fa...We consider the large time behavior of a non-autonomous third grade fluid sys- tem, which could be viewed as a perturbation of the classical Navier-Stokes system. Under proper assumptions, we firstly prove that the family of processes generated by the problem ad- mits a uniform attractor in the natural phase space. Then we prove the upper-semicontinuity of the uniform attractor when the perturbation tends to zero.展开更多
The study aimed to reveal the effectiveness of the integration between some constructive learning strategies in teaching a unit of the English language course to collect translation skills, using grammar, and the acqu...The study aimed to reveal the effectiveness of the integration between some constructive learning strategies in teaching a unit of the English language course to collect translation skills, using grammar, and the acquisition of critical thinking skills for intermediate third grade students in Mecca. Also, it aimed to acknowledge the statistical differences between the modified averages for the study sample groups degrees in the dimensional collecting of grammar and translation skills at the knowledge of the grammar level and using it, and at the macro level for collecting translation and grammar skills after adjusting the old collecting, as well as the knowledge of the statistical differences between the modified averages for the study sample groups in the total telemetric for the critical thinking skills after adjusting the old collecting. To achieve the study objectives, the researcher used the semi-experimental method that had several experimental groups （four groups）, and applied it to a sample of intermediate third-grade students in the city of Makkah （99 students） in teaching the unit of the English language course, which is （Healthy Eating） in the second semester in 2011/2012. After using the appropriate statistical methods, the study came to a result that there are no statistically significant differences in the old implementation for the test of skills of academic achievement of grammar, translation, and critical thinking skills, and that there are statistically significant differences in the new implementation due to the four strategies. According to the results of the study, the researcher recommended a number of recommendations including： the necessity to focus on the constructive theory in teaching English language skills, the importance of expanding the use of the suggested integrative oriented and its development in the field of English language teaching, to hold an intensive training courses for teachers of the English language to train them on using the suggested integrative strategy, the emphasis on the importance of the curriculum activities which focus on the integration between the constructive learning strategies, the importance of expanding of scientific research in the field of integrative strategies, and the development of synthesis methods that combine two strategies or more.展开更多
A theoretical investigation concerning hematocrit and slip velocity influence on the flow of blood and heat transfer by taking into account the externally applied magnetic field has been carried out. The mathematical ...A theoretical investigation concerning hematocrit and slip velocity influence on the flow of blood and heat transfer by taking into account the externally applied magnetic field has been carried out. The mathematical models considered in this work treated blood as a non-Newtonian fluid obeying the third grade fluid model. A suitable geometry of the stenosis is taken into account. Galerkin weighted residual and Newton Raphson methods are used to solve the equations that govern the flow of blood and heat transfer. Analytical expression for the velocity profile, temperature profile, volume flow rate, wall shear stress and resistance to flow were obtained. Graphical representation of results shows that the flow velocity, volumetric flow rate and shear stress increase while resistance to flow and heat transfer rate decrease when the slip velocity increases. Also, flow velocity and volume flow rate decrease while shear stress, heat transfer rate, and resistance to flow increase when the hematocrit parameter increases. Finally, increases in magnetic field parameter lead to decrease in flow velocity, flow rate and shear stress but increase the flow resistance.展开更多
In this research, we modeled MHD third grade blood flow in a stenosed artery. The blood viscosity and the density have been modeled into the shear thinning/thickening parameters, the most important rheological propert...In this research, we modeled MHD third grade blood flow in a stenosed artery. The blood viscosity and the density have been modeled into the shear thinning/thickening parameters, the most important rheological properties of blood. We used regular perturbation method and obtained the flow characteristics such as the flow velocity, the volume flow rate, the shear stress and the resistance to the flow considering a single layered stenosed artery. The results however showed that there is significant increase in volume flow rate and the velocity with increase in the magnetic field intensity H and the shear thinning Λ and reduces with increase in the shear thickening Ω.展开更多
Characteristics of heat transfer and flow of Newtonian and non-Newtonian fluids through porous walls and in porous media are studied due to their wide range of applications including geothermal reservoirs,heat exchang...Characteristics of heat transfer and flow of Newtonian and non-Newtonian fluids through porous walls and in porous media are studied due to their wide range of applications including geothermal reservoirs,heat exchangers,marine propulsion,and aerodynamics.The current study investigates the characteristics of heat transport in a reactive third-grade fluid,moving through permeable parallel plates,with uniform suction/injection velocity.The two permeable,parallel plates are maintained at the same,constant temperature.After being transformed into its dimensionless equivalent,governing equations are solved by employing the Least Squares Method(LSM).The LSM results are further validated with numerical solutions for temperature and velocity.The impact of cross-flow Reynolds number,Peclet number,heat generation parameter,non-Newtonian parameter,and Brinkman number on entropy generation,velocity,temperature,and Bejan number are investigated.Theresults indicate that temperature distribution is significantly influenced by the third-grade fluid parameter.The maximum temperature drops from almost 0.12 to 0.10 as the third-grade fluid parameter increases from0.05 to 0.4.When the cross-flow Reynolds number is raised from 0.05 to 3,the maximum temperature drops from 0.12 to around 0.09.Temperature is strongly influenced by the heat generation parameter.A greater understanding of the thermal characteristics necessary for the design of a variety of systems,such as heat exchangers,marine propulsion,aerodynamic systems,etc.,may be gained from the findings of the current study.展开更多
This paper makes the thermodynamic analysis in forced convective flow of a third grade fluid through a vertical channel. Due to the reactive nature of the fluid, the effect of internal heat generation is considered an...This paper makes the thermodynamic analysis in forced convective flow of a third grade fluid through a vertical channel. Due to the reactive nature of the fluid, the effect of internal heat generation is considered and assumed to be a linear function of temperature. The coupled nonlinear dimensionless ordinary differential equations governing the fluid flow are solved by using the Adomian decomposition method（ADM）. The effects of various physical parameters such as third grade material parameter, buoyancy parameter and heat generation parameter on the thermal structure of flow are presented and discussed.展开更多
The aim of the present communication is to discuss the analytical solution for the unsteady flow of a third grade fluid which occupies the space y 〉 0 over an infinite porous plate. The flow is generated due to the m...The aim of the present communication is to discuss the analytical solution for the unsteady flow of a third grade fluid which occupies the space y 〉 0 over an infinite porous plate. The flow is generated due to the motion of the plate in its own plane with an impulsive velocity V（t）. Translational symmetries in variables t and y are utilized to reduce the governing non-linear partial differential equation into an ordinary differential equation. The reduced problem is then solved using homotopy analysis method（HAM）. Graphs representing the solution are plotted and discussed and proper conclusions are drawn.展开更多
The Cattaneo-Christov heat flux in the two-dimensional （2D） flow of a third- grade fluid towards an exponentially stretching sheet is investigated. The energy equation is considered through thermal relaxation. Simil...The Cattaneo-Christov heat flux in the two-dimensional （2D） flow of a third- grade fluid towards an exponentially stretching sheet is investigated. The energy equation is considered through thermal relaxation. Similarity transformations are accounted to obtain the ordinary differential systems. The converted non-dimensional equations are solved for the series solutions. The convergence analysis of the computed solutions is reported. The graphical results of the velocity and temperature profiles are plotted and elaborated in detail. The results show that the thermal relaxation enhances the temper- ature gradient while reduces the temperature profile.展开更多
In this paper, a non-Newtonian third-grade blood in coronary and femoral arteries is simulated analytically and numerically. The blood is considered as the third- grade non-Newtonian fluid under the periodic body acce...In this paper, a non-Newtonian third-grade blood in coronary and femoral arteries is simulated analytically and numerically. The blood is considered as the third- grade non-Newtonian fluid under the periodic body acceleration motion and the pulsatile pressure gradient. The hybrid multi-step differential transformation method （Hybrid-Ms- DTM） and the Crank-Nicholson method （CNM） are used to solve the partial differential equation （PDE）, and a good agreement between them is observed in the results. The effects of the some physical parameters such as the amplitude, the lead angle, and the body acceleration frequency on the velocity and shear stress profiles are considered. The results show that increasing the amplitude, Ag, and reducing the lead angle of body acceleration, 9, make higher velocity profiles on the center line of both arteries. Also, the maximum wall shear stress increases when Ag increases.展开更多
This study is devoted to the investigation of thermal criticality for a reactive gravity driven thin film flow of a third-grade fluid with adiabatic free surface down an inclined isothermal plane. It is assumed that t...This study is devoted to the investigation of thermal criticality for a reactive gravity driven thin film flow of a third-grade fluid with adiabatic free surface down an inclined isothermal plane. It is assumed that the reaction is exothermic under Arrhenius kinetics, neglecting the consumption of the material. The governing non-linear equations for conservation of momentum and energy are obtained and solved by using a new computational approach based on a special type of Hermite-Padé approximation technique implemented in MAPLE. This semi-numerical scheme offers some advantages over solutions obtained with traditional methods such as finite differences, spectral method, and shooting method. It reveals the analytical structure of the solution function. Important properties of overall flow structure including velocity field, temperature field, thermal criticality, and bifurcations are discussed.展开更多
The well-known problem of unidirectional plane flow of a fluid in a non-porous half-space due to the impulsive motion of the rigid plane wall it rests upon is discussed in the context of an unsteady MHD third-grade fl...The well-known problem of unidirectional plane flow of a fluid in a non-porous half-space due to the impulsive motion of the rigid plane wall it rests upon is discussed in the context of an unsteady MHD third-grade fluid in presence of Hall currents. The governing non-linear partial differential equations describing the problem are converted to a system of non-linear ordinary differential equations by using the similarity transformations. The complex analytical solution is found by using the homotopy analysis method (HAM). The existing literature on the topic shows that it is the first study regarding the effects of Hall current on flow of an unsteady MHD third-grade fluid over an impulsively moving plane wall. The convergence of the obtained complex series solutions is carefully analyzed. The effects of dimensionless parameters on the velocity are illustrated through plots and the effects of the pertinent parameters on the local skin friction coefficient at the surface of the wall are presented numerically in tabular form.展开更多
文摘＂ Analysis is performed to study the slip effects on the peristaltic flow of non-Newtonian fluid in a curved channel with wall properties. The resulting nonlinear partial differential equations are transformed to a single ordinary differential equation in a stream function by using the assumptions of long wavelength and low Reynolds number. This differential equation is solved numerically by employing the built-in routine for solving nonlinear boundary value problems （BVPs） through the software Mathematica. In addition, the analytic solutions for small Deborah number are computed with a regular perturbation technique. It is noticed that the symmetry of bolus is destroyed in a curved channel. An intensification in the slip effect results in a larger magnitude of axial velocity. Further, the size and circulation of the trapped boluses increase with an increase in the slip parameter. Different from the case of planar channel, the axial velocity profiles are tilted towards the lower part of the channel. A comparative study between analytic and numerical solutions shows excellent agreement.
文摘This article addresses the magnetohydrodynamics(MHD) flow of a third grade fluid over an exponentially stretching sheet. Analysis is carried out in the presence of first order chemical reaction. Both cases of constructive and destructive chemical reactions are reported. Convergent solutions of the resulting differential systems are presented in series forms. Characteristics of various sundry parameters on the velocity, concentration, skin friction and local Sherwood number are analyzed and discussed.
基金funded by the Deanship of Scientific Research (DSR), King Abdulaziz University (KAU), under Grant No. 37-130-35-HiCi
文摘Two-dimensional boundary layer flow of an incompressible third grade nanofluid over a stretching surface is investigated.Influence of thermophoresis and Brownian motion is considered in the presence of Newtonian heating and viscous dissipation.Governing nonlinear problems of velocity, temperature and nanoparticle concentration are solved via homotopic procedure.Convergence is examined graphically and numerically. Results of temperature and nanoparticle concentration are plotted and discussed for various values of material parameters, Prandtl number, Lewis number, Newtonian heating parameter, Eckert number and thermophoresis and Brownian motion parameters. Numerical computations are performed. The results show that the change in temperature and nanoparticle concentration distribution functions is similar when we use higher values of material parameters β1 andβ2. It is seen that the temperature and thermal boundary layer thickness are increasing functions of Newtonian heating parameter γ.An increase in thermophoresis and Brownian motion parameters tends to an enhancement in the temperature.
文摘This work investigates the flow of a third grade fluid in a rotating frame of reference. The fluid is incompressible and magnetohydrodynamic （MHD）. The flow is bounded between two porous plates, the lower of which is shrinking linearly. Mathematical modelling of the considered flow leads to a nonlinear problem. The solution of this nonlinear problem is computed by the homotopy analysis method （HAM）. Graphs are presented to demonstrate the effect of several emerging parameters, which clearly describe the flow characteristics.
文摘Here thermal dependence conductivity and nonlinear convection features in third-grade liquid flow bounded by moving surface having varying thickness are formulated. Stagnation point flow is considered. Revised FourierFick relations and double stratification phenomena are utilized for modeling energy and concentration expressions.Mathematical model of considered physical problem is achieved by implementing the idea of boundary layer theory. The acquired partial differential system is transformed into ordinary ones by employing relevant variables. The homotopic scheme yield convergent solutions of governing nonlinear expressions. Graphs are constructed for distinct values of physical constraints to elaborate the heat/mass transportation mechanisms.
文摘The magnetohydrodynamic （MHD） flow of the third grade fluid between two permeable disks with heat transfer is investigated. The governing partial differential equa- tions are converted into the ordinary differential equations by suitable transformations. The transformed equations are solved by the homotopy analysis method （HAM）. The expressions for square residual errors are defined, and the optimal values of convergence- control parameters are selected. The dimensionless velocity and temperature fields are examined for various dimensionless parameters. The skin friction coefficient and the Nus- selt number are tabulated to analyze the effects of dimensionless parameters.
基金Supported by NSFC(11301003,11426031,11501560)the Research Fund for Doctor Station of the Education Ministry of China(20123401120005)NSF of Anhui Province(1308085QA02)
文摘We consider the large time behavior of a non-autonomous third grade fluid sys- tem, which could be viewed as a perturbation of the classical Navier-Stokes system. Under proper assumptions, we firstly prove that the family of processes generated by the problem ad- mits a uniform attractor in the natural phase space. Then we prove the upper-semicontinuity of the uniform attractor when the perturbation tends to zero.
文摘The study aimed to reveal the effectiveness of the integration between some constructive learning strategies in teaching a unit of the English language course to collect translation skills, using grammar, and the acquisition of critical thinking skills for intermediate third grade students in Mecca. Also, it aimed to acknowledge the statistical differences between the modified averages for the study sample groups degrees in the dimensional collecting of grammar and translation skills at the knowledge of the grammar level and using it, and at the macro level for collecting translation and grammar skills after adjusting the old collecting, as well as the knowledge of the statistical differences between the modified averages for the study sample groups in the total telemetric for the critical thinking skills after adjusting the old collecting. To achieve the study objectives, the researcher used the semi-experimental method that had several experimental groups （four groups）, and applied it to a sample of intermediate third-grade students in the city of Makkah （99 students） in teaching the unit of the English language course, which is （Healthy Eating） in the second semester in 2011/2012. After using the appropriate statistical methods, the study came to a result that there are no statistically significant differences in the old implementation for the test of skills of academic achievement of grammar, translation, and critical thinking skills, and that there are statistically significant differences in the new implementation due to the four strategies. According to the results of the study, the researcher recommended a number of recommendations including： the necessity to focus on the constructive theory in teaching English language skills, the importance of expanding the use of the suggested integrative oriented and its development in the field of English language teaching, to hold an intensive training courses for teachers of the English language to train them on using the suggested integrative strategy, the emphasis on the importance of the curriculum activities which focus on the integration between the constructive learning strategies, the importance of expanding of scientific research in the field of integrative strategies, and the development of synthesis methods that combine two strategies or more.
文摘A theoretical investigation concerning hematocrit and slip velocity influence on the flow of blood and heat transfer by taking into account the externally applied magnetic field has been carried out. The mathematical models considered in this work treated blood as a non-Newtonian fluid obeying the third grade fluid model. A suitable geometry of the stenosis is taken into account. Galerkin weighted residual and Newton Raphson methods are used to solve the equations that govern the flow of blood and heat transfer. Analytical expression for the velocity profile, temperature profile, volume flow rate, wall shear stress and resistance to flow were obtained. Graphical representation of results shows that the flow velocity, volumetric flow rate and shear stress increase while resistance to flow and heat transfer rate decrease when the slip velocity increases. Also, flow velocity and volume flow rate decrease while shear stress, heat transfer rate, and resistance to flow increase when the hematocrit parameter increases. Finally, increases in magnetic field parameter lead to decrease in flow velocity, flow rate and shear stress but increase the flow resistance.
文摘In this research, we modeled MHD third grade blood flow in a stenosed artery. The blood viscosity and the density have been modeled into the shear thinning/thickening parameters, the most important rheological properties of blood. We used regular perturbation method and obtained the flow characteristics such as the flow velocity, the volume flow rate, the shear stress and the resistance to the flow considering a single layered stenosed artery. The results however showed that there is significant increase in volume flow rate and the velocity with increase in the magnetic field intensity H and the shear thinning Λ and reduces with increase in the shear thickening Ω.
文摘Characteristics of heat transfer and flow of Newtonian and non-Newtonian fluids through porous walls and in porous media are studied due to their wide range of applications including geothermal reservoirs,heat exchangers,marine propulsion,and aerodynamics.The current study investigates the characteristics of heat transport in a reactive third-grade fluid,moving through permeable parallel plates,with uniform suction/injection velocity.The two permeable,parallel plates are maintained at the same,constant temperature.After being transformed into its dimensionless equivalent,governing equations are solved by employing the Least Squares Method(LSM).The LSM results are further validated with numerical solutions for temperature and velocity.The impact of cross-flow Reynolds number,Peclet number,heat generation parameter,non-Newtonian parameter,and Brinkman number on entropy generation,velocity,temperature,and Bejan number are investigated.Theresults indicate that temperature distribution is significantly influenced by the third-grade fluid parameter.The maximum temperature drops from almost 0.12 to 0.10 as the third-grade fluid parameter increases from0.05 to 0.4.When the cross-flow Reynolds number is raised from 0.05 to 3,the maximum temperature drops from 0.12 to around 0.09.Temperature is strongly influenced by the heat generation parameter.A greater understanding of the thermal characteristics necessary for the design of a variety of systems,such as heat exchangers,marine propulsion,aerodynamic systems,etc.,may be gained from the findings of the current study.
文摘This paper makes the thermodynamic analysis in forced convective flow of a third grade fluid through a vertical channel. Due to the reactive nature of the fluid, the effect of internal heat generation is considered and assumed to be a linear function of temperature. The coupled nonlinear dimensionless ordinary differential equations governing the fluid flow are solved by using the Adomian decomposition method（ADM）. The effects of various physical parameters such as third grade material parameter, buoyancy parameter and heat generation parameter on the thermal structure of flow are presented and discussed.
基金supported by the National Research Foundation(NRF) of South Africa for research grant
文摘The aim of the present communication is to discuss the analytical solution for the unsteady flow of a third grade fluid which occupies the space y 〉 0 over an infinite porous plate. The flow is generated due to the motion of the plate in its own plane with an impulsive velocity V（t）. Translational symmetries in variables t and y are utilized to reduce the governing non-linear partial differential equation into an ordinary differential equation. The reduced problem is then solved using homotopy analysis method（HAM）. Graphs representing the solution are plotted and discussed and proper conclusions are drawn.
文摘The Cattaneo-Christov heat flux in the two-dimensional （2D） flow of a third- grade fluid towards an exponentially stretching sheet is investigated. The energy equation is considered through thermal relaxation. Similarity transformations are accounted to obtain the ordinary differential systems. The converted non-dimensional equations are solved for the series solutions. The convergence analysis of the computed solutions is reported. The graphical results of the velocity and temperature profiles are plotted and elaborated in detail. The results show that the thermal relaxation enhances the temper- ature gradient while reduces the temperature profile.
文摘In this paper, a non-Newtonian third-grade blood in coronary and femoral arteries is simulated analytically and numerically. The blood is considered as the third- grade non-Newtonian fluid under the periodic body acceleration motion and the pulsatile pressure gradient. The hybrid multi-step differential transformation method （Hybrid-Ms- DTM） and the Crank-Nicholson method （CNM） are used to solve the partial differential equation （PDE）, and a good agreement between them is observed in the results. The effects of the some physical parameters such as the amplitude, the lead angle, and the body acceleration frequency on the velocity and shear stress profiles are considered. The results show that increasing the amplitude, Ag, and reducing the lead angle of body acceleration, 9, make higher velocity profiles on the center line of both arteries. Also, the maximum wall shear stress increases when Ag increases.
基金supported by the National Research Foundation of South Africa Thuthuka Programme
文摘This study is devoted to the investigation of thermal criticality for a reactive gravity driven thin film flow of a third-grade fluid with adiabatic free surface down an inclined isothermal plane. It is assumed that the reaction is exothermic under Arrhenius kinetics, neglecting the consumption of the material. The governing non-linear equations for conservation of momentum and energy are obtained and solved by using a new computational approach based on a special type of Hermite-Padé approximation technique implemented in MAPLE. This semi-numerical scheme offers some advantages over solutions obtained with traditional methods such as finite differences, spectral method, and shooting method. It reveals the analytical structure of the solution function. Important properties of overall flow structure including velocity field, temperature field, thermal criticality, and bifurcations are discussed.
文摘The well-known problem of unidirectional plane flow of a fluid in a non-porous half-space due to the impulsive motion of the rigid plane wall it rests upon is discussed in the context of an unsteady MHD third-grade fluid in presence of Hall currents. The governing non-linear partial differential equations describing the problem are converted to a system of non-linear ordinary differential equations by using the similarity transformations. The complex analytical solution is found by using the homotopy analysis method (HAM). The existing literature on the topic shows that it is the first study regarding the effects of Hall current on flow of an unsteady MHD third-grade fluid over an impulsively moving plane wall. The convergence of the obtained complex series solutions is carefully analyzed. The effects of dimensionless parameters on the velocity are illustrated through plots and the effects of the pertinent parameters on the local skin friction coefficient at the surface of the wall are presented numerically in tabular form.
