Based on the AfKdV equation of Xu et al.([1]), a theory on the velocities of the precursor soliton generation in two-layer flow over topography is presented in the present paper. Moving velocities of precursor soliton...Based on the AfKdV equation of Xu et al.([1]), a theory on the velocities of the precursor soliton generation in two-layer flow over topography is presented in the present paper. Moving velocities of precursor solitons, of the first zero-crossing of the tailing wavetrain and of the flow behind the topography are found theoretically. It is shown that for a given topography, when its moving velocities are at the resonant points, we have the following rules: the ratio of the moving velocity of the precursor solitons to that of the first zero-crossing of the tailing wavetrain equals -4/3. At the same time, the ratio of the width of generating region of the precursor solitons to that of the depressed water region equals also -4/3. The theoretical results are examined by means of numerical calculation. The comparison between the theoretical and numerical results are found in good agreement. For different stratified parameters of two-layer how, the velocities of the precursor soliton generation are also predicted in terms of the present theoretical results.展开更多
The steady laminar mixed convection boundary layer flow and heat transfer of a micropolar fluid near the stagnation point on a stretched vertical surface with prescribed skin friction were considered.The governing par...The steady laminar mixed convection boundary layer flow and heat transfer of a micropolar fluid near the stagnation point on a stretched vertical surface with prescribed skin friction were considered.The governing partial differential equations were transformed into a system of ordinary differential equations,which were then solved numerically using the shooting method.Results for the stretching velocity,the local Nusselt number,the temperature,and the velocity profiles are presented for various values of the mixed convection parameter λ and material parameter K when the Prandtl number is equal to 1.Both assisting（heated plate） and opposing（cooled plate） flow regions are considered.It is found that dual solutions exist for both assisting and opposing flows.展开更多
An analysis is carried out for dual solutions of the boundary layer flow of Maxwell fluid over a permeable shrinking sheet. In the investigation, a constant wall mass transfer is considered. With the help of similarit...An analysis is carried out for dual solutions of the boundary layer flow of Maxwell fluid over a permeable shrinking sheet. In the investigation, a constant wall mass transfer is considered. With the help of similarity transformations, the governing partial differential equations（PDEs） are converted into a nonlinear self-similar ordinary differential equation（ODE）. For the numerical solution of transformed self-similar ODE, the shooting method is applied. The study reveals that the steady flow of Maxwell fluid is possible with a smaller amount of imposed mass suction compared with the viscous fluid flow. Dual solutions for the velocity distribution are obtained. Also, the increase of Deborah number reduces the boundary layer thickness for both solutions.展开更多
The linear instabilities of incompressible confluent mixing layer and boundary layer were analyzed.The mixing layers include wake,shear layer and their combination.The mean velocity profile of confluent flow is taken ...The linear instabilities of incompressible confluent mixing layer and boundary layer were analyzed.The mixing layers include wake,shear layer and their combination.The mean velocity profile of confluent flow is taken as a superposition of a hyperbolic and exponential function to model a mixing layer and the Blasius similarity solution for a flat plate boundary layer.The stability equation of confluent flow was solved by using the global numerical method.The unstable modes associated with both the mixing and boundary layers were identified.They are the boundary layer mode,mixing layer mode 1（nearly symmetrical mode）and mode 2（nearly anti-symmetrical mode）.The interactions between the mixing layer stability and the boundary layer stability were examined.As the mixing layer approaches the boundary layer,the neutral curves of the boundary layer mode move to the upper left,the resulting critical Reynolds number decreases,and the growth rate of the most unstable mode increases.The wall tends to stabilize the mixing layer modes at low frequency.In addition,the mode switching behavior of the relative level of the spatial growth rate between the mixing layer mode 1 and mode 2 with the velocity ratio is found to occur at low frequency.展开更多
This paper studies the thermal-diffusion and diffusion thermo-effects in the hydro-magnetic unsteady flow by a mixed convection boundary layer past an imperme- able vertical stretching sheet in a porous medium in the ...This paper studies the thermal-diffusion and diffusion thermo-effects in the hydro-magnetic unsteady flow by a mixed convection boundary layer past an imperme- able vertical stretching sheet in a porous medium in the presence of chemical reaction. The velocity of t^he stretching surface, the surface temperature, and the concentration are assumed to vary linearly with the distance along the surface. The governing partial differential equations are transformed into self-similar unsteady equations using similarity transformations .and solved numerically by the Runge-Kutta fourth order scheme in as- sociation with the shooting method for the whole transient domain from the initial state to the final steady state flow. Numerical results for the velocity, the temperature, the concentration, the skin friction, and the Nusselt and Sherwood numbers are shown graph- ically for various flow parameters. The results reveal that there is a smooth transition of flow from unsteady state to the final steady state. A special case of our results is in good agreement with an earlier published work.展开更多
The effect of the solid matrix and porosity of the porous medium are first introduced to the study of power-law nanofluids, and the Marangoni boundary layer flow with heat generation is investigated. Two cases of soli...The effect of the solid matrix and porosity of the porous medium are first introduced to the study of power-law nanofluids, and the Marangoni boundary layer flow with heat generation is investigated. Two cases of solid matrix of porous medium including glass balls and aluminum foam are considered. The governing partial differential equations are simplified by dimensionless variables and similarity transformations, and are solved numerically by using a shooting method with the fourth-fifth-order Runge-Kutta integration technique. It is indicated that the increase of the porosity leads to the enhancement of heat transfer in the surface of the Marangoni boundary layer flow.展开更多
As a basic problem in many engineering applications, transition from laminar to turbulence still remains a difficult problem in computational fluid dynamics （CFD）. A numerical study of one transitional flow in two-d...As a basic problem in many engineering applications, transition from laminar to turbulence still remains a difficult problem in computational fluid dynamics （CFD）. A numerical study of one transitional flow in two-dimensional is conducted by Reynolds averaged numerical simulation （RANS） in this paper. Turbulence model plays a significant role in the complex flows＇ simulation, and four advanced turbulence models are evaluated. Numerical solution of frictional resistance coefficient is compared with the measured one in the transitional zone, which indicates that Wilcox （2006） k-ω model with correction is the best candidate. Comparisons of numerical and analytical solutions for dimensionless velocity show that averaged streamwise dimensionless velocity profiles correct the shape rapidly in transitional region. Furthermore, turbulence quantities such as turbulence kinetic energy, eddy viscosity, and Reynolds stress are also studied, which are helpful to learn the transition＇s behavior.展开更多
A theory of tailing wavetrain generation for the precursor soliton generation in two-layer flow is presented by using averaged KdV equations (AKdV), which are derived by the authors in terms of Whitham's method of...A theory of tailing wavetrain generation for the precursor soliton generation in two-layer flow is presented by using averaged KdV equations (AKdV), which are derived by the authors in terms of Whitham's method of averaging([1,2]). From the AKdV equations, group velocities of the tailing wavetrain generation are obtained by means of generating conditions of the tailing wavetrains, furthermore an analytical solution of the tailing wavetrain generation is found theoretically. A comparison between the theoretical and numerical results is carried out in the present paper, which shows that the theoretical results are in good agreement with the numerical ones, obtained from the fKdV equation in two-layer flow with the depth of unity in the rest.展开更多
Hydraulic falls of single-layer now are determined theoretically in terms of a time-dependent averaged fKdV equation(AfKdV equation)in phase coordinate. From the theory of the present paper it was known that differenc...Hydraulic falls of single-layer now are determined theoretically in terms of a time-dependent averaged fKdV equation(AfKdV equation)in phase coordinate. From the theory of the present paper it was known that difference of the asymptotic mean levels upstream and downsream at the subcritical cutoff points is just equal to a subcritical value of the AfKdV equation An experiment is carried out to examine the theoretical results. From comparison between theoreticaland experimental results, it was shown that they are in good agreement.At the same time, it should be pointed out that the theory of the present paper is agreement with the experimental and numerical results of Forbes and can be employed to find the generating properties of the precursor solitons at near-resonance.展开更多
Hydraulic falls and asymptotic mean levels of two-layer flow are determined by means of AfKdV equation in phase coordinate theoretically. By present theory, the hydraulic falls Hf depend on a characteristic value of t...Hydraulic falls and asymptotic mean levels of two-layer flow are determined by means of AfKdV equation in phase coordinate theoretically. By present theory, the hydraulic falls Hf depend on a characteristic value of the MfKdV equation at the subcritical cutoff points It is proved that the differences of the asymptotic mean levels upstream and downstream at the subcritical cutoff points are equal to 2 A relation between and the asymptotic mean levels at the subcritical cutoff points is also found in terms of the solution of the hydraulic falls. Because the AfKdV equation is derived based on the small topography assumption, for semicircular topography the valid region of this theory is α< 0. 35, in which α is radius of the semicircular topography. An experiment is carried out to examine the theory of the present paper. From comparisons between the theoretical and experimental results. it is shown that they are in better agreement. Under conditions of different stratified parameters, the hydraulic falls of two-layer flow are predicted theoretically. This work was supered by the Foundation of the State Education COmmission 'The dynamics of upper ocean'.展开更多
Unsteady mixed convective boundary layer flow of viscous incompressible fluid along isothermal horizontal plate is analyzed through Similarity Solutions. The governing partial differential equations are transformed in...Unsteady mixed convective boundary layer flow of viscous incompressible fluid along isothermal horizontal plate is analyzed through Similarity Solutions. The governing partial differential equations are transformed into ordinary differential equations using the similarity transformation and solved numerically along with shooting technique. The flow field for the fluid velocity, temperature and concentration at the plate surface are significantly influenced by the governing parameters such as unsteadiness parameter, permeability parameter, Prandtl number, Schmidt number and the other driving parameters. The results show that both fluid velocity and temperature decrease but no significant effect on concentration for the increasing values of Prandtl number. It is also exposed that velocity and concentration is higher at lower Schmidt number for low Prandtl fluid. Finally, the dependency of the Skin-friction co-efficient, Nusselt number and Sherwood number, which are of physical interest, are also illustrated in tabular form for the governing parameters.展开更多
In this study, the moving velocitiy of precursor solitons, of the flow in depressed region, and of the zero-crossing of the trailing wavetrain relative to the moving disturbance for single-layer flow over topography w...In this study, the moving velocitiy of precursor solitons, of the flow in depressed region, and of the zero-crossing of the trailing wavetrain relative to the moving disturbance for single-layer flow over topography were theorecticaly determined in terms of the mass and energy conservation theorems, and were examined with numerical calculations showing good agreement with theoretical results.展开更多
This article studies the nonlinear evolution of disturbance waves in supersonic nonparallel boundary layer flows by using nonlinear parabolic stability equations （NPSE）. An accurate numerical method is developed to ...This article studies the nonlinear evolution of disturbance waves in supersonic nonparallel boundary layer flows by using nonlinear parabolic stability equations （NPSE）. An accurate numerical method is developed to solve the equations and march the NPSE in a stable manner. Through computation,are obtained the curves of amplitude and disturbance shape function of harmonic waves. Especially are demonstrated the physical characteristics of nonlinear stability of various harmonic waves,including instantaneous stream wise vortices,spanwise vortices and Λ structure etc,and are used to study and analyze the mechanism of the transition process. The calculated results have evidenced the effectiveness of the proposed NPSE method to research the nonlinear stability of the supersonic boundary layers.展开更多
The steady two-dimensional laminar boundary layer flow and heat transfer of a viscous incompressible electrically conducting fluid over an exponentially stretching surface in the presence of a uniform magnetic field w...The steady two-dimensional laminar boundary layer flow and heat transfer of a viscous incompressible electrically conducting fluid over an exponentially stretching surface in the presence of a uniform magnetic field with thermal radiation are investigated. The governing boundary layer equations are transformed to ordinary differential equations by taking suitable similarity transformation and solved numerically by shooting method. The effects of various parameters such as magnetic parameter, radiation parameter, Prandtl number and Eckert number on local skin-friction coefficient, local Nusselt number, velocity and temperature distributions are computed and represented graphically.展开更多
An unsteady boundary layer flow of viscous incompressible fluid over a stretching plate has been considered to solve heat flow problem with variable thermal conductivity. First, using similarity transformation, the ve...An unsteady boundary layer flow of viscous incompressible fluid over a stretching plate has been considered to solve heat flow problem with variable thermal conductivity. First, using similarity transformation, the velocity components have been obtained, and then the heat flow problem has been attempted in the following two ways: 1) prescribed stretching surface temperature (PST), and 2) prescribed stretching surface heat flux (PHF) Flow and temperature fields have been analyzed through graphs. The expressions for skin friction and coefficient of convective heat transfer Nusselt number in PST and PHF cases have been derived.展开更多
The problem of boundary layer flows at a flat plate surface with velocity-slip and temperature-jump boundary conditions is analyzed. With the velocity slip conditions, there are multiple physical factors lumped togeth...The problem of boundary layer flows at a flat plate surface with velocity-slip and temperature-jump boundary conditions is analyzed. With the velocity slip conditions, there are multiple physical factors lumped together, and the boundary layer solutions significantly change their behaviors. The self-similarity in the solutions degenerates, however, the problem is still an ordinary differential equation which can be solved. Shooting methods are applied to solve the flowfield. The results include velocity and temperature for both the surface and flowfield. Unlike the traditional Blasius fiat plate boundary layer solutions which are self-similar through all the plate boundary layer, the new solutions indicate that the front tip is actually a singularity point, especially at locations within one mean flee path from the leading edge.展开更多
This paper presents the study of convective heat transfer characteristics of an incompressible dusty fluid past a vertical stretching sheet. The governing partial differential equations are reduced to nonlinear ordina...This paper presents the study of convective heat transfer characteristics of an incompressible dusty fluid past a vertical stretching sheet. The governing partial differential equations are reduced to nonlinear ordinary differential equations by using similarity transformation. The transformed equations are solved numerically by applying Runge Kutta Fehlberg fourth-fifth order method (RKF45 Method). Here obtained non-dimensional velocity and temperature profiles has been carried out to study the effect of different physical parameters such as fluid-particle interaction parameter, Grashof number, Prandtl number, Eckert number. Comparison of the obtained numerical results is made with previously published results.展开更多
In the present article a numerical analysis has been carried out to study the boundary layer flow behavior and heat transfer characteristics of a nanofluid over an exponential stretching sheet. By assuming the stretch...In the present article a numerical analysis has been carried out to study the boundary layer flow behavior and heat transfer characteristics of a nanofluid over an exponential stretching sheet. By assuming the stretching sheet to be impermeable, the effect of chemical reaction, thermal radiation, thermopherosis, Brownian motion and suction parameters in the presence of uniform magnetic field on heat and mass transfer are addressed. The governing system of equations is transformed into coupled nonlinear ordinary differential equations using suitable similarity transformations. The transformed equations are then solved numerically using the well known Runge-Kutta-Fehlberg method of fourth-fifth order. A detailed parametric study is performed to access the influence of the physical parameters on longitudinal velocity, temperature and nanoparticle volume fraction profiles as well as the local skin-friction coefficient, local Nusselt number and the local Sherwood number and the results are presented in both graphical and tabular forms.展开更多
In the present paper, the boundary layer flow of Walters Liquid B Model over a stretching plate has been considered to solve heat flow problem with variable conductivity. First, using similarity transformation, the ve...In the present paper, the boundary layer flow of Walters Liquid B Model over a stretching plate has been considered to solve heat flow problem with variable conductivity. First, using similarity transformation, the velocity components of velocity have been obtained. Then, the heat flow problem has been considered in two ways: 1) prescribed surface temperature (PST), and 2) prescribed stretching plate heat flux (PHF) in case of variable conductivity. Due to variable conductivity, temperature profile has its two part- one mean tempera-ture and other temperature profile induced due to variable conductivity. The related results have been dis-cussed with the help of graphs.展开更多
In this article, electromagnetic control of turbulent boundary layer on a ship hull is numerically investigated. This study is conducted on the geometry of tanker model hull. For this purpose, a combination of electri...In this article, electromagnetic control of turbulent boundary layer on a ship hull is numerically investigated. This study is conducted on the geometry of tanker model hull. For this purpose, a combination of electric and magnetic fields is applied to a region of boundary layer on stern so that produce wall parallel Lorentz forces in streamwise direction as body forces in stern flow. The governing equations including RANS equations with SST k-ω?turbulent model coupled with electric potential equation are numerically solved by using Ansys Fluent codes. Accuracy of this turbulent model of Fluent in predicting Turbulent flow around a ship is also tested by comparing with available experimental results that it shows a good agreement with experimental data. The results obtained for ship flow show that by applying streamwise Lorentz forces that are large enough, flow is accelerated. The results are caused to delay or avoid the flow separation in stern, increase the propeller inlet velocity, create uniform flow distribution behind the ship’s hull in order to improve the propeller performance, and finally decrease the pressure resistance and total resistance.展开更多
基金The project supported by the National Natural Science Foundation of China under the Grant No.49776284
文摘Based on the AfKdV equation of Xu et al.([1]), a theory on the velocities of the precursor soliton generation in two-layer flow over topography is presented in the present paper. Moving velocities of precursor solitons, of the first zero-crossing of the tailing wavetrain and of the flow behind the topography are found theoretically. It is shown that for a given topography, when its moving velocities are at the resonant points, we have the following rules: the ratio of the moving velocity of the precursor solitons to that of the first zero-crossing of the tailing wavetrain equals -4/3. At the same time, the ratio of the width of generating region of the precursor solitons to that of the depressed water region equals also -4/3. The theoretical results are examined by means of numerical calculation. The comparison between the theoretical and numerical results are found in good agreement. For different stratified parameters of two-layer how, the velocities of the precursor soliton generation are also predicted in terms of the present theoretical results.
基金the financial supports received in the form of fundamental research grant scheme (FRGS)the financial supports received in the form of research university grant (GUP)
文摘The steady laminar mixed convection boundary layer flow and heat transfer of a micropolar fluid near the stagnation point on a stretched vertical surface with prescribed skin friction were considered.The governing partial differential equations were transformed into a system of ordinary differential equations,which were then solved numerically using the shooting method.Results for the stretching velocity,the local Nusselt number,the temperature,and the velocity profiles are presented for various values of the mixed convection parameter λ and material parameter K when the Prandtl number is equal to 1.Both assisting（heated plate） and opposing（cooled plate） flow regions are considered.It is found that dual solutions exist for both assisting and opposing flows.
基金the financial support of National Board for Higher Mathematics(NBHM),DAE,Mumbai,Indiapartially supported by Deanship of Scientific Research(DSR),King Abdulaziz University,Jeddah,Saudi Arabia
文摘An analysis is carried out for dual solutions of the boundary layer flow of Maxwell fluid over a permeable shrinking sheet. In the investigation, a constant wall mass transfer is considered. With the help of similarity transformations, the governing partial differential equations（PDEs） are converted into a nonlinear self-similar ordinary differential equation（ODE）. For the numerical solution of transformed self-similar ODE, the shooting method is applied. The study reveals that the steady flow of Maxwell fluid is possible with a smaller amount of imposed mass suction compared with the viscous fluid flow. Dual solutions for the velocity distribution are obtained. Also, the increase of Deborah number reduces the boundary layer thickness for both solutions.
基金supported by the National Natural Science Foundation of China (No. 51476152)
文摘The linear instabilities of incompressible confluent mixing layer and boundary layer were analyzed.The mixing layers include wake,shear layer and their combination.The mean velocity profile of confluent flow is taken as a superposition of a hyperbolic and exponential function to model a mixing layer and the Blasius similarity solution for a flat plate boundary layer.The stability equation of confluent flow was solved by using the global numerical method.The unstable modes associated with both the mixing and boundary layers were identified.They are the boundary layer mode,mixing layer mode 1（nearly symmetrical mode）and mode 2（nearly anti-symmetrical mode）.The interactions between the mixing layer stability and the boundary layer stability were examined.As the mixing layer approaches the boundary layer,the neutral curves of the boundary layer mode move to the upper left,the resulting critical Reynolds number decreases,and the growth rate of the most unstable mode increases.The wall tends to stabilize the mixing layer modes at low frequency.In addition,the mode switching behavior of the relative level of the spatial growth rate between the mixing layer mode 1 and mode 2 with the velocity ratio is found to occur at low frequency.
文摘This paper studies the thermal-diffusion and diffusion thermo-effects in the hydro-magnetic unsteady flow by a mixed convection boundary layer past an imperme- able vertical stretching sheet in a porous medium in the presence of chemical reaction. The velocity of t^he stretching surface, the surface temperature, and the concentration are assumed to vary linearly with the distance along the surface. The governing partial differential equations are transformed into self-similar unsteady equations using similarity transformations .and solved numerically by the Runge-Kutta fourth order scheme in as- sociation with the shooting method for the whole transient domain from the initial state to the final steady state flow. Numerical results for the velocity, the temperature, the concentration, the skin friction, and the Nusselt and Sherwood numbers are shown graph- ically for various flow parameters. The results reveal that there is a smooth transition of flow from unsteady state to the final steady state. A special case of our results is in good agreement with an earlier published work.
基金Supported by the National Natural Science Foundation of China under Grant No 51305080
文摘The effect of the solid matrix and porosity of the porous medium are first introduced to the study of power-law nanofluids, and the Marangoni boundary layer flow with heat generation is investigated. Two cases of solid matrix of porous medium including glass balls and aluminum foam are considered. The governing partial differential equations are simplified by dimensionless variables and similarity transformations, and are solved numerically by using a shooting method with the fourth-fifth-order Runge-Kutta integration technique. It is indicated that the increase of the porosity leads to the enhancement of heat transfer in the surface of the Marangoni boundary layer flow.
基金Foundation item： Supported by the National Natural Science Foundation of China （Nos. 51309040, 51379025）, and the Fundamental Research Funds for the Central Universities （Nos. 3132014224, 3132014318）.
文摘As a basic problem in many engineering applications, transition from laminar to turbulence still remains a difficult problem in computational fluid dynamics （CFD）. A numerical study of one transitional flow in two-dimensional is conducted by Reynolds averaged numerical simulation （RANS） in this paper. Turbulence model plays a significant role in the complex flows＇ simulation, and four advanced turbulence models are evaluated. Numerical solution of frictional resistance coefficient is compared with the measured one in the transitional zone, which indicates that Wilcox （2006） k-ω model with correction is the best candidate. Comparisons of numerical and analytical solutions for dimensionless velocity show that averaged streamwise dimensionless velocity profiles correct the shape rapidly in transitional region. Furthermore, turbulence quantities such as turbulence kinetic energy, eddy viscosity, and Reynolds stress are also studied, which are helpful to learn the transition＇s behavior.
基金The project is supported by the National Natural Science Foundation of China(No.49776284)
文摘A theory of tailing wavetrain generation for the precursor soliton generation in two-layer flow is presented by using averaged KdV equations (AKdV), which are derived by the authors in terms of Whitham's method of averaging([1,2]). From the AKdV equations, group velocities of the tailing wavetrain generation are obtained by means of generating conditions of the tailing wavetrains, furthermore an analytical solution of the tailing wavetrain generation is found theoretically. A comparison between the theoretical and numerical results is carried out in the present paper, which shows that the theoretical results are in good agreement with the numerical ones, obtained from the fKdV equation in two-layer flow with the depth of unity in the rest.
文摘Hydraulic falls of single-layer now are determined theoretically in terms of a time-dependent averaged fKdV equation(AfKdV equation)in phase coordinate. From the theory of the present paper it was known that difference of the asymptotic mean levels upstream and downsream at the subcritical cutoff points is just equal to a subcritical value of the AfKdV equation An experiment is carried out to examine the theoretical results. From comparison between theoreticaland experimental results, it was shown that they are in good agreement.At the same time, it should be pointed out that the theory of the present paper is agreement with the experimental and numerical results of Forbes and can be employed to find the generating properties of the precursor solitons at near-resonance.
文摘Hydraulic falls and asymptotic mean levels of two-layer flow are determined by means of AfKdV equation in phase coordinate theoretically. By present theory, the hydraulic falls Hf depend on a characteristic value of the MfKdV equation at the subcritical cutoff points It is proved that the differences of the asymptotic mean levels upstream and downstream at the subcritical cutoff points are equal to 2 A relation between and the asymptotic mean levels at the subcritical cutoff points is also found in terms of the solution of the hydraulic falls. Because the AfKdV equation is derived based on the small topography assumption, for semicircular topography the valid region of this theory is α< 0. 35, in which α is radius of the semicircular topography. An experiment is carried out to examine the theory of the present paper. From comparisons between the theoretical and experimental results. it is shown that they are in better agreement. Under conditions of different stratified parameters, the hydraulic falls of two-layer flow are predicted theoretically. This work was supered by the Foundation of the State Education COmmission 'The dynamics of upper ocean'.
文摘Unsteady mixed convective boundary layer flow of viscous incompressible fluid along isothermal horizontal plate is analyzed through Similarity Solutions. The governing partial differential equations are transformed into ordinary differential equations using the similarity transformation and solved numerically along with shooting technique. The flow field for the fluid velocity, temperature and concentration at the plate surface are significantly influenced by the governing parameters such as unsteadiness parameter, permeability parameter, Prandtl number, Schmidt number and the other driving parameters. The results show that both fluid velocity and temperature decrease but no significant effect on concentration for the increasing values of Prandtl number. It is also exposed that velocity and concentration is higher at lower Schmidt number for low Prandtl fluid. Finally, the dependency of the Skin-friction co-efficient, Nusselt number and Sherwood number, which are of physical interest, are also illustrated in tabular form for the governing parameters.
文摘In this study, the moving velocitiy of precursor solitons, of the flow in depressed region, and of the zero-crossing of the trailing wavetrain relative to the moving disturbance for single-layer flow over topography were theorecticaly determined in terms of the mass and energy conservation theorems, and were examined with numerical calculations showing good agreement with theoretical results.
基金National Natural Science Foundation of China (10772082)Doctoral Foundation of Ministry of Education of China (20070287005)
文摘This article studies the nonlinear evolution of disturbance waves in supersonic nonparallel boundary layer flows by using nonlinear parabolic stability equations （NPSE）. An accurate numerical method is developed to solve the equations and march the NPSE in a stable manner. Through computation,are obtained the curves of amplitude and disturbance shape function of harmonic waves. Especially are demonstrated the physical characteristics of nonlinear stability of various harmonic waves,including instantaneous stream wise vortices,spanwise vortices and Λ structure etc,and are used to study and analyze the mechanism of the transition process. The calculated results have evidenced the effectiveness of the proposed NPSE method to research the nonlinear stability of the supersonic boundary layers.
文摘The steady two-dimensional laminar boundary layer flow and heat transfer of a viscous incompressible electrically conducting fluid over an exponentially stretching surface in the presence of a uniform magnetic field with thermal radiation are investigated. The governing boundary layer equations are transformed to ordinary differential equations by taking suitable similarity transformation and solved numerically by shooting method. The effects of various parameters such as magnetic parameter, radiation parameter, Prandtl number and Eckert number on local skin-friction coefficient, local Nusselt number, velocity and temperature distributions are computed and represented graphically.
文摘An unsteady boundary layer flow of viscous incompressible fluid over a stretching plate has been considered to solve heat flow problem with variable thermal conductivity. First, using similarity transformation, the velocity components have been obtained, and then the heat flow problem has been attempted in the following two ways: 1) prescribed stretching surface temperature (PST), and 2) prescribed stretching surface heat flux (PHF) Flow and temperature fields have been analyzed through graphs. The expressions for skin friction and coefficient of convective heat transfer Nusselt number in PST and PHF cases have been derived.
文摘The problem of boundary layer flows at a flat plate surface with velocity-slip and temperature-jump boundary conditions is analyzed. With the velocity slip conditions, there are multiple physical factors lumped together, and the boundary layer solutions significantly change their behaviors. The self-similarity in the solutions degenerates, however, the problem is still an ordinary differential equation which can be solved. Shooting methods are applied to solve the flowfield. The results include velocity and temperature for both the surface and flowfield. Unlike the traditional Blasius fiat plate boundary layer solutions which are self-similar through all the plate boundary layer, the new solutions indicate that the front tip is actually a singularity point, especially at locations within one mean flee path from the leading edge.
文摘This paper presents the study of convective heat transfer characteristics of an incompressible dusty fluid past a vertical stretching sheet. The governing partial differential equations are reduced to nonlinear ordinary differential equations by using similarity transformation. The transformed equations are solved numerically by applying Runge Kutta Fehlberg fourth-fifth order method (RKF45 Method). Here obtained non-dimensional velocity and temperature profiles has been carried out to study the effect of different physical parameters such as fluid-particle interaction parameter, Grashof number, Prandtl number, Eckert number. Comparison of the obtained numerical results is made with previously published results.
文摘In the present article a numerical analysis has been carried out to study the boundary layer flow behavior and heat transfer characteristics of a nanofluid over an exponential stretching sheet. By assuming the stretching sheet to be impermeable, the effect of chemical reaction, thermal radiation, thermopherosis, Brownian motion and suction parameters in the presence of uniform magnetic field on heat and mass transfer are addressed. The governing system of equations is transformed into coupled nonlinear ordinary differential equations using suitable similarity transformations. The transformed equations are then solved numerically using the well known Runge-Kutta-Fehlberg method of fourth-fifth order. A detailed parametric study is performed to access the influence of the physical parameters on longitudinal velocity, temperature and nanoparticle volume fraction profiles as well as the local skin-friction coefficient, local Nusselt number and the local Sherwood number and the results are presented in both graphical and tabular forms.
文摘In the present paper, the boundary layer flow of Walters Liquid B Model over a stretching plate has been considered to solve heat flow problem with variable conductivity. First, using similarity transformation, the velocity components of velocity have been obtained. Then, the heat flow problem has been considered in two ways: 1) prescribed surface temperature (PST), and 2) prescribed stretching plate heat flux (PHF) in case of variable conductivity. Due to variable conductivity, temperature profile has its two part- one mean tempera-ture and other temperature profile induced due to variable conductivity. The related results have been dis-cussed with the help of graphs.
文摘In this article, electromagnetic control of turbulent boundary layer on a ship hull is numerically investigated. This study is conducted on the geometry of tanker model hull. For this purpose, a combination of electric and magnetic fields is applied to a region of boundary layer on stern so that produce wall parallel Lorentz forces in streamwise direction as body forces in stern flow. The governing equations including RANS equations with SST k-ω?turbulent model coupled with electric potential equation are numerically solved by using Ansys Fluent codes. Accuracy of this turbulent model of Fluent in predicting Turbulent flow around a ship is also tested by comparing with available experimental results that it shows a good agreement with experimental data. The results obtained for ship flow show that by applying streamwise Lorentz forces that are large enough, flow is accelerated. The results are caused to delay or avoid the flow separation in stern, increase the propeller inlet velocity, create uniform flow distribution behind the ship’s hull in order to improve the propeller performance, and finally decrease the pressure resistance and total resistance.
