本文提出了一种新型数值求解方法,该方法将四阶Runge-Kutta法与Newton迭代法相结合,旨在高效求解流体力学中的Blasius方程边值问题。首先,我们将Blasius方程转化为一组一阶微分方程组,并采用四阶Runge-Kutta法(RK4)进行数值求解。随后,...本文提出了一种新型数值求解方法,该方法将四阶Runge-Kutta法与Newton迭代法相结合,旨在高效求解流体力学中的Blasius方程边值问题。首先,我们将Blasius方程转化为一组一阶微分方程组,并采用四阶Runge-Kutta法(RK4)进行数值求解。随后,引入Newton迭代法动态调整初始条件,以确保满足边界条件的要求。实验结果表明,与传统的打靶法和结合打靶法的四阶Runge-Kutta法(SRK)进行对比实验,新方法在迭代次数和计算时间上均展现显著优势,同时求解精度也得到提升。In this paper, we propose a novel numerical solution method that combines the fourth-order Runge-Kutta method with the Newton iterative method, aiming to efficiently solve the margin problem of Blasius equation in fluid mechanics. Firstly, we transform the Blasius equation into a set of first-order differential equations and solve it numerically using the fourth-order Runge-Kutta method (RK4). Subsequently, the Newton iteration method is dynamically introduced to adjust the initial conditions to ensure that the boundary conditions are satisfied. The experimental results show that the new method exhibits significant advantages in terms of the number of iterations and computation time, as well as improved solution accuracy, in comparison experiments with the traditional shooting method and the Runge-Kutta method (SRK) combined with the improved shooting method.展开更多
This investigation deals with the effects of slip, magnetic field, and non- Newtonian flow parameters on the flow and heat transfer of an incompressible, electrically conducting fourth-grade fluid past an infinite por...This investigation deals with the effects of slip, magnetic field, and non- Newtonian flow parameters on the flow and heat transfer of an incompressible, electrically conducting fourth-grade fluid past an infinite porous plate. The heat transfer analysis is carried out for two heating processes. The system of highly non-linear differential equations is solved by the shooting method with the fourth-order Runge-Kutta method for moderate values of the parameters. The effective Broyden technique is adopted in order to improve the initial guesses and to satisfy the boundary conditions at infinity. An exceptional cross-over is obtained in the velocity profile in the presence of slip. The fourth-grade fluid parameter is found to increase the momentum boundary layer thickness, whereas the slip parameter substantially decreases it. Similarly, the non-Newtonian fluid parameters and the slip have opposite effects on the thermal boundary layer thickness.展开更多
In this paper, the Adomian methods, differential transform methods, and Taylor series methods are applied to non-linear differential equations which is called Blasius problem in fluid mechanics. The solutions of the B...In this paper, the Adomian methods, differential transform methods, and Taylor series methods are applied to non-linear differential equations which is called Blasius problem in fluid mechanics. The solutions of the Blasius problem for two cases are obtained by using these methods and their results are shown in table.展开更多
In this paper mathematical techniques have been used for the solution of Blasius differential equation. The method uses optimized artificial neural networks approximation with Sequential Quadratic Programming algorith...In this paper mathematical techniques have been used for the solution of Blasius differential equation. The method uses optimized artificial neural networks approximation with Sequential Quadratic Programming algorithm and hybrid AST-INP techniques. Numerical treatment of this problem reported in the literature is based on Shooting and Finite Differences Method, while our mathematical approach is very simple. Numerical testing showed that solutions obtained by using the proposed methods are better in accuracy than those reported in literature. Statistical analysis provided the convergence of the proposed model.展开更多
In the present research,Tiwari and Das model are used for the impact of a magnetic field on non-Newtonian nanofluid flow in the presence of injection and suction.The PDEs are converted into ordinary differential equat...In the present research,Tiwari and Das model are used for the impact of a magnetic field on non-Newtonian nanofluid flow in the presence of injection and suction.The PDEs are converted into ordinary differential equations(ODEs)using the similarity method.The obtained ordinary differential equations are solved numerically using shooting method along with RK-4.Part of the present study uses nanoparticles(NPs)like TiO_(2) andAl_(2)O_(3) and sodium carboxymethyl cellulose(CMC/water)is considered as a base fluid(BF).This study is conducted to find the influence of nanoparticles,Prandtl number,and magnetic field on velocity and temperature profile,however,the Nusselt number and coefficient of skin friction parameters are also presented in detail with the variation of nanoparticles and parameters.The obtained results of the present study are presented usingMATLAB.In addition to these,some simulations of partial differential equations are also shown using software for graphing surface plots of velocity profile and streamlines along with surface plots and isothermal contours of the temperature profile.展开更多
Momentum and energy laminar boundary layers of an incompressible fluid with thermal radiation about a moving plate in a quiescent ambient fluid are investigated numerically. Also, it has been underlined that the analy...Momentum and energy laminar boundary layers of an incompressible fluid with thermal radiation about a moving plate in a quiescent ambient fluid are investigated numerically. Also, it has been underlined that the analysis of the roles of both velocity and temperature gradient at infinity is of key relevance for our results.展开更多
文摘本文提出了一种新型数值求解方法,该方法将四阶Runge-Kutta法与Newton迭代法相结合,旨在高效求解流体力学中的Blasius方程边值问题。首先,我们将Blasius方程转化为一组一阶微分方程组,并采用四阶Runge-Kutta法(RK4)进行数值求解。随后,引入Newton迭代法动态调整初始条件,以确保满足边界条件的要求。实验结果表明,与传统的打靶法和结合打靶法的四阶Runge-Kutta法(SRK)进行对比实验,新方法在迭代次数和计算时间上均展现显著优势,同时求解精度也得到提升。In this paper, we propose a novel numerical solution method that combines the fourth-order Runge-Kutta method with the Newton iterative method, aiming to efficiently solve the margin problem of Blasius equation in fluid mechanics. Firstly, we transform the Blasius equation into a set of first-order differential equations and solve it numerically using the fourth-order Runge-Kutta method (RK4). Subsequently, the Newton iteration method is dynamically introduced to adjust the initial conditions to ensure that the boundary conditions are satisfied. The experimental results show that the new method exhibits significant advantages in terms of the number of iterations and computation time, as well as improved solution accuracy, in comparison experiments with the traditional shooting method and the Runge-Kutta method (SRK) combined with the improved shooting method.
文摘This investigation deals with the effects of slip, magnetic field, and non- Newtonian flow parameters on the flow and heat transfer of an incompressible, electrically conducting fourth-grade fluid past an infinite porous plate. The heat transfer analysis is carried out for two heating processes. The system of highly non-linear differential equations is solved by the shooting method with the fourth-order Runge-Kutta method for moderate values of the parameters. The effective Broyden technique is adopted in order to improve the initial guesses and to satisfy the boundary conditions at infinity. An exceptional cross-over is obtained in the velocity profile in the presence of slip. The fourth-grade fluid parameter is found to increase the momentum boundary layer thickness, whereas the slip parameter substantially decreases it. Similarly, the non-Newtonian fluid parameters and the slip have opposite effects on the thermal boundary layer thickness.
文摘In this paper, the Adomian methods, differential transform methods, and Taylor series methods are applied to non-linear differential equations which is called Blasius problem in fluid mechanics. The solutions of the Blasius problem for two cases are obtained by using these methods and their results are shown in table.
文摘In this paper mathematical techniques have been used for the solution of Blasius differential equation. The method uses optimized artificial neural networks approximation with Sequential Quadratic Programming algorithm and hybrid AST-INP techniques. Numerical treatment of this problem reported in the literature is based on Shooting and Finite Differences Method, while our mathematical approach is very simple. Numerical testing showed that solutions obtained by using the proposed methods are better in accuracy than those reported in literature. Statistical analysis provided the convergence of the proposed model.
基金The fifth author also thanks Prince Sultan University for funding this work through research-group number RG-DES2017-01-17.
文摘In the present research,Tiwari and Das model are used for the impact of a magnetic field on non-Newtonian nanofluid flow in the presence of injection and suction.The PDEs are converted into ordinary differential equations(ODEs)using the similarity method.The obtained ordinary differential equations are solved numerically using shooting method along with RK-4.Part of the present study uses nanoparticles(NPs)like TiO_(2) andAl_(2)O_(3) and sodium carboxymethyl cellulose(CMC/water)is considered as a base fluid(BF).This study is conducted to find the influence of nanoparticles,Prandtl number,and magnetic field on velocity and temperature profile,however,the Nusselt number and coefficient of skin friction parameters are also presented in detail with the variation of nanoparticles and parameters.The obtained results of the present study are presented usingMATLAB.In addition to these,some simulations of partial differential equations are also shown using software for graphing surface plots of velocity profile and streamlines along with surface plots and isothermal contours of the temperature profile.
文摘Momentum and energy laminar boundary layers of an incompressible fluid with thermal radiation about a moving plate in a quiescent ambient fluid are investigated numerically. Also, it has been underlined that the analysis of the roles of both velocity and temperature gradient at infinity is of key relevance for our results.
