scholarly journals Study on the training model of football movement trajectory drop point based on fractional differential equation

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Yuefeng Che ◽  
Mohammed Yousuf Abo Keir
Keyword(s):  
Angular Velocity ◽  
Differential Equations ◽  
Rotation Axis ◽  
Numerical Study ◽  
Vertical Direction ◽  
Training Model ◽  
Movement Trajectory ◽  
Air Resistance ◽  
Resistance Moment ◽  
Ball Trajectory

Abstract To study the landing point of the curved football track, the dynamic differential equations of the football were derived in this paper. The air resistance moment was taken into account, and the rotation axis was no longer confined to the vertical direction. We compare various soccer movement regularity of different initial angular velocity 0, in turn, using standard numerical methods to solve differential equations, the selection of the initial angular velocity of three typical 0s has been carried on the detailed numerical study, and the results show that: in the same velocity V play football, corresponding to different initial angular velocity 0, the movement of football is an obvious difference. Conclusion: For the same V = 5 + 28 + 11 m/s, when no rotation Ω 0 = 0, the trajectory of the football is the usual trajectory of the projectile. When 0 = 2 − 2 + 16 rad/s, the trajectory of the football is a typical banana ball trajectory; When 0 = 13+0+0 rad/s, the trajectory of the football shows the phenomenon of left-right fluttering, similar to the fallen leaf ball.

Numerical Study of the Combined Free-Forced Convection and Mass Transfer Flow Past a Vertical Porous Plate in a Porous Medium with Heat Generation and Thermal Diffusion

2006 ◽  
Vol 11 (4) ◽  
pp. 331-343 ◽  
Author(s):  
M. S. Alam ◽  
M. M. Rahman ◽  
M. A. Samad
Keyword(s):  
Mass Transfer ◽  
Flow Field ◽  
Differential Equations ◽  
Forced Convection ◽  
Heat Generation ◽  
Numerical Study ◽  
Porous Plate ◽  
Integration Scheme ◽  
Suction Parameter ◽  
Transfer Flow

The problem of combined free-forced convection and mass transfer flow over a vertical porous flat plate, in presence of heat generation and thermaldiffusion, is studied numerically. The non-linear partial differential equations and their boundary conditions, describing the problem under consideration, are transformed into a system of ordinary differential equations by using usual similarity transformations. This system is solved numerically by applying Nachtsheim-Swigert shooting iteration technique together with Runge-Kutta sixth order integration scheme. The effects of suction parameter, heat generation parameter and Soret number are examined on the flow field of a hydrogen-air mixture as a non-chemical reacting fluid pair. The analysis of the obtained results showed that the flow field is significantly influenced by these parameters.

Finite difference code for velocity and surface traction of a Fluid between Two Eccentric Spheres

2015 ◽  
Vol 11 (1) ◽  
pp. 2960-2971
Author(s):  
M.Abdel Wahab
Keyword(s):  
Velocity Field ◽  
Angular Velocity ◽  
Finite Difference ◽  
Numerical Study ◽  
Outer Sphere ◽  
Equation Of Motion ◽  
Annular Region ◽  
Surface Traction ◽  
Angular Velocities ◽  
Axis Passing

The Numerical study of the flow of a fluid in the annular region between two eccentric sphere susing PHP Code isinvestigated. This flow is created by considering the inner sphere to rotate with angular velocity 1  and the outer sphererotate with angular velocity 2  about the axis passing through their centers, the z-axis, using the three dimensionalBispherical coordinates (, ,) .The velocity field of fluid is determined by solving equation of motion using PHP Codeat different cases of angular velocities of inner and outer sphere. Also Finite difference code is used to calculate surfacetractions at outer sphere.

scholarly journals Numerical study of time-fractional fourth-order differential equations with variable coefficients

2011 ◽  
Vol 23 (1) ◽  
pp. 91-98 ◽  
Author(s):  
Najeeb Alam Khan ◽  
Nasir-Uddin Khan ◽  
Muhammad Ayaz ◽  
Amir Mahmood ◽  
Noor Fatima
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Numerical Study ◽  
Variable Coefficients

scholarly journals Numerical Study of Viscoelastic Micropolar Heat Transfer from a Vertical Cone for Thermal Polymer Coating

2019 ◽  
Vol 8 (1) ◽  
pp. 449-460 ◽  
Author(s):  
K. Madhavi ◽  
V. Ramachandra Prasad ◽  
A. Subba Rao ◽  
O. Anwar Bég ◽  
A. Kadir
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Angular Velocity ◽  
Numerical Study ◽  
Relaxation Times ◽  
Viscoelastic Model ◽  
Deborah Number ◽  
Convection Boundary Layer ◽  
Density Parameter ◽  
R Ratio

Abstract A mathematical model is developed to study laminar, nonlinear, non-isothermal, steady-state free convection boundary layer flow and heat transfer of a micropolar viscoelastic fluid from a vertical isothermal cone. The Eringen model and Jeffery’s viscoelastic model are combined to simulate the non-Newtonian characteristics of polymers, which constitutes a novelty of the present work. The transformed conservation equations for linear momentum, angular momentum and energy are solved numerically under physically viable boundary conditions using a finite difference scheme (Keller Box method). The effects of Deborah number (De), Eringen vortex viscosity parameter (R), ratio of relaxation to retardation times (λ), micro-inertia density parameter (B), Prandtl number (Pr) and dimensionless stream wise coordinate (ξ) on velocity, surface temperature and angular velocity in the boundary layer regime are evaluated. The computations show that with greater ratio of retardation to relaxation times, the linear and angular velocity are enhanced whereas temperature (and also thermal boundary layer thickness) is reduced. Greater values of the Eringen parameter decelerate both the linear velocity and micro-rotation values and enhance temperatures. Increasing Deborah number decelerates the linear flow and Nusselt number whereas it increases temperatures and boosts micro-rotation magnitudes. The study is relevant to non-Newtonian polymeric thermal coating processes.

scholarly journals Numerical Exploration via Least Squares Estimation on Three Dimensional MHD Yield Exhibiting Nanofluid Model with Porous Stretching Boundaries

2021 ◽  
Vol 5 (4) ◽  
pp. 167
Author(s):  
Tamour Zubair ◽  
Muhammad Usman ◽  
Umar Nazir ◽  
Poom Kumam ◽  
Muhammad Sohail
Keyword(s):  
Differential Equations ◽  
Numerical Study ◽  
Nonlinear Partial Differential Equations ◽  
Three Dimensional ◽  
Least Square Method ◽  
Least Square ◽  
Comparison Study ◽  
Nano Fluid ◽  
Complicated Geometry ◽  
Maple Code

The numerical study of a three-dimensional magneto-hydrodynamic (MHD) Casson nano-fluid with porous and stretchy boundaries is the focus of this paper. Radiation impacts are also supposed. A feasible similarity variable may convert a verbalized set of nonlinear “partial” differential equations (PDEs) into a system of nonlinear “ordinary” differential equations (ODEs). To investigate the solutions of the resulting dimensionless model, the least-square method is suggested and extended. Maple code is created for the expanded technique of determining model behaviour. Several simulations were run, and graphs were used to provide a thorough explanation of the important parameters on velocities, skin friction, local Nusselt number, and temperature. The comparison study attests that the suggested method is well-matched, trustworthy, and accurate for investigating the governing model’s answers. This method may be expanded to solve additional physical issues with complicated geometry.

Numerical Solution for Boundary Layer Flow of a Dusty Micropolar Fluid Due to a Stretching Sheet with Constant Wall Temperature

2021 ◽  
Vol 87 (1) ◽  
pp. 30-40
Author(s):  
Anisah Dasman ◽  
Abdul Rahman Mohd Kasim ◽  
Iskandar Waini ◽  
Najiyah Safwa Khashi’ie
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Wall Temperature ◽  
Micropolar Fluid ◽  
Stretching Sheet ◽  
Numerical Solutions ◽  
Numerical Study ◽  
Particle Interaction ◽  
Dust Particles ◽  
Constant Wall Temperature

This paper aims to present the numerical study of a dusty micropolar fluid due to a stretching sheet with constant wall temperature. Using the suitable similarity transformation, the governing partial differential equations for two-phase flows of the fluid and the dust particles are reduced to the form of ordinary differential equations. The ordinary differential equations are then numerically analysed using the bvp4c function in the Matlab software. The validity of present numerical results was checked by comparing them with the previous study. The results graphically show the numerical solutions of velocity, temperature and microrotation distributions for several values of the material parameter K, fluid-particle interaction parameter and Prandtl number for both fluid and dust phase. The effect of microrotation is investigated and analysed as well. It is found that the distributions are significantly influenced by the investigated parameters for both phases.

Numerical Study of Thermal Convection in Boussinesq-Stokes Suspension Occupying a Rectangular Box

2011 ◽  
Author(s):  
S. Manjunath ◽  
N. P. Chandrashekara
Keyword(s):  
Aspect Ratio ◽  
Thermal Convection ◽  
Couple Stress ◽  
Numerical Study ◽  
Critical Rayleigh Number ◽  
Vertical Direction ◽  
Heat Conducting ◽  
Linear Temperature ◽  
Vertical Walls ◽  
Vertical Cavity

This paper is a Fourier–series assisted numerical study of two-dimensional thermal convection in Boussinesq–Stokes suspensions occupying a cavity. The suspension is modeled as a couple stress liquid. The horizontal walls of the cavity are assumed to be perfectly heat conducting and the vertical walls are non-uniformly heated to establish a linear temperature in the vertical direction. The critical Rayleigh number is obtained numerically as a function of couple stress parameter and aspect ratio, and the same is plotted graphically. The results of slender vertical cavity, classical Rayleigh-Be´nard convection, rectangular and square cavities of finite aspect-ratio heated from below are obtained as limiting cases of the study.

scholarly journals Differential Rotation as an Axisymmetric Resonant Mode of Convection

1991 ◽  
Vol 130 ◽  
pp. 178-181
Author(s):  
Kwing L. Chan ◽  
Hans G. Mayr
Keyword(s):  
Angular Velocity ◽  
Differential Rotation ◽  
Rotation Axis ◽  
Numerical Models ◽  
Resonant Mode ◽  
Analytical Models ◽  
Resonance Model ◽  
Solar Convection Zone ◽  
Solar Differential Rotation ◽  
Solar Convection

Recent results from helioseismology (see Goode, these Proceedings) have shown that the inferred contours of the solar angular velocity are more or less radial in the convection region, and the rotation becomes uniform below. These observations contradict the prevailing numerical models of Taylor columns which predict angular velocity contours parallel to the rotation axis of the Sun. Thus, an alternative explanation of solar differential rotation is called for.Presently, it is not feasible to construct a thermally-relaxed, dynamically self-consistent numerical model of the solar convection zone (see Chan and Serizawa, these Proceedings). It is then appropriate to explore simplified models that may shed some light. A number of analytical models have been proposed for the solar differential rotation, and the reader is referred to the book by Rüdiger (1989) for a comprehensive review of this subject. Here, we report on some recent development on the convective resonance model proposed by Chan et al. (1987; hereafter referred as CSM).

On the Path of a Rotating Spherical Projectile. Part II

1897 ◽  
Vol 21 ◽  
pp. 116-116
Author(s):  
Tait
Keyword(s):  
Approximate Solution ◽  
Angular Velocity ◽  
Differential Equations ◽  
Gravitational Effect ◽  
Thin Metal ◽  
Paradoxical Result

In addition to the authorities quoted in the first part of the paper, memoirs by Clerk-Maxwell and by Lord Rayleigh are referred to, also a passage in the Beiblätter zu den Ann. d. Physik. (1895, p. 289), which cites Hélie, Traíté de Balistique.The Author then considers the more obvious defects of the rudely approximate solution of the differential equations which is given in Part I., especially the omission of the direct gravitational effect on the speed, and shows how to take account of the effect of the observed gradual diminution of the angular velocity of the projectile. An improved solution of the problem of § 8 of the paper is also given.The Author stated that lie had occasionally succeeded in obtaining the kink spoken of in Part I., the projectile being a humming-top made of very thin metal. He had also occasionally obtained a cusp, thus exhibiting the paradoxical result of a projectile's path which is at no point concave downwards.

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