A NOVEL ANALYTICAL METHOD TO INVESTIGATE EFFECT OF RADIATION ON FLOW OF A MAGNETO-MICROPOLAR FLUID PAST A CONTINUOUSLY MOVING PLATE WITH SUCTION AND BLOWING

2010 ◽  
Vol 01 (02) ◽  
pp. 219-238
Author(s):  
MOHAMMAD MEHDI RASHIDI ◽  
ESMAEEL ERFANI
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Analytical Method ◽  
Velocity Profiles ◽  
Nonlinear Ordinary Differential Equations ◽  
Moving Plate ◽  
Transform Method ◽  
Surface Mass ◽  
Mass Transfer Parameter ◽  
Suction And Blowing

In this article, Differential Transform Method (DTM) and Padé approximants (DTM-Padé), are considered for finding analytical solutions of a magneto-micropolar flow past a continuously moving plate with suction and blowing and radiation effect. This technique is extended to give solutions for system of nonlinear ordinary differential equations with boundary conditions at infinity. The analytic solutions of the system of nonlinear ordinary differential equations are constructed in the ratio of two polynomials. Graphical results are presented to investigate influence of the radiation parameter, magnetic field parameter, Prandtl number, coupling constant parameter and the surface mass transfer parameter on velocity profiles, angular velocity profiles and temperature profiles. In addition, the numerical method is used to investigate the validity of this analytical method, an excellent agreement is observed between the solutions obtained from the DTM-Padé and numerical results. The results reveal that the DTM-Padé is very effective and convenient for solving engineering problems especially for boundary-layer problems.

scholarly journals New dynamical behaviour of the coronavirus (COVID-19) infection system with nonlocal operator from reservoirs to people

2020 ◽  
Author(s):  
P. Veeresha ◽  
D. G. Prakasha ◽  
Naveen Sanju Malagi ◽  
Haci Mehmet Baskonus ◽  
Wei Gao
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Arbitrary Order ◽  
Dynamical Behaviour ◽  
Nonlocal Operator ◽  
Nonlinear Ordinary Differential Equations ◽  
Transform Method ◽  
Homotopy Analysis ◽  
The Fixed Point Theorem ◽  
The Mathematical Model

Abstract The fundamental aim of the present study is to analyse and find the solution for the system of nonlinear ordinary differential equations describing the deadly and most dangerous virus from the lost three months called coronavirus. The mathematical model consisting of six nonlinear ordinary differential equations are exemplified and the corresponding solution is studied within the frame of 𝑞-homotopy analysis transform method (𝑞-HATM). Moreover, a newly defined fractional operator is employed in order to understand more effectively, known as Atangana-Baleanu (AB) operator. For the obtained results, the fixed point theorem is hired to present the exactness as well as uniqueness. For diverse arbitrary order, the behaviour of the outcomes is presented in terms of plots. Finally, the present study may help to examine the wild class of real-world models and also aid to predict their behaviour with respect to parameters considered in the models.

What Is a Spectral Model?

1998 ◽  
Author(s):  
T. N. Krishnamurti ◽  
H. S. Bedi ◽  
V. M. Hardiker
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Spectral Method ◽  
Basis Functions ◽  
Nonlinear Ordinary Differential Equations ◽  
Transform Method ◽  
Spectral Modeling ◽  
Vertical Coordinate ◽  
Dependent Variables ◽  
Simple Models

If one takes a closed system of the basic meteorological equations and introduces within this system a finite expansion of the dependent variables using functions such as double Fourier or Fourier-Legendre functions in space, then the use of the orthogonality properties of these spatial functions enables one to obtain a set of coupled nonlinear ordinary differential equations for the coefficients of these functions. These coefficients are functions of time and the vertical coordinate, since the horizontal spatial dependence has been removed by taking a Fourier or a Fourier-Legendre transform of the equations. The coupled nonlinear ordinary differential equations for the coefficients are usually solved by simple time-differencing and vertical finite-differencing schemes. The mapping of the solution requires the multiplication of the coefficients with the spatial functions summed over a set of chosen finite spatial basis functions. This is what defines spectral modeling. Meteorological application of the spectral method was initiated by Silberman (1954), who studied the nondivergent barotropic vorticity equation in the spherical coordinate system using the spectral technique. In its earlier days, the spectral method was particularly suitable for low-resolution simple models. The equations of these simple models involved nonlinear terms evaluated at each time step. Evaluation of the nonlinear terms was performed using the interaction coefficient method and thus required large memory allocations, which was an undesirable proposition. However, with the introduction of the transform method, developed independently by Eliasen et al. (1970) and Orszag (1970), the method for evaluation of these nonlinear terms changed completely. This transform method also made it feasible to include nonadiabatic effects in the model equations. For the past couple of decades, the spectral method has be come an increasingly popular technique for studies of general circulation and numerical weather prediction at the operational and research centers. This method forms the basis for spectral modeling, and it is easy to understand if the reader has some background in linear algebra. We have a set of linearly independent functions θi(x), which are called the basis functions. The dependent variables of the problem are represented by a finite sum of these basis functions.

Nonlinear Dynamics of Axially Moving Plates With Rotational Springs

2013 ◽  
Author(s):  
Mergen H. Ghayesh ◽  
Marco Amabili
Keyword(s):  
Nonlinear Dynamics ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Plate Theory ◽  
Lagrange Equation ◽  
Global Dynamics ◽  
Nonlinear Ordinary Differential Equations ◽  
Moving Plate ◽  
Time Histories ◽  
Axially Moving

In this paper, the in-plane and out-of-plane nonlinear dynamics of an axially moving plate with distributed rotational springs at boundaries is examined numerically. The Von Kármán plate theory along with the Kirchhoff’s hypothesis are employed to construct the kinetic and potential energies of the system. The Lagrange equation is used so as to obtain the equations of motion which are in the form of a set of second-order nonlinear ordinary differential equations. This set is recast into a set of first-order nonlinear ordinary differential equations with coupled terms. Gear’s backward-differentiation-formula is employed to integrate this set of equations numerically, yielding the generalized coordinates of the system as a function of time. The bifurcation diagrams of Poincaré maps are then constructed by sectioning these time histories in every period of the external excitation force. The results are shown in the form of time histories, phase-plane portraits, and Poincaré sections. The effect of the stiffness of the rotational springs on the global dynamics of the system is also investigated.

scholarly journals Parametric Analysis of Entropy Generation in Magneto-Hemodynamic Flow in a Semi-Porous Channel with OHAM and DTM

2014 ◽  
Vol 11 (1-2) ◽  
pp. 47-60 ◽  
Author(s):  
M. M. Rashidi ◽  
A. Basiri Parsa ◽  
O. Anwar Bég ◽  
L. Shamekhi ◽  
S. M. Sadri ◽  
...  
Keyword(s):  
Reynolds Number ◽  
Entropy Generation ◽  
Hartmann Number ◽  
Fluid Velocity ◽  
Velocity Profiles ◽  
Porous Channel ◽  
Moving Plate ◽  
Optimal Homotopy Analysis Method ◽  
Transform Method ◽  
Mass Transfer Parameter

The magneto-hemodynamic laminar viscous flow of a conducting physiological fluid in a semi-porous channel under a transverse magnetic field has been analyzed by the optimal Homotopy Analysis Method (OHAM) and Differential Transform Method (DTM) under physically realistic boundary conditions first. Then as the main purpose of this study the important designing subject, entropy generation of this system, has been analyzed. The influence of Hartmann number (Ha) and transpiration Reynolds number (mass transfer parameter, Re) on the fluid velocity profiles in the channel are studied in detail first. After finding the fluid velocity profiles, graphical results are presented to investigate effects of the Reynolds number, Hartmann number,x-velocity of the moving plate, suspension height and dimensionless horizontal coordinate on the entropy generation.

scholarly journals Impact of double-diffusive convection and motile gyrotactic microorganisms on magnetohydrodynamics bioconvection tangent hyperbolic nanofluid

Open Physics ◽  
2020 ◽  
Vol 18 (1) ◽  
pp. 74-88 ◽  
Author(s):  
Tanveer Sajid ◽  
Muhammad Sagheer ◽  
Shafqat Hussain ◽  
Faisal Shahzad
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Transfer Rate ◽  
Mass Transfer Rate ◽  
Physical Nature ◽  
Working Fluid ◽  
Nonlinear Ordinary Differential Equations ◽  
Gyrotactic Microorganisms ◽  
Motile Gyrotactic Microorganisms ◽  
Double Diffusive

AbstractThe double-diffusive tangent hyperbolic nanofluid containing motile gyrotactic microorganisms and magnetohydrodynamics past a stretching sheet is examined. By adopting the scaling group of transformation, the governing equations of motion are transformed into a system of nonlinear ordinary differential equations. The Keller box scheme, a finite difference method, has been employed for the solution of the nonlinear ordinary differential equations. The behaviour of the working fluid against various parameters of physical nature has been analyzed through graphs and tables. The behaviour of different physical quantities of interest such as heat transfer rate, density of the motile gyrotactic microorganisms and mass transfer rate is also discussed in the form of tables and graphs. It is found that the modified Dufour parameter has an increasing effect on the temperature profile. The solute profile is observed to decay as a result of an augmentation in the nanofluid Lewis number.

A Multiple Interval Chebyshev-Gauss-Lobatto Collocation Method for Ordinary Differential Equations

2016 ◽  
Vol 9 (4) ◽  
pp. 619-639 ◽  
Author(s):  
Zhong-Qing Wang ◽  
Jun Mu
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Collocation Method ◽  
Initial Value Problems ◽  
Numerical Experiments ◽  
High Order Accuracy ◽  
Nonlinear Ordinary Differential Equations ◽  
Initial Value ◽  
Order Accuracy ◽  
Long Time

AbstractWe introduce a multiple interval Chebyshev-Gauss-Lobatto spectral collocation method for the initial value problems of the nonlinear ordinary differential equations (ODES). This method is easy to implement and possesses the high order accuracy. In addition, it is very stable and suitable for long time calculations. We also obtain thehp-version bound on the numerical error of the multiple interval collocation method underH1-norm. Numerical experiments confirm the theoretical expectations.

Sign in / Sign up

Export Citation Format

Share Document