Nonsteady Three-Dimensional Stagnation-Point Flow

1971 ◽  
Vol 38 (1) ◽  
pp. 282-287 ◽  
Author(s):  
E. H. W. Cheng ◽  
M. N. O¨zis¸ik ◽  
J. C. Williams
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Stagnation Point ◽  
Potential Flow ◽  
Blunt Body ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Special Cases ◽  
Layer Flow ◽  
Two Parameters

The equations of motion for the three-dimensional nonsteady flow of incompressible viscous fluid in the vicinity of a forward stagnation point are reduced to three ordinary differential equations for a potential flow field chosen to vary inversely as a linear function of time. The resulting ordinary differential equations contain two parameters C and D, the former characterizes the type of curvature of the surface around the stagnation point and the latter the degree of acceleration or deceleration of the potential flow. The simple stagnation-point problems which have been studied previously are obtainable as special cases of the present analysis by assigning particular values to C and D. Exact solutions have been computed numerically for the velocity field and the pressure distribution in the boundary-layer flow around the stagnation point of a three-dimensional blunt body for the values of the parameter C from 0–1.

Three-Dimensional Stagnation-Point Flow and Heat Transfer of a Dusty Fluid Toward a Stretching Sheet

2016 ◽  
Vol 138 (11) ◽  
Author(s):  
M. R. Mohaghegh ◽  
Asghar B. Rahimi
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Stagnation Point ◽  
Similarity Solution ◽  
Stretching Sheet ◽  
Three Dimensional ◽  
Stagnation Point Flow ◽  
Velocity Parameter ◽  
Flow And Heat Transfer

The steady three-dimensional stagnation-point flow and heat transfer of a dusty fluid toward a stretching sheet is investigated by using similarity solution approach. The freestream along z-direction impinges on the stretching sheet to produce a flow with different velocity components. The governing equations are transformed into ordinary differential equations by introducing appropriate similarity variables and an exact solution is obtained. The nonlinear ordinary differential equations are solved numerically using Runge–Kutta fourth-order method. The effects of the physical parameters like velocity ratio, fluid and thermal particle interaction parameter, ratio of freestream velocity parameter to stretching sheet velocity parameter, Prandtl number, and Eckert number on the flow field and heat transfer characteristics are obtained, illustrated graphically, and discussed. Also, a comparison of the obtained numerical results is made with two-dimensional cases existing in the literature and good agreement is approved. Moreover, it is found that the heat transfer coefficient and shear stress on the surface for axisymmetric case are larger than nonaxisymmetric case. Also, for stationary flat plat case, a similarity solution is presented and a comparison of the obtained results is made with previously published results and full agreement is reported.

ON THE STRUCTURE OF THE SOLUTIONS OF A TWO-PARAMETER FAMILY OF THREE-DIMENSIONAL ORDINARY DIFFERENTIAL EQUATIONS

2003 ◽  
Vol 13 (05) ◽  
pp. 1287-1298 ◽  
Author(s):  
SERKAN T. IMPRAM ◽  
RUSSELL JOHNSON ◽  
RAFFAELLA PAVANI
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Dynamical Behavior ◽  
Three Dimensional ◽  
Wide Range ◽  
Two Parameters ◽  
Two Parameter ◽  
Autonomous Ordinary Differential Equation

We analyze the global structure of the solutions of a three-dimensional, autonomous ordinary differential equation which depends on two parameters. We use graphical, heuristic, and rigorous arguments to show that as the parameters vary, a wide range of dynamical behavior is displayed.

Methods for Automated Dynamic Analysis of Discrete Mechanical Systems

1973 ◽  
Vol 40 (3) ◽  
pp. 809-811 ◽  
Author(s):  
Y. O. Bayazitoglu ◽  
M. A. Chace
Keyword(s):  
Differential Equations ◽  
Dynamic Analysis ◽  
Ordinary Differential Equations ◽  
Mechanical System ◽  
Dynamic Systems ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Constrained Systems ◽  
Lower Pair ◽  
Linear And Nonlinear

The equations of motion for any discrete, lower pair mechanical system can be obtained by analyzing a branched, three-dimensional compound pendulum of indefinite length. In this paper, a set of expressions which provides the equations of motion of arbitrary mechanical dynamic systems directly as ordinary differential equations are presented. These expressions and the associated technique is applicable to linear and nonlinear unconstrained dynamic systems, kinematic systems and multidegree-of-freedom constrained systems.

Vibration of a Functionally Graded Timoshenko Beam on an Elastic Foundation due to a Moving Mass

2014 ◽  
Author(s):  
Khashayar Teimoori ◽  
Ali M. Sadegh
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Elastic Foundation ◽  
Timoshenko Beam ◽  
Biomedical Application ◽  
Equations Of Motion ◽  
Functionally Graded ◽  
Moving Mass ◽  
Special Cases ◽  
Application Fields

In the past decade, beams that are made of functionally graded materials (FGM) have been employed in many engineering and biomedical application fields. In this paper, dynamic response of a FGM Timoshenko beam that is supported by an elastic foundation and is subjected to a moving mass, i.e., the effects of boundary flexibility, has been investigated. It is assumed that the material properties of the beam will change only in the thickness direction. The governing equations of motion are derived using Hamilton’s principles. The partial governing differential equations of motion are reduced to a set of ordinary differential equations by using Petrov-Galerkin method. Runge-Kutta numerical scheme is employed to solve the obtained set of ordinary differential equations. After verification of the results for some special cases with known sloutions the effect of various parameters such as the velocity of moving loads, the boundary flexibility, the power-law index on the vibration of the beam have been investigated. The special case of the solution of the problem was compared with the study of Mesut Simsek [2010] and H. P. Lee [1998] which showed excellent agreement. The results have also been compared to the similar beam without FGM and the advantages of FGM have been discussed.

Dynamic Thermal Analysis of Laminated Cylinder with a Piezoelectric Layer Based on Three-Dimensional Elasticity Solution

2012 ◽  
Vol 186 ◽  
pp. 16-25
Author(s):  
A.R. Daneshmehr ◽  
S. Akbari ◽  
A. Nateghi
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Piezoelectric Layer ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Longitudinal Direction ◽  
Elasticity Solution ◽  
Galerkin Finite Element Method ◽  
Galerkin Finite Element ◽  
Three Dimensional Elasticity

Three-dimensional elasticity solution is presented for finite length, simply supported, laminated cylinder with a piezoelectric layer under dynamic thermal load and pressure. The piezoelectric layer can be used as an actuator or a sensor. The ordinary differential equations are obtained from partial differential equations of motion by means of trigonometric function expansion in longitudinal direction. Galerkin finite element method is used to solve the resulting ordinary differential equations. Finally numerical results are discussed for different situations.

scholarly journals A New Numerical Approach for the Laminar Boundary Layer Flow and Heat Transfer along a Stretching Cylinder Embedded in a Porous Medium with Variable Thermal Conductivity

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
S. Shateyi ◽  
G. T. Marewo
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Porous Medium ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Laminar Boundary Layer ◽  
Boundary Layer Flow ◽  
Stretching Cylinder ◽  
Special Cases ◽  
Layer Flow

The study presents an axisymmetric laminar boundary layer flow of a viscous incompressible fluid and heat transfer over a stretching cylinder embedded in a porous medium. A suitable similarity transformation is employed to transform the partial differential equations corresponding to the momentum and heat equations into nonlinear ordinary differential equations. The resultant ordinary differential equations are then solved using a successive relaxation method (SRM). The effects of significant parameters on the velocity and temperature profiles have been analyzed graphically. The obtained results are also compared with previously published results in some special cases and were found to be in excellent agreement. The skin friction as well as the heat transfer rate at the surface are increased as the values of the curvature parameter increase.

MHD STAGNATION POINT FLOW OF HYPERBOLIC TANGENT FLUID WITH VISCOUS DISSIPATION AND CHEMICAL REACTION

2021 ◽  
Vol 21 (2) ◽  
pp. 569-588
Author(s):  
KINZA ARSHAD ◽  
MUHAMMAD ASHRAF
Keyword(s):  
Magnetic Field ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Stagnation Point ◽  
Viscous Dissipation ◽  
Chemical Reaction ◽  
Normal Velocity ◽  
Hyperbolic Tangent ◽  
Linear Ordinary Differential Equations ◽  
Non Linear

In the present work, two dimensional flow of a hyperbolic tangent fluid with chemical reaction and viscous dissipation near a stagnation point is discussed numerically. The analysis is performed in the presence of magnetic field. The governing partial differential equations are converted into non-linear ordinary differential equations by using appropriate transformation. The resulting higher order non-linear ordinary differential equations are discretized by finite difference method and then solved by SOR (Successive over Relaxation parameter) method. The impact of the relevant parameters is scrutinized by plotting graphs and discussed in details. The main conclusion is that the large value of magnetic field parameter and wiessenberg numbers decrease the streamwise and normal velocity while increase the temperature distribution. Also higher value of the Eckert number Ec results in increases in temperature profile.

THREE-DIMENSIONAL STAGNATION-POINT FLOW OVER A PERMEABLE STRETCHING/SHRINKING SHEET WITH A SECOND ORDER SLIP FLOW

2021 ◽  
Vol 10 (9) ◽  
pp. 3273-3282
Author(s):  
M.E.H. Hafidzuddin ◽  
R. Nazar ◽  
N.M. Arifin ◽  
I. Pop
Keyword(s):  
Differential Equations ◽  
Stagnation Point ◽  
Flow Model ◽  
Nonlinear Partial Differential Equations ◽  
Slip Flow ◽  
Three Dimensional ◽  
Flow Characteristics ◽  
Second Order ◽  
Stagnation Point Flow ◽  
Shrinking Sheet

The problem of steady laminar three-dimensional stagnation-point flow on a permeable stretching/shrinking sheet with second order slip flow model is studied numerically. Similarity transformation has been used to reduce the governing system of nonlinear partial differential equations into the system of ordinary (similarity) differential equations. The transformed equations are then solved numerically using the \texttt{bvp4c} function in MATLAB. Multiple solutions are found for a certain range of the governing parameters. The effects of the governing parameters on the skin friction coefficients and the velocity profiles are presented and discussed. It is found that the second order slip flow model is necessary to predict the flow characteristics accurately.

Sign in / Sign up

Export Citation Format

Share Document