Unsteady flow of a Maxwell fluid with fractional derivatives in a circular cylinder moving with a nonlinear velocity

2014 ◽  
Vol 37 (1) ◽  
pp. 139-156 ◽  
Author(s):  
M. Athar ◽  
A.U. Awan ◽  
Corina Fetecau ◽  
Mehwish Rana
Keyword(s):  
Circular Cylinder ◽  
Unsteady Flow ◽  
Fractional Derivatives ◽  
Maxwell Fluid ◽  
Nonlinear Velocity

scholarly journals A computational approach for the unsteady flow of maxwell fluid with Caputo fractional derivatives

2018 ◽  
Vol 57 (4) ◽  
pp. 2601-2608 ◽  
Author(s):  
Ehsan Ul Haque ◽  
Aziz Ullah Awan ◽  
Nauman Raza ◽  
Muhammad Abdullah ◽  
Maqbool Ahmad Chaudhry
Keyword(s):  
Unsteady Flow ◽  
Fractional Derivatives ◽  
Maxwell Fluid ◽  
Computational Approach ◽  
Caputo Fractional Derivatives

scholarly journals Semi-analytical technique for the solution of fractional Maxwell fluid

2017 ◽  
Vol 95 (5) ◽  
pp. 472-478 ◽  
Author(s):  
M. Abdullah ◽  
Asma Rashid Butt ◽  
Nauman Raza ◽  
Ehsan Ul Haque
Keyword(s):  
Circular Cylinder ◽  
Fractional Derivatives ◽  
Bessel Functions ◽  
Maxwell Fluid ◽  
Inverse Transformation ◽  
Physical Parameters ◽  
Time Dynamic ◽  
Analytical Technique ◽  
In Series ◽  
The Impact

In this work, the flow of a fractional Maxwell fluid is discussed. The velocity function and time-dependent shear stress of a Maxwell fluid with fractional derivatives are calculated. It is considered that the fluid in the infinitely long circular cylinder is moving with a velocity ft. The fluid in the infinitely long circular cylinder of radius R is initially at rest and at t = 0+, because of shear, it instantly starts to move longitudinally. To obtain the solutions, we have employed Laplace transformation and modified Bessel equation. The solutions are in series form, which are expressed in terms of modified Bessel functions [Formula: see text] and [Formula: see text], and satisfy all given conditions. In this paper, Laplace inverse transformation has been calculated numerically by using MATLAB. The behavior of the following physical parameters on the flow are investigated: relaxation time, dynamic viscosity, kinematics viscosity, similarity parameters of fractional derivatives and radius of the circular cylinder. Finally, the impact of the fractional parameter and material elements is shown by graphical demonstration.

scholarly journals Vortex motion in the early stages of unsteady flow around a circular cylinder

Sadhana ◽  
1984 ◽  
Vol 7 (2) ◽  
pp. 119-135 ◽  
Author(s):  
Guo-Can Ling ◽  
Xie-Yuan Yin
Keyword(s):  
Circular Cylinder ◽  
Unsteady Flow ◽  
Vortex Motion ◽  
Early Stages

scholarly journals The drag-adjoint field of a circular cylinder wake at Reynolds numbers 20, 100 and 500

2013 ◽  
Vol 730 ◽  
pp. 145-161 ◽  
Author(s):  
Qiqi Wang ◽  
Jun-Hui Gao
Keyword(s):  
Circular Cylinder ◽  
Flow Field ◽  
Unsteady Flow ◽  
Numerical Solutions ◽  
Reynolds Numbers ◽  
Adjoint Equations ◽  
Cylinder Wake ◽  
Near Wake ◽  
Navier Stokes Equation ◽  
D 20

AbstractThis paper analyses the adjoint solution of the Navier–Stokes equation. We focus on flow across a circular cylinder at three Reynolds numbers, ${\mathit{Re}}_{D} = 20, 100$ and $500$. The quantity of interest in the adjoint formulation is the drag on the cylinder. We use classical fluid mechanics approaches to analyse the adjoint solution, which is a vector field similar to a flow field. Production and dissipation of kinetic energy of the adjoint field is discussed. We also derive the evolution of circulation of the adjoint field along a closed material contour. These analytical results are used to explain three numerical solutions of the adjoint equations presented in this paper. The adjoint solution at ${\mathit{Re}}_{D} = 20$, a viscous steady state flow, exhibits a downstream suction and an upstream jet, the opposite of the expected behaviour of a flow field. The adjoint solution at ${\mathit{Re}}_{D} = 100$, a periodic two-dimensional unsteady flow, exhibits periodic, bean-shaped circulation in the near-wake region. The adjoint solution at ${\mathit{Re}}_{D} = 500$, a turbulent three-dimensional unsteady flow, has complex dynamics created by the shear layer in the near wake. The magnitude of the adjoint solution increases exponentially at the rate of the first Lyapunov exponent. These numerical results correlate well with the theoretical analysis presented in this paper.

scholarly journals Numerical investigation of unsteady flow past a circular cylinder using 2-D finite volume method

1970 ◽  
Vol 4 (1) ◽  
pp. 27-42 ◽  
Author(s):  
Md Mahbubar Rahman ◽  
Md. Mashud Karim ◽  
Md Abdul Alim
Keyword(s):  
Circular Cylinder ◽  
Unsteady Flow ◽  
Turbulent Flow ◽  
Finite Volume Method ◽  
Finite Volume ◽  
Turbulence Models ◽  
Drag Coefficients ◽  
Pressure Formulation ◽  
Lift And Drag ◽  
Volume Method

The dynamic characteristics of the pressure and velocity fields of unsteady incompressible laminar and turbulent wakes behind a circular cylinder are investigated numerically and analyzed physically. The governing equations, written in the velocity pressure formulation are solved using 2-D finite volume method. The initial mechanism for vortex shedding is demonstrated and unsteady body forces are evaluated. The turbulent flow for Re = 1000 & 3900 are simulated using k-? standard, k-? Realizable and k-? SST turbulence models. The capabilities of these turbulence models to compute lift and drag coefficients are also verified. The frequencies of the drag and lift oscillations obtained theoretically agree well with the experimental results. The pressure and drag coefficients for different Reynolds numbers were also computed and compared with experimental and other numerical results. Due to faster convergence, 2-D finite volume method is found very much prospective for turbulent flow as well as laminar flow.Keywords: Viscous unsteady flow, laminar & turbulent flow, finite volume method, circular cylinder.DOI: 10.3329/jname.v4i1.914Journal of Naval Architecture and Marine Engineering 4(2007) 27-42

A comparative study of heat transfer analysis of fractional Maxwell fluid by using Caputo and Caputo–Fabrizio derivatives

2020 ◽  
Vol 98 (1) ◽  
pp. 89-101 ◽  
Author(s):  
Nauman Raza ◽  
Muhammad Asad Ullah
Keyword(s):  
Exact Solutions ◽  
Fractional Derivatives ◽  
Numerical Solutions ◽  
Maxwell Fluid ◽  
Heat Transfer Analysis ◽  
Flow Parameters ◽  
Fluid Parameter ◽  
Laplace Transform Technique ◽  
The Laplace Transform ◽  
Temperature And Velocity Fields

A comparative analysis is carried out to study the unsteady flow of a Maxwell fluid in the presence of Newtonian heating near a vertical flat plate. The fractional derivatives presented by Caputo and Caputo–Fabrizio are applied to make a physical model for a Maxwell fluid. Exact solutions of the non-dimensional temperature and velocity fields for Caputo and Caputo–Fabrizio time-fractional derivatives are determined via the Laplace transform technique. Numerical solutions of partial differential equations are obtained by employing Tzou’s and Stehfest’s algorithms to compare the results of both models. Exact solutions with integer-order derivative (fractional parameter α = 1) are also obtained for both temperature and velocity distributions as a special case. A graphical illustration is made to discuss the effect of Prandtl number Pr and time t on the temperature field. Similarly, the effects of Maxwell fluid parameter λ and other flow parameters on the velocity field are presented graphically, as well as in tabular form.

Sign in / Sign up

Export Citation Format

Share Document