scholarly journals Influence of MHD on Some Oscillating Motions of a Fractional Burgers' Fluid

2015 ◽  
Vol 12 (1) ◽  
pp. 221-237
Author(s):  
Baghdad Science Journal
Keyword(s):  
Exact Solution ◽  
Shear Stress ◽  
Velocity Field ◽  
Fractional Calculus ◽  
Integral Transforms ◽  
Constitutive Relationship ◽  
Oscillating Flows ◽  
Flow Parameters ◽  
Relationship Model ◽  
Burgers Fluid

This paper presents a study for the influence of magnetohydrodynamic (MHD) on the oscillating flows of fractional Burgers’ fluid. The fractional calculus approach in the constitutive relationship model is introduced and a fractional Burgers’ model is built. The exact solution of the oscillating motions of a fractional Burgers’ fluid due to cosine and sine oscillations of an infinite flat plate are established with the help of integral transforms (Fourier sine and Laplace transforms). The expressions for the velocity field and the resulting shear stress that have been obtained, presented under integral and series form in terms of the generalized Mittag-Leffler function, satisfy all imposed initial and boundary conditions. Finally, the obtained solutions are graphically analyzed for variations of interesting flow parameters. While the MATHEMATICA package is used to draw the figures velocity components in the plane.

scholarly journals The Influence of Magnetohydrodynamic Flow and Slip Condition on Generalized Burgers’ Fluid with Fractional Derivative

2020 ◽  
Vol 17 (1) ◽  
pp. 0150
Author(s):  
Nassief Et al.
Keyword(s):  
Shear Stress ◽  
Fractional Calculus ◽  
Fractional Derivative ◽  
Velocity Distribution ◽  
Constant Pressure ◽  
Fluid Model ◽  
Magnetohydrodynamic Flow ◽  
Slip Condition ◽  
Constitutive Relationship ◽  
Burgers Fluid

This paper investigates the effect of magnetohydrodynamic (MHD) of an incompressible generalized burgers’ fluid including a gradient constant pressure and an exponentially accelerate plate where no slip hypothesis between the burgers’ fluid and an exponential plate is no longer valid. The constitutive relationship can establish of the fluid model process by fractional calculus, by using Laplace and Finite Fourier sine transforms. We obtain a solution for shear stress and velocity distribution. Furthermore, 3D figures are drawn to exhibit the effect of magneto hydrodynamic and different parameters for the velocity distribution.

Axial MHD Flow of a Generalized Oldroyd-B Fluid Due to Two Oscillating Cylinders

2011 ◽  
Vol 354-355 ◽  
pp. 83-86
Author(s):  
Ya Qing Liu ◽  
Lian Cun Zheng ◽  
Jun Tie
Keyword(s):  
Shear Stress ◽  
Velocity Field ◽  
Fractional Calculus ◽  
Laplace Transform ◽  
Fluid Velocity ◽  
Mhd Flow ◽  
Hankel Transform ◽  
Constitutive Relationship ◽  
Relationship Of ◽  
Fluid Velocity Field

Axial magnetohydrodynamic (MHD) flows for Oldroyd-B fluid are investigated between two cylinders. The motion of the fluid is produced by the two oscillating cylinders. The fractional calculus approach is introduced to establish the constitutive relationship of a viscolastic fluid. Velocity field and shear stress of the motion are determined in terms of Bessel function and generalized Mittag-Leffler function by using Laplace transform and Hankel transform. The influence of pertinent parameters on the flows is delineated and appropriate conclusions are drawn.

scholarly journals First Problem of Stokes for Generalized Burgers' Fluids

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Muhammad Jamil
Keyword(s):  
Shear Stress ◽  
Steady State ◽  
Velocity Field ◽  
Integral Transforms ◽  
Newtonian Fluids ◽  
Rheological Parameters ◽  
Second Grade ◽  
Material Parameters ◽  
Transient Solutions ◽  
Similar Solutions

The velocity field and the adequate shear stress corresponding to the first problem of Stokes for generalized Burgers’ fluids are determined in simple forms by means of integral transforms. The solutions that have been obtained, presented as a sum of steady and transient solutions, satisfy all imposed initial and boundary conditions. They can be easily reduced to the similar solutions for Burgers, Oldroyd-B, Maxwell, and second-grade and Newtonian fluids. Furthermore, as a check of our calculi, for small values of the corresponding material parameters, their diagrams are almost identical to those corresponding to the known solutions for Newtonian and Oldroyd-B fluids. Finally, the influence of the rheological parameters on the fluid motions, as well as a comparison between models, is graphically illustrated. The non-Newtonian effects disappear in time, and the required time to reach steady-state is the lowest for Newtonian fluids.

scholarly journals Exact solutions for rotational flow of a fractional Maxwell fluid in a circular cylinder

2012 ◽  
Vol 16 (2) ◽  
pp. 345-355 ◽  
Author(s):  
Imran Siddiqu ◽  
Dumitru Vieru
Keyword(s):  
Shear Stress ◽  
Relaxation Time ◽  
Circular Cylinder ◽  
Maxwell Fluid ◽  
Time Dependent ◽  
Constitutive Relationship ◽  
Rotational Flow ◽  
Maxwell Fluids ◽  
Relationship Model ◽  
Fractional Parameter

This paper deals with the rotational flow of a fractional Maxwell fluid in an infinite circular cylinder, due to the torsional variable time-dependent shear stress that is prescribed on the boundary of the cylinder. The fractional calculus approach in the constitutive relationship model of a Maxwell fluid is introduced. The velocity field and the resulting shear stress are determined by means of the Laplace and finite Hankel transforms to satisfy all imposed initial and boundary conditions. The solutions corresponding to ordinary Maxwell fluids as well as those for Newtonian fluids, performing the same motion, are obtained as limiting cases of our general solutions. Finally, the influence of the relaxation time and the fractional parameter on the velocity of the fluid is analyzed by graphical illustrations.

Mkhitar Djrbashian and his contribution to Fractional Calculus

2020 ◽  
Vol 23 (6) ◽  
pp. 1797-1809
Author(s):  
Sergei Rogosin ◽  
Maryna Dubatovskaya
Keyword(s):  
Cauchy Problem ◽  
Fractional Calculus ◽  
Fractional Order ◽  
Approximation Theory ◽  
Fractional Derivatives ◽  
Complex Analysis ◽  
Integral Transforms ◽  
Modern Theory ◽  
Survey Paper ◽  
The Cauchy Problem

Abstract This survey paper is devoted to the description of the results by M.M. Djrbashian related to the modern theory of Fractional Calculus. M.M. Djrbashian (1918-1994) is a well-known expert in complex analysis, harmonic analysis and approximation theory. Anyway, his contributions to fractional calculus, to boundary value problems for fractional order operators, to the investigation of properties of the Queen function of Fractional Calculus (the Mittag-Leffler function), to integral transforms’ theory has to be understood on a better level. Unfortunately, most of his works are not enough popular as in that time were published in Russian. The aim of this survey is to fill in the gap in the clear recognition of M.M. Djrbashian’s results in these areas. For same purpose, we decided also to translate in English one of his basic papers [21] of 1968 (joint with A.B. Nersesian, “Fractional derivatives and the Cauchy problem for differential equations of fractional order”), and were invited by the “FCAA” editors to publish its re-edited version in this same issue of the journal.

Interface Shear Stress of Concrete Beams Strengthened with FRP in Salt Water

2012 ◽  
Vol 446-449 ◽  
pp. 3499-3502
Author(s):  
Chen Zhao ◽  
Pei Yan Huang ◽  
Zhong Song Chen
Keyword(s):  
Shear Stress ◽  
Concrete Beam ◽  
Salt Water ◽  
Interfacial Shear Stress ◽  
Interfacial Properties ◽  
Interfacial Shear ◽  
Interface Shear ◽  
Interface Shear Stress ◽  
Bond Slip ◽  
Relationship Model

Based on existing methods and results of other research, the bond-slip relationship model is given and the distrubition of shear stress of concrete beam strengthened by FRP in salt water is derived. Through a specific example to analyze the distribution of interfacial shear stress, and the different effects caused by different aggressive environment on the interfacial properties. The results show that: 1) Interfacial shear stress will sharply reduce with increasing distance from the end; 2) Different environments have different effects on the interface properties of FRP strengthened beams. Salt water erosion influnce the interfacial properties of FRP strengthened beams significantly.

scholarly journals Research on Rock Creep Characteristics Based on the Fractional Calculus Meshless Method

2018 ◽  
Vol 2018 ◽  
pp. 1-6
Author(s):  
Gang Peng ◽  
Zhanqing Chen ◽  
Jiarui Chen
Keyword(s):  
Fractional Calculus ◽  
Meshless Method ◽  
Test System ◽  
Constitutive Relationship ◽  
Creep Process ◽  
Kelvin Model ◽  
Related Data ◽  
Model Based ◽  
Rock Creep ◽  
Generalized Kelvin Model

The application of fractional calculus in the rheological problems has been widely accepted. In this study, the constitutive relationship of the generalized Kelvin model based on fractional calculus was studied, and the meshless method was introduced so as to derive a new meshless algorithm formula based on the fractional calculus of the generalized Kelvin model. By using the MTS815.02 hydraulic servo rock mechanics test system, the creep test of mudstones is carried out, and the related data of the creep process were obtained. Based on the generalized Kelvin model of fractional calculus, the related creep parameters of the argillaceous sandstone under compression were fitted. The results showed that the solution of the generalized Kelvin model based on fractional calculus was greatly consistent with the numerical method solution. Meanwhile, the meshless algorithm based on fractional calculus had a favorable stability and accuracy.

scholarly journals Global energy fluxes in turbulent channels with flow control

2018 ◽  
Vol 857 ◽  
pp. 345-373 ◽  
Author(s):  
Davide Gatti ◽  
Andrea Cimarelli ◽  
Yosuke Hasegawa ◽  
Bettina Frohnapfel ◽  
Maurizio Quadrio
Keyword(s):  
Reynolds Number ◽  
Shear Stress ◽  
Energy Dissipation ◽  
Velocity Field ◽  
Flow Control ◽  
Reynolds Shear Stress ◽  
Power Input ◽  
Energy Fluxes ◽  
Mean Velocity ◽  
The Mean

This paper addresses the integral energy fluxes in natural and controlled turbulent channel flows, where active skin-friction drag reduction techniques allow a more efficient use of the available power. We study whether the increased efficiency shows any general trend in how energy is dissipated by the mean velocity field (mean dissipation) and by the fluctuating velocity field (turbulent dissipation). Direct numerical simulations (DNS) of different control strategies are performed at constant power input (CPI), so that at statistical equilibrium, each flow (either uncontrolled or controlled by different means) has the same power input, hence the same global energy flux and, by definition, the same total energy dissipation rate. The simulations reveal that changes in mean and turbulent energy dissipation rates can be of either sign in a successfully controlled flow. A quantitative description of these changes is made possible by a new decomposition of the total dissipation, stemming from an extended Reynolds decomposition, where the mean velocity is split into a laminar component and a deviation from it. Thanks to the analytical expressions of the laminar quantities, exact relationships are derived that link the achieved flow rate increase and all energy fluxes in the flow system with two wall-normal integrals of the Reynolds shear stress and the Reynolds number. The dependence of the energy fluxes on the Reynolds number is elucidated with a simple model in which the control-dependent changes of the Reynolds shear stress are accounted for via a modification of the mean velocity profile. The physical meaning of the energy fluxes stemming from the new decomposition unveils their inter-relations and connection to flow control, so that a clear target for flow control can be identified.

The MHD Flows for a Heated Generalized Oldroyd-B Fluid With Fractional Derivative

2010 ◽  
Author(s):  
Yaqing Liu ◽  
Liancun Zheng ◽  
Xinxin Zhang ◽  
Fenglei Zong
Keyword(s):  
Fractional Calculus ◽  
Viscoelastic Fluid ◽  
Mhd Flow ◽  
Hankel Transform ◽  
Constitutive Relationship ◽  
Temperature Fields ◽  
Fractional Partial Differential Equations ◽  
Relation Model ◽  
Velocity And Temperature Fields ◽  
Relationship Of

In this paper, we present a circular motion of magnetohydrodynamic (MHD) flow for a heated generalized Oldroyd-B fluid. The fractional calculus approach is introduced to establish the constitutive relationship of a viscoelastic fluid. The velocity and temperature fields of the flow are described by fractional partial differential equations. Exact analytical solutions of velocity and temperature fields are obtained by using Hankel transform and Laplace transform for fractional calculus. Results for ordinary viscous flow are deduced by making the fractional order of differential tend to one and zero. It is shown that the fractional constitutive relation model is more useful than the conventional model for describing the properties of viscoelastic fluid.

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