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and an exponentially accelerate plate where no slip hypothesis between the burgers’ fluid and an exponential plate is no longer valid.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.

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.

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.

ROTATING FLOWOF A GENERALIZED BURGERS' FLUID WITH SLIP CONDITION

2010 ◽  
Vol 13 (9) ◽  
pp. 839-845 ◽  
Author(s):  
Tasawar Hayat ◽  
S. Najam ◽  
S. Asghar
Keyword(s):  
Slip Condition ◽  
Burgers Fluid

scholarly journals A remark on local fractional calculus and ordinary derivatives

2016 ◽  
Vol 14 (1) ◽  
pp. 1122-1124 ◽  
Author(s):  
Ricardo Almeida ◽  
Małgorzata Guzowska ◽  
Tatiana Odzijewicz
Keyword(s):  
Fractional Calculus ◽  
Fractional Derivative ◽  
Short Note ◽  
General Definition ◽  
Local Fractional Derivative ◽  
Fundamental Properties ◽  
Local Fractional Calculus ◽  
Definition Of

AbstractIn this short note we present a new general definition of local fractional derivative, that depends on an unknown kernel. For some appropriate choices of the kernel we obtain some known cases. We establish a relation between this new concept and ordinary differentiation. Using such formula, most of the fundamental properties of the fractional derivative can be derived directly.

Half-lives of spherical proton emitters within the framework of fractional calculus

2014 ◽  
Vol 23 (09) ◽  
pp. 1450044 ◽  
Author(s):  
Abdullah Engin Çalik ◽  
Hüseyin Şirin ◽  
Hüseyin Ertik ◽  
Buket Öder ◽  
Mürsel Şen
Keyword(s):  
Fractional Calculus ◽  
Fractional Derivative ◽  
Nuclear Structure ◽  
Caputo Fractional Derivative ◽  
Half Life ◽  
Nuclear Decay ◽  
Life Values ◽  
Derivative Order

In this paper, the half-life values of spherical proton emitters such as Sb , Tm , Lu , Ta , Re , Ir , Au , Tl and Bi have been calculated within the framework of fractional calculus. Nuclear decay equation, related to this phenomenon, has been resolved by using Caputo fractional derivative. The order of fractional derivative μ being considered is 0 < μ ≤ 1, and characterizes the fractality of time. Half-life values have been calculated equivalent with empirical ones. The dependence of fractional derivative order μ on the nuclear structure has also been investigated.

The bouncing ball and the Grünwald-Letnikov definition of fractional derivative

2021 ◽  
Vol 24 (4) ◽  
pp. 1003-1014
Author(s):  
J. A. Tenreiro Machado
Keyword(s):  
Fractional Calculus ◽  
Fractional Derivative ◽  
Fractional Order ◽  
Restitution Coefficient ◽  
Classical Physics ◽  
Bouncing Ball ◽  
Mechanical Experiment ◽  
Fractional Models ◽  
Definition Of

Abstract This paper proposes a conceptual experiment embedding the model of a bouncing ball and the Grünwald-Letnikov (GL) formulation for derivative of fractional order. The impacts of the ball with the surface are modeled by means of a restitution coefficient related to the coefficients of the GL fractional derivative. The results are straightforward to interpret under the light of the classical physics. The mechanical experiment leads to a physical perspective and allows a straightforward visualization. This strategy provides not only a motivational introduction to students of the fractional calculus, but also triggers possible discussion with regard to the use of fractional models in mechanics.

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.

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.

scholarly journals Analysis of dynamics variation against thixotropic parameter’s preferential range

2018 ◽  
Vol 45 (2) ◽  
pp. 231-251
Author(s):  
Nazish Shahid
Keyword(s):  
Shear Stress ◽  
Pressure Gradient ◽  
Flow Rate ◽  
Axial Velocity ◽  
Fluid Model ◽  
Current Model ◽  
Velocity Shear ◽  
Structural Parameter ◽  
Velocity Flow ◽  
Analysis Of Dynamics

Variation in the dynamics of a steady-state blood flow through a stenosed tapered artery has been investigated corresponding to changes in thixotropic parameter ? over the range [0,1]. To probe the role of parameter ? and differentiate the current model from other known non-Newtonian models, expressions of axial velocity, shear stress, wall shear stress and flow rate have been calculated depending upon this parameter and pressure gradient. Also, pressure gradient has been deduced uniquely with the help of the continuity equation. Our choice of calculating pressure gradient has led to obtaining shear stress such that its dependence on the structural parameter of our model, unlike most available results, motivates for further investigation. The simultaneous effects of varying yield stress and parameter ? on axial velocity, flow resistance and flow rate have been studied such that the differences between the Herschel?Bulkley fluid model and our current model can be pointed out. To validate the suitability of our model and some results in history, we have also obtained limiting results for particular values of ?.

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