scholarly journals Exact solutions for unsteady axial Couette flow of a fractional Maxwell fluid due to an accelerated shear

2011 ◽  
Vol 16 (2) ◽  
pp. 135-151 ◽  
Author(s):  
Muhammad Athar ◽  
Corina Fetecau ◽  
Muhammad Kamran ◽  
Ahmad Sohail ◽  
Muhammad Imran
Keyword(s):  
Shear Stress ◽  
Positive Real Number ◽  
Fractional Integration ◽  
Maxwell Fluid ◽  
Unsteady Motion ◽  
Positive Real ◽  
Special Cases ◽  
Multiple Integrals ◽  
Similar Solutions ◽  
R Functions

The velocity field and the adequate shear stress corresponding to the flow of a fractional Maxwell fluid (FMF) between two infinite coaxial cylinders, are determined by means of the Laplace and finite Hankel transforms. The motion is produced by the inner cylinder that at time t = 0+ applies a shear stress fta (a ≥ 0) to the fluid. The solutions that have been obtained, presented under series form in terms of the generalized G and R functions, satisfy all imposed initial and boundary conditions. Similar solutions for ordinary Maxwell and Newtonian fluids are obtained as special cases of general solutions. The unsteady solutions corresponding to a = 1, 2, 3, ... can be written as simple or multiple integrals of similar solutions for a = 0 and we extend this for any positive real number a expressing in fractional integration. Furthermore, for a = 0, 1 and 2, the solutions corresponding to Maxwell fluid compared graphically with the solutions obtained in [1–3], earlier by a different technique. For a = 0 and 1 the unsteady motion of a Maxwell fluid, as well as that of a Newtonian fluid ultimately becomes steady and the required time to reach the steady-state is graphically established. Finally a comparison between the motions of FMF and Maxwell fluid is underlined by graphical illustrations.

scholarly journals The analytic solutions for the unsteady rotating flows of the generalized Maxwell fluid between coaxial cylinders

2020 ◽  
Vol 24 (6 Part B) ◽  
pp. 4041-4048
Author(s):  
Fan Wang ◽  
Wang-Cheng Shen ◽  
Jin-Ling Liu ◽  
Ping Wang
Keyword(s):  
Shear Stress ◽  
Maxwell Fluid ◽  
Analytic Solutions ◽  
Rotating Flows ◽  
Circular Cylinders ◽  
Rotating Flow ◽  
Coaxial Cylinders ◽  
Similar Solutions ◽  
Generalized Maxwell Fluid ◽  
R Functions

In this paper, we consider the unsteady rotating flow of the generalized Maxwell fluid with fractional derivative model between two infinite straight circular cylinders, where the flow is due to an infinite straight circular cylinder rotating and oscillating pressure gradient. The velocity field is determined by means of the combine of the Laplace and finite Hankel transforms. The analytic solutions of the velocity and the shear stress are presented by series form in terms of the generalized G and R functions. The similar solutions can be also obtained for ordinary Maxwell and Newtonian fluids as limiting cases.

Exact Solutions for the Flow of Fractional Maxwell Fluid in Pipe-Like Domains

2016 ◽  
Vol 8 (5) ◽  
pp. 784-794 ◽  
Author(s):  
Vatsala Mathur ◽  
Kavita Khandelwal
Keyword(s):  
Shear Stress ◽  
Velocity Field ◽  
Newtonian Fluid ◽  
Outer Cylinder ◽  
Fluid Motion ◽  
Maxwell Fluid ◽  
Circular Cylinders ◽  
Generalized Solutions ◽  
Special Cases ◽  
Graphical Illustration

AbstractThis paper presents an analysis of unsteady flow of incompressible fractional Maxwell fluid filled in the annular region between two infinite coaxial circular cylinders. The fluid motion is created by the inner cylinder that applies a longitudinal time-dependent shear stress and the outer cylinder that is moving at a constant velocity. The velocity field and shear stress are determined using the Laplace and finite Hankel transforms. Obtained solutions are presented in terms of the generalized G and R functions. We also obtain the solutions for ordinary Maxwell fluid and Newtonian fluid as special cases of generalized solutions. The influence of different parameters on the velocity field and shear stress are also presented using graphical illustration. Finally, a comparison is drawn between motions of fractional Maxwell fluid, ordinary Maxwell fluid and Newtonian fluid.

General Solutions for the Unsteady Flow of Second-Grade Fluids over an Infinite Plate that Applies Arbitrary Shear to the Fluid

2011 ◽  
Vol 66 (12) ◽  
pp. 753-759 ◽  
Author(s):  
Constantin Fetecau ◽  
Corina Fetecau ◽  
Mehwish Rana
Keyword(s):  
Shear Stress ◽  
Unsteady Flow ◽  
Infinite Plate ◽  
Unsteady Motion ◽  
Newtonian Fluids ◽  
Second Grade ◽  
Moving Plate ◽  
General Solutions ◽  
Similar Solutions ◽  
Second Grade Fluids

General solutions corresponding to the unsteady motion of second-grade fluids induced by an infinite plate that applies a shear stress ƒ (t) to the fluid are established. These solutions can immediately be reduced to the similar solutions for Newtonian fluids. They can be used to obtain known solutions from the literature or any other solution of this type by specifying the function ƒ (.). Furthermore, in view of a simple remark, general solutions for the flow due to a moving plate can be developed.

EXACT SOLUTIONS FOR THE POISEUILLE FLOW OF A GENERALIZED MAXWELL FLUID INDUCED BY TIME-DEPENDENT SHEAR STRESS

2010 ◽  
Vol 51 (4) ◽  
pp. 416-429 ◽  
Author(s):  
W. AKHTAR ◽  
CORINA FETECAU ◽  
A. U. AWAN
Keyword(s):  
Shear Stress ◽  
Velocity Field ◽  
Circular Cylinder ◽  
Poiseuille Flow ◽  
Fluid Motion ◽  
Maxwell Fluid ◽  
Time Dependent ◽  
Infinite Cylinder ◽  
Similar Solutions ◽  
Generalized Maxwell Fluid

AbstractThe Poiseuille flow of a generalized Maxwell fluid is discussed. The velocity field and shear stress corresponding to the flow in an infinite circular cylinder are obtained by means of the Laplace and Hankel transforms. The motion is caused by the infinite cylinder which is under the action of a longitudinal time-dependent shear stress. Both solutions are obtained in the form of infinite series. Similar solutions for ordinary Maxwell and Newtonian fluids are obtained as limiting cases. Finally, the influence of the material and fractional parameters on the fluid motion is brought to light.

Effect of side walls on the motion of a viscous fluid induced by an infinite plate that applies an oscillating shear stress to the fluid

Open Physics ◽  
2011 ◽  
Vol 9 (3) ◽  
Author(s):  
Constantin Fetecau ◽  
Dumitru Vieru ◽  
Corina Fetecau
Keyword(s):  
Shear Stress ◽  
Steady State ◽  
Viscous Fluid ◽  
Fourier Transforms ◽  
Fluid Motion ◽  
Infinite Plate ◽  
Unsteady Motion ◽  
Side Walls ◽  
Oscillating Shear Stress ◽  
Similar Solutions

AbstractThe velocity field corresponding to the unsteady motion of a viscous fluid between two side walls perpendicular to a plate is determined by means of the Fourier transforms. The motion of the fluid is produced by the plate which after the time t = 0, applies an oscillating shear stress to the fluid. The solutions that have been obtained, presented as a sum of the steady-state and transient solutions satisfy the governing equation and all imposed initial and boundary conditions. In the absence of the side walls they are reduced to the similar solutions corresponding to the motion over an infinite plate. Finally, the influence of the side walls on the fluid motion, the required time to reach the steady-state, as well as the distance between the walls for which the velocity of the fluid in the middle of the channel is unaffected by their presence, are established by means of graphical illustrations.

scholarly journals GRAPH ORIENTATION ALGORITHMS TO MINIMIZE THE MAXIMUM OUTDEGREE

2007 ◽  
Vol 18 (02) ◽  
pp. 197-215 ◽  
Author(s):  
YUICHI ASAHIRO ◽  
EIJI MIYANO ◽  
HIROTAKA ONO ◽  
KOUHEI ZENMYO
Keyword(s):  
Approximation Algorithm ◽  
Real Number ◽  
Positive Real Number ◽  
Weighted Graph ◽  
Combinatorial Formula ◽  
Input Graph ◽  
Positive Real ◽  
Graph Orientation ◽  
Special Cases ◽  
Unweighted Graph

This paper studies the problem of orienting all edges of a weighted graph such that the maximum weighted outdegree of vertices is minimized. This problem, which has applications in the guard arrangement for example, can be shown to be [Formula: see text]-hard generally. In this paper we first give optimal orientation algorithms which run in polynomial time for the following special cases: (i) the input is an unweighted graph, and (ii) the input graph is a tree. Then, by using those algorithms as sub-procedures, we provide a simple, combinatorial, [Formula: see text]-approximation algorithm for the general case, where wmax and wmin are the maximum and the minimum weights of edges, respectively, and ε is some small positive real number that depends on the input.

A note on fractional integral operator associated with multiindex Mittag-Leffler functions

Filomat ◽  
2016 ◽  
Vol 30 (7) ◽  
pp. 1931-1939 ◽  
Author(s):  
Junesang Choi ◽  
Praveen Agarwal
Keyword(s):  
Integral Operator ◽  
Fractional Calculus ◽  
Fractional Integral ◽  
Fractional Integration ◽  
Fractional Integral Operator ◽  
Integration Formula ◽  
Special Cases

Recently Kiryakova and several other ones have investigated so-called multiindex Mittag-Leffler functions associated with fractional calculus. Here, in this paper, we aim at establishing a new fractional integration formula (of pathway type) involving the generalized multiindex Mittag-Leffler function E?,k[(?j,?j)m;z]. Some interesting special cases of our main result are also considered and shown to be connected with certain known ones.

scholarly journals Finding of principle square root of a real number by using interpolation method

2018 ◽  
Vol 7 (1) ◽  
pp. 77-83
Author(s):  
Rajendra Prasad Regmi
Keyword(s):  
Real Number ◽  
Positive Real Number ◽  
Interpolation Method ◽  
Square Root ◽  
Real Numbers ◽  
Positive Real ◽  
Unknown Quantity ◽  
Square Roots

There are various methods of finding the square roots of positive real number. This paper deals with finding the principle square root of positive real numbers by using Lagrange’s and Newton’s interpolation method. The interpolation method is the process of finding the values of unknown quantity (y) between two known quantities.

Some remarks on the solvability of non-local elliptic problems with the Hardy potential

2014 ◽  
Vol 16 (04) ◽  
pp. 1350046 ◽  
Author(s):  
B. Barrios ◽  
M. Medina ◽  
I. Peral
Keyword(s):  
Real Number ◽  
Sobolev Inequality ◽  
Positive Real Number ◽  
Fractional Power ◽  
Existence Of Solution ◽  
Sharp Constant ◽  
Hardy Potential ◽  
Positive Real ◽  
Existence And Multiplicity ◽  
Non Local

The aim of this paper is to study the solvability of the following problem, [Formula: see text] where (-Δ)s, with s ∈ (0, 1), is a fractional power of the positive operator -Δ, Ω ⊂ ℝN, N > 2s, is a Lipschitz bounded domain such that 0 ∈ Ω, μ is a positive real number, λ < ΛN,s, the sharp constant of the Hardy–Sobolev inequality, 0 < q < 1 and [Formula: see text], with αλ a parameter depending on λ and satisfying [Formula: see text]. We will discuss the existence and multiplicity of solutions depending on the value of p, proving in particular that p(λ, s) is the threshold for the existence of solution to problem (Pμ).

Ultradiversities and their spherical completeness

2020 ◽  
Vol 26 (2) ◽  
pp. 231-240
Author(s):  
Gholamreza H. Mehrabani ◽  
Kourosh Nourouzi
Keyword(s):  
Real Number ◽  
Finite Subset ◽  
Positive Real Number ◽  
Metric Spaces ◽  
Nonexpansive Mappings ◽  
Ultrametric Spaces ◽  
Positive Real

AbstractDiversities are a generalization of metric spaces which associate a positive real number to every finite subset of the space. In this paper, we introduce ultradiversities which are themselves simultaneously diversities and a sort of generalization of ultrametric spaces. We also give the notion of spherical completeness for ultradiversities based on the balls defined in such spaces. In particular, with the help of nonexpansive mappings defined between ultradiversities, we show that an ultradiversity is spherically complete if and only if it is injective.

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