The Rayleigh–Stokes problem for an edge in a generalized Oldroyd-B fluid

Jamil, Muhammad Kamran; Fetecău, Constantin; Vieru, Dumitru

doi:10.1007/s00033-008-8055-5

Cited by 60 publications

(47 citation statements)

References 18 publications

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“…Assume u, Au ∈ C(R + , X). Then, integrating both sides of the governing equation in (1), by the use of (5) and the identity (J 1−α t Au)(0) = 0, we obtain:…”

Section: Integral Reformulation Of the Problemmentioning

confidence: 99%

“…For example, if the operator A is some realization of the Laplace operator, then Problem (1) is the Rayleigh-Stokes problem for a generalized second-grade fluid; see e.g., [1][2][3]. Exact solutions of this problem in the form of eigenfunction expansion on a bounded space domain are obtained in [4,5].…”

Section: Introductionmentioning

confidence: 99%

“…3) has been successfully applied to inverse problems [17], for asymptotic analysis of diffusion wave equations [18], for the study of stochastic solutions [19], semilinear equations of fractional order [20], systems of fractional order equations [21], nonlocal fragmentation models with the Michaud time derivative [22], etc. This gives the author the motivation to present an analogous principle for Problem (1).…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Subordination Principle for a Class of Fractional Order Differential Equations

Bazhlekova

2015

Mathematics

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The fractional order differential equationis studied, where A is an operator generating a strongly continuous one-parameter semigroup on a Banach space X, D α t is the Riemann-Liouville fractional derivative of order α ∈ (0, 1), γ > 0 and f is an X-valued function. Equations of this type appear in the modeling of unidirectional viscoelastic flows. Well-posedness is proven, and a subordination identity is obtained relating the solution operator of the considered problem and the C 0 -semigroup, generated by the operator A. As an example, the Rayleigh-Stokes problem for a generalized second-grade fluid is considered.

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“…Assume u, Au ∈ C(R + , X). Then, integrating both sides of the governing equation in (1), by the use of (5) and the identity (J 1−α t Au)(0) = 0, we obtain:…”

Section: Integral Reformulation Of the Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Subordination Principle for a Class of Fractional Order Differential Equations

Bazhlekova

2015

Mathematics

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“…The main advantage of using this kind of fluids is it can predict the stress relaxation whilst other differential-type fluids cannot predict such effects. Maxwell fluid widely used in the field of viscoelastic fluid in where the relaxation time (dimensionless) is insignificant however, it's beneficial for significant relaxation time in concentrated polymeric fluids of low molecular weight Ibáñez et al (2016) and Fetecau et al (2003). Khan et al investigated MHD heat and mass transfer axisymmetric chemically reactive Maxwell fluid flow of driven by exothermal and isothermal stretching disks.…”

Section: Introductionmentioning

confidence: 99%

Chemically Reactive Viscoelastic Fluid Flow in Presence of Nano Particle Through Porous Stretching Sheet

Arifuzzaman¹,

Hossain²,

Roy³

et al. 2017

Frontiers in Heat and Mass Transfer

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Present study concerned with the theoretical work with numerical investigation of MHD transient naturally convective and higher order chemically reactive viscoelastic fluid with nano-particle flow through a vertical porous stretching sheet with the effects of heat generation and radiation absorption. A boundary layer approximation is carried out to develop a flow model representing time dependent momentum, energy, and concentration equations. The governing model equations in partial differential equations (PDEs) form were transformed into a set of nonlinear ordinary differential equation (ODEs) by using non-similar technique. Explicit Finite Difference Method (EFDM) was employed by implementing an algorithm in Compaq Visual Fortran 6.6a to solve the obtained set of nonlinear coupled ODEs. For optimizing the system parameter and accuracy of the system, the stability and convergence analysis (SCA) was carried out. It was observed that with initial boundary conditions, for 0.005

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“…Khan et al [9][10][11] found (i) Exact solution for MHD flow of a generalized Oldroyd-B fluid with modified Darcy's law, (ii) Influence of Hall current on the flows of a generalized Oldroyd-B fluid in a porous space and (iii) New exact solutions of magnetohydrodynamic flows of an Oldroyd-B fluid. Fetecau et al [12,13] analyzed the problem of unsteady flow of an Oldroyd-B fluid induced by the impulsive motion of a plate between two side walls perpendicular to the plate in one paper while in the other they described the Rayleigh-Stokes problem for an edge in a generalized Oldroyd-B fluid. Tong et al [14] obtained exact solutions for the unsteady rotational flow of a non-Newtonian fluid in an annular pipe.…”

Section: Introductionmentioning

confidence: 99%

On Hydromagnetic Flow of an Oldroyd-B Fluid Between Two Oscillating Plates

Ghosh

Datta

Sen

2015

Int. J. Appl. Comput. Math

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An initial value investigation is made of the motion of an incompressible, viscoelastic, electrically conducting Oldroyd-B fluid bounded by two infinite rigid nonconducting plates. The flow is generated impulsively from rest in the fluid due to rectilinear oscillations of given frequencies superimposed on the plates in their own planes in presence of an external magnetic field acting transversely to the plates. The operational method is used to derive exact solutions for the fluid velocity and the shear stress on the walls. The quantitative evaluation of the results is considered when two plates oscillate in phase but with different frequencies. The results are shown graphically for different time periods of oscillations of the plates which represent the cases: (i) the lower plate oscillates with a time period less than the upper, (ii) both the plates oscillate with the same time period and (iii) the lower plate oscillates with a time period grater than the upper. It is seen that the effect of fluid elasticity on the flow depends on the advancing and retarding motion of the plates. On the other hand, the magnetic field damps the fluid motion for all values of the time period of oscillations of the plates. The drag on the plates, for small and large time, are shown graphically when the time period of oscillation of the lower plate is small. For small values of time, the drag on the lower plate is negative with the amplitude decreasing continuously till the oscillations occur from moderately large values of time. Similar phenomenon also occurs for the drag which is positive at the upper plate for small values of time. In all cases, the amount of drag on the plates increases with the increase of the elasticity of the fluid and the magnetic field. Some particular results for the fluid velocity are derived as special cases of the present solution.

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The Rayleigh–Stokes problem for an edge in a generalized Oldroyd-B fluid

Cited by 60 publications

References 18 publications

Subordination Principle for a Class of Fractional Order Differential Equations

Subordination Principle for a Class of Fractional Order Differential Equations

Chemically Reactive Viscoelastic Fluid Flow in Presence of Nano Particle Through Porous Stretching Sheet

On Hydromagnetic Flow of an Oldroyd-B Fluid Between Two Oscillating Plates

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