New Exact Solutions for an Oldroyd-B Fluid with Fractional Derivatives: Stokes' First Problem
-
Muhammad Jamil
,
Najeeb Alam Khan
Abstract
The first problem of Stokes for an incompressible Oldroyd-B fluid with fractional derivatives is studied using Fourier sine and Laplace transforms. The solutions that have been obtained, unlike the known solutions from the literature, are presented as a sum between the Newtonian solutions and the non-Newtonian contributions. The non-Newtonian contributions, as expected, tend to zero for α = β and λ → λr. Furthermore, the solutions for ordinary Oldroyd-B, fractional and ordinary Maxwell, fractional and ordinary second grade fluid, performing the same motion, are also obtained as limiting cases of general solutions. The present solution for ordinary Oldroyd-B and second grade fluids are verified by comparison with the previously well known results. Finally, the influence of material and fractional parameters on the fluid motion, as well as a comparison among fractional Oldroyd-B, fractional Maxwell, fractional second grade and Newtonian fluids, is also analyzed by graphical illustrations.
©[2013] by Walter de Gruyter Berlin Boston
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Artikel in diesem Heft
- Masthead
- A New Model for Plastic-Viscoelastic Magnetohydrodynamic (MHD) Flow with Radiation Thermal Transfer
- New Exact Solutions for an Oldroyd-B Fluid with Fractional Derivatives: Stokes' First Problem
- A Modified Variational Iteration Method for Nonlinear Oscillators
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- On a Problem of Nonstationary 2D Motion of Micropolar Fluid in the Half-plane Subjected to a Uniform Magnetic Field when Normal Stresses and Tangential Velocities are Given on the Boundary
- Non-equilibrium Shock Structure Calculation with High-order Modified Navier–Stokes Equations
- A New Coupled Fractional Reduced Differential Transform Method for Solving Time Fractional Coupled KdV Equations
- A New Nonlinear Integrable Couplings of Solioton Hierarchy and its Hamiltonian Structure with Kronecker Product
- Control Volume Based Finite Element Method Study of Nano-fluid Natural Convection Heat Transfer in an Enclosure Between a Circular and a Sinusoidal Cylinder
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