A Beale-Kato-Madja breakdown criterion for an Oldroyd-B fluid in the creeping flow regime

A Beale-Kato-Madja Criterion for Magneto-Micropolar Fluid Equations with Partial Viscosity

Transient Electro-osmotic Slip Flow of an Oldroyd-B Fluid with Time-fractional Caputo-Fabrizio Derivative

In this article, the electro-osmotic flow of Oldroyd-B fluid in a circular micro-channel with slip boundary condition is considered. The corresponding fractional system is represented by using a newly defined time-fractional Caputo-Fabrizio derivative without singular kernel. Closed form solutions for the velocity field are acquired by means of Laplace and finite Hankel transforms. Additionally...

A note on the flow induced by a constantly accelerating edge in an Oldroyd-B fluid

Analytical expressions for the velocity field and the tangential stresses that are induced due to a constantly accelerating edge in an Oldroyd-B fluid have been established for all values of material constants. The solutions that have been obtained satisfy the governing differential equations and all the imposed initial and boundary conditions. These solutions reduce to those for the Maxwell, s...

The Beale-Kato-Majda criterion to the 3D Magneto-hydrodynamics equations

Here u, b describe the flow velocity vector and the magnetic field vector respectively, p is a scalar pressure, ν > 0 is the kinematic viscosity and η > 0 is the magnetic diffusivity, while u0 and b0 are the given initial velocity and initial magnetic field respectively, with ∇ · u0 = ∇ · b0 = 0. If ν = η = 0, (1.1) is called the ideal MHD equations. Using the standard energy method, it can be ...

A note on an unsteady flow of an Oldroyd-B fluid

The laminar flow of a number of fluids such as polymeric liquids, food products, paints, slurries, foams, and so forth cannot be adequately described by the help of the classical linearly viscous Newtonian model. Thus, there is a need to have at hand an arsenal of non-Newtonian fluid models and over the past several decades a variety of models have been developed. While the fluids of the differ...