Extended Stokes' First Problem of an Oldroyd-B Fluid for Relatively Moving Half-Planes

Extended Stokes’ First Problem of an Oldroyd-B Fluid for Relatively Moving Half-Planes

An Oldroyd-B fluid suddenly disturbed by relatively moving half-planes is theoretically studied in this paper. This new problem, extended from the traditional Stokes’ problem, recently attracts a great deal of attention due to its potential applications in engineering. Using integral transformations and dividing the original system into two subsystems, the exact solution is derived and shown in...

Extended Stokes ’ problems for relatively moving porous half - planes

Moving Porous Half-Planes

A shear flow motivated by relatively moving half-planes is theoretically studied in this paper. Either the mass influx or the mass efflux is allowed on the boundary. This flow is called the extended Stokes’ problems. Traditionally, exact solutions to the Stokes’ problems can be readily obtained by directly applying the integral transforms to the momentum equation and the associated boundary and...

Stokes first problem for an unsteady MHD fourth-grade fluid in a non-porous half space with Hall currents

The well-known problem of unidirectional plane flow of a fluid in a non-porous half-space due to the impulsive motion of the rigid plane wall it rests upon is discussed in the context of an unsteady MHD fourthgrade fluid in presence of Hall currents. The governing non-linear partial differential equations describing the problem are converted to a system of non-linear ordinary differential equat...

A Dual Mixed Formulation for Non-isothermal Oldroyd–Stokes Problem

We propose a mixed formulation for non-isothermal Oldroyd–Stokes problem where the both extra stress and the heat flux’s vector are considered. Based on such a formulation, a dual mixed finite element is constructed and analyzed. This finite element method enables us to obtain precise approximations of the dual variable which are, for the non-isothermal fluid flow problems, the viscous and poly...