Unsteady MHD Flow of Elastico-Viscous Incompressible Fluid through a Porous Medium between Two Parallel Plates under the Influence of a Magnetic Field

An unsteady flow of elastico-viscous incompressible and electrically conducting fluid through a porous medium between two parallel plates under the influence of transverse magnetic field is examined. Initially, the flow is generated by a constant pressure gradient parallel to the bounding fluids. After attaining the steady state, the pressure gradient is suddenly withdrawn and the resulting fluid motion between the parallel plates under the influence of magnetic field is then to be investigated. The problem is solved in two stages: the first stage is a steady motion between the parallel plates under the influence of a constant pressure gradient and the magnetic parameter. The momentum equation of steady state does not involve the elastic-viscosity parameter; however, the influence Darcian friction would appear in it. The solution of the momentum equation at this stage will be the initial condition for the subsequent flow. The second stage concerns with an unsteady motion for which the initial value for the velocity will be that obtained in stage one together with the no-slip condition on the boundary plates. The problem was solved employing Laplace transformation technique. It was found that the effect of the applied transverse magnetic field has significant contribution on the velocity profiles.Defence Science Journal, Vol. 65, No. 2, March 2015, pp.119-125, DOI:http://dx.doi.org/10.14429/dsj.65.795

Stokes' first problem for some non-Newtonian fluids: Results and mistakes

The well-known problem of unidirectional plane flow of a fluid in a half-space due to the impulsive motion of the plate it rests upon is discussed in the context of the second-grade and the Oldroyd-B non-Newtonian fluids. The governing equations are derived from the conservation laws of mass and momentum and three correct known representations of their exact solutions given. Common mistakes made in the literature are identified. Simple numerical schemes that corroborate the analytical solutions are constructed.Comment: 10 pages, 2 figures; accepted for publication in Mechanics Research Communications; v2 corrects a few typo

Resonant oscillations of a plate in an electrically conducting rotating Johnson-Segalman fluid

AbstractAn analysis of hydromagnetic flow is examined in a semi-infinite expanse of electrically conducting rotating Johnson-Segalman fluid bounded by nonconducting plate in the presence of a transverse magnetic field and the governing equations are modeled first time. The structure of the velocity distribution and the associated hydromagnetic boundary layers are investigated including the case of resonant oscillations. It is shown that unlike the hydrodynamic situation for the case of resonance, the hydromagnetic steady solution satisfies the boundary condition at infinity. The inherent difficulty involved in the hydrodynamic resonance case has been resolved in the presence analysis

Unsteady Hele Shaw Flow of a Conducting Rivlin Ericksen Fluid .

This paper aims to study the unsteady Hele-Shaw flow of conducting Rivlin-Ericksen fluid under the influence of a uniform transverse magnetic field. The study has been carried out when the pressure gradient is (i) proportional to e/sup int/, (ii) zero for t < 0 and equal to a constant for t >= 0, and (iii) proportional to e/sup -nt/. It is interesting to note that the time for the motion to become steady when started from rest(case ii) is of the order ~ 4 s/sup 2/ / where s is the viscoelastic parameter. The rheological equation of the Rivlin-Ericksen fluid is described in section 2. The expressions for velocity components u and v of the fluid in x and y directions are derived in section 3. The effects of magnetic field and viscoelasticity are discussed in section 4

Non-linear differential equations and rotating disc electrodes: Padé approximation technique.

Rotating disc electrodes are preferred devices to analyze electrochemical reactions in electrochemical cells and various rotating machinery such as fans, turbines, and centrifugal pumps. This model contains system of fully coupled and highly non-linear equations. This manuscript outlines the steady state solution of rotating disc flow coupled through the fluid viscosity, to the mass-concentration field of chemical species and heat transfer of power-law fluid over rotating disk. Furthermore, a simple analytical expression (Padé approximation) of velocity component/ self-similar velocity profiles is derived from the short and long distance expression. Our analytical results for all distance are compared with previous small and long distance and numerical solutions (Runge-Kutta method), which are in satisfactory agreement

A mathematical analysis of the hydro-mechanics associated with the Vitros Immunodiagnostic System.

Ortho-Clinical Diagnostics, a Johnson & Johnson company, has developed a new machine called 'Vitros Immunodiagnostic System' which can be used for the diagnosis of a wide range of auto-immune diseases. The design and manufacture of the Vitros Instrument has neither been directed nor supported by mathematical analysis. The aim and purpose of the present dissertation is to set up a working mathematical model of the hydro-mechanics within the instrumentation cycle of the Vitros System. A description of the Vitros Immunodi agnostic System is given in Chapter 1. In Chapter 2, a mathematical model is developed to describe the structure of the mixture within the well. In Chapter 3, dynamical equations are formulated with respect to a moving frame of reference at rest relative to the well. In particular, with reference to two especial states of motion, that of a 'sweep' at constant angular velocity of the outer carousel ring, and that of a 'jiggle' at rapidly fluctuating angular velocity. In the former the equations admit a solution in which the fluid moves as if it were rigid. Whereas, in the latter the equations admit an axially symmetric motion of the mixture. In Chapter 4, the equations describing the primary flow and the (incipient) secondary flow are solved exactly for a hemispherical shaped well. This analytic solution gives a powerful description of the flow, being valid for the whole spectrum of values of the Reynolds number. The analysis shows that for large values of the Reynolds number the flow varies rapidly in the region immediately adjacent to the boundary wall, but elsewhere the flow is approximately a rigid body rotation. In Chapter 5, a similar type analysis is carried out for a cylindrical shaped well. The results obtained run much in parallel (and support) the findings of the previous chapter. Chapter 6 is concerned with the problem of determining the way in which the suspended reagents drift through the patient sample, and of ascertaining the pattern they create when becoming entrapped on the boundary wall. The results are interesting: the reagents have preferred orientation within the flow and result in a preferred coverage of the well boundary wall, and are not uniformly placed as previously anticipated. Finally, some relevant remarks are added in Chapter 7 together with an outline of a (possible) programme of further research