Showing papers on "Second-order fluid published in 2015"

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

Abstract: 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 After attaining the steady state, the pressure gradient is suddenly withdrawn and the resulting fluid motion between the parallel plates under the influence of magnetic field is then to be investigated.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.65.7958

Oscillatory MHD Convective Flow of Second Order Fluid Through Porous Medium in a Vertical Rotating Channel in Slip-Flow Regime with Heat Radiation

Abstract: An analysis of an oscillatory magnetohydrodynamic (MHD) convective flow of a second order (viscoelastic), incompressible, and electrically conducting fluid through a porous medium bounded by two infinite vertical parallel porous plates is presented.The two porous plates with slip-flow condition and the no-slip condition are subjected respectively to a constant injection and suction velocity. The pressure gradient in the channel varies periodically with time. A magnetic field of uniform strength is applied in the direction perpendicular to the planes of the plates. The induced magnetic field is neglected due to the assumption of small magnetic Reynolds number. The temperature of the plate with no-slip condition is nonuniform and oscillates periodically with time and temperature difference of the two plates is assumed high enough to induce heat radiation.The entire system rotates in unison about the axis perpendicular to planes of the plates. Adopting complex variable notations, a closed form solution of the problem is obtained. The analytical results are evaluated numerically and then presented graphically to discuss indetail the effects of different parameters entering into the problem. The velocity, temperature and the skin-friction in terms of its amplitude and phase angle have been shown graphically to observe the effects of viscoelastic parameter γ, rotation parameter Ω, suction parameter , Grashof number Gr, Hartmann number M, the pressure A, Prandtl number Pr, Radiation parameter N and the frequency of oscillation .

Numerical Investigation of Unsteady MHD Flow of Second Order Fluid in a Tube of Elliptical Cross-Section on the Porous Boundary

Abstract: Exact solution of an unsteady MHD flow of elasticoviscous fluid through a porous media in a tube of elliptic cross section under the influence of magnetic field and constant pressure gradient has been obtained in this paper. Initially, the flow is generated by a constant pressure gradient. After attaining the steady state, the pressure gradient is suddenly withdrawn and the resulting fluid motion in a tube of elliptical cross section by taking into account of the porosity factor and magnetic parameter of the bounding surface is investigated. The problem is solved in two-stages the first stage is a steady motion in tube under the influence of a constant pressure gradient, the second stage concern with an unsteady motion. The problem is solved employing separation of variables technique. The results are expressed in terms of a non-dimensional porosity parameter, magnetic parameter and elastico-viscosity parameter, which depends on the Non-Newtonian coefficient. The flow parameters are found to be identical with that of Newtonian case as elastic-viscosity parameter, magnetic parameter tends to zero, and porosity tends to infinity. The numerical results were simulated in MATLAB software to analyze the effect of Elastico-viscous parameter, porosity parameter, and magnetic parameter on velocity profile. Boundary conditions were satisfied. It is seen that the effect of elastico-viscosity parameter, porosity parameter and magnetic parameter of the bounding surface has significant effect on the velocity parameter. Keywords—Elastico-viscous fluid, Porous media, Elliptic crosssection, Magnetic parameter, Numerical Simulation.

Fluctuating Flow of a Second Order Fluid between Two Co-Axial Circular Pipes

Abstract: In this paper an analytical solution to the flow of a second order fluid is presented expressing the pressure gradient in the form of Fourier series. The effect of the amplitude coefficient of the mean-velocity for different values of frequency of excitation is shown in different graphs. 2000 Mathematics Subject Classification: 76A05

Unsteady Second order Fluid Flow between Two Oscillating Plates

Abstract: Unsteady flow of second grade fluid problem is examined between two horizontal oscillating parallel plates. Plates are oscillating with same periods. We consider three unsteady fluid flow problems. We use the OHAM method to solve the non-linear problems arising from the modeling. The physical effect of various modeled parameters on the velocity and temperature fields is discussed and their numerical results are presented. The industrial and technological applications of non-Newtonian fluids greatly change from the Newtonian fluids due to their rheological characteristics. These type liquids do not follow the Newton's law of viscosity. Actually, such fluids are significantly used in geophysics, petroleum, chemical, nuclear industries and many others scientific technologies. Since non-Newtonian fluids cannot be totally defined by one of constitutive equation. One of the very important models suggested for non-Newtonian fluids is called the second grade fluid. In past scholars gives the considerable attention to the second grade fluid which is a simplest subclass of differential type non-Newtonian fluids. Second grade fluid was employed to study many problems due to their comparatively simple model. Few recent articles discussed the flow of second grade fluid have been proposed in literature (1-6).

On the Class of Exact Solutions of MHD Layer Fluid Flow of Second Order Type by Creating Sinusoidal Disturbances on the Porous Boundary

Abstract: Exact solution of an incompressible fluid of second order type by causing disturbances in the liquid which is initially at rest due to bottom oscillating sinusoid ally has been obtained in this paper. The results presented are in terms of non-dimensional elastic-viscosity parameter (β) which depends on the non-Newtonian coefficient and the frequency of excitation (σ) of the external disturbance while considering the magnetic parameter (m) and porosity (k) of the medium into account. The flow parameters are found to be identical with that of Newtonian case as β →0 , m→0 and k→∞ .

Flow of a Second Order Fluid through Constricted Tube with Slip Velocity at Wall Using Integral Method

Abstract: Abstract---The steady flow of a second order fluid through constricted tube with slip velocity at wall is modeled and analyzed theoretically. The governing equations are simplified by implying no slip in radial direction. Based on Karman Pohlhausen procedure polynomial solution for axial velocity profile is presented. Expressions for pressure gradient, shear stress, separation and reattachment points, and radial velocity are also calculated. The effect of slip and no slip velocity on magnitude velocity, shear stress, and pressure gradient are discussed and depicted graphically. It is noted that when Reynolds number increases magnitude velocity of the fluid decreases in both slip and no slip conditions. It is also found that the wall shear stress, separation, and reattachment points are strongly affected by Reynolds number.

Gravity Driven Flow of an Unsteady Second Order Fluid Between two Parallel and Vertical Oscillating Plates.

Abstract: The flow of magnetohydrodynamic unsteady second grade fluid problem is examined between two vertical and oscillating parallel plates. The parallel plates are oscillating and the fluid drain down due to gravity. A uniform magnetic field is applied perpendicularly to the plates in the presence of temperature field. The model differential equations are solved analytically by using Optimal Homotopy Asymptotic Method (OHAM). The effect of various physical parameters are studied and discussed.

Instability investigation of creeping viscoelastic flows between the rotating cylinders

Abstract: In this paper, instability in the creeping viscoelastic flow between the rotating cylinders is investigated numerically. Due to the low speed of flow field, the second order fluid (SOF) model is used as the constitutive equation and the governing equations are solved by a second order finite difference method based on the artificial compressibility algorithm in a staggered mesh. The effects of normal stress differences on the flow stability are investigated for a wide range of gap ratios. Unlike the previous studies, the origin and mechanism of flow instability resulted from normal stress differences are investigated in detail. Numerical results indicate that the hoop stress and radial-normal stress components are appeared in viscoelastic flows between the rotating cylinders and they have an important role on the flow stability.