Infinite Porous Plate Research Articles

Some simple flows of a Johnson-Segalman fluid

Unlike most other fluid models, the Johnson-Segalman fluid allows for a non-monotonic relationship between the shear stress and rate of shear in a simple shear flow for certain values of the material parameter. This has been used for explaining a phenomenon such as “spurt”. Here, we study three simple flows of a Johnson-Segalman fluid with a view towards understanding its response characteristics. We find that boundary conditions can have a very interesting effect on the regularity of the solution; changing them continuously leads to solutions that change their regularity. First, we consider the flow through a circular pipe and find solutions that have discontinuous velocity profiles which have been used to explain the phenomenon of “spurt” (cf. [10], [11]). Second, we consider the flow past an infinite porous plate and show that it will not admit solutions which have discontinuous velocity gradients, the solutions being necessarity smooth. Lastly, we study Poiseuille flow in a concentric annulus with porous boundaries. While “spurt” could be explained alternatively by allowing for “stick-slip” at the wall, the Johnson-Segalman model seems particularly suited in describing the appearance of “shear-layers” (cf. [13]).

Numerical analysis of a viscous steady laminar flow due to a mass transfer from a porous plate

Considers the motion of a viscous fluid within the narrow gap under a floating disk above an infinite porous plate. The flow is caused by a uniform blowing from the porous surface. If we ignore edge effects, after scaling the variables, an expression for the vertical component of the velocity is found with two particularities in the sense of an asymptotic expansion and for a self‐similar solution. We obtain an expression for the pressure distribution under the disk. Then, with this solution, Navier‐Stokes equations are reduced into one non‐linear equation of the fourth order with two points boundary conditions. First, we used a development of this equation by Newton’s method. The purpose of this paper is to show that the numerical scheme of quasilinearization gives rapid convergence to solution of this boundary layer problem. The vertical force balance gives the prediction for the height of the disk floating above the porous surface when the mass of the disk is known. Without any previous hypothesis, “TRIO”, a general computer code for thermal and fluid flow analysis developed at the CEA (Commissariat à l’Energie Atomique), confirms our main hypothesis and all our results. These two numerical solutions are well in keeping with the analytical and experimental solutions of Hinch and Lemaitre in 1994.

Radiation and free convection flow through a porous medium

Steady two dimensional free convection flow through a very porous medium bounded by a vertical infinite porous plate by the presence of radiation is condsidered. Expressions for the velocity and temperature are obtained. Effects of the radiation on the velocity field are discussed.

Analytical solutions for free convection flow of a particulate suspension past an infinite vertical surface

Continuum equations governing steady, laminar, free convection flow of a particulate suspension past an infinite porous vertical flat plate are developed. These equation account for particulate viscous effects which are absent from most two-phase flow models. Analytical solutions for inviscid and viscous particle phase of uniform density distribution are obtained. Graphical results for velocity and temperature profiles of both phases based on the analytical solutions are presented and discussed. In addition, tabulated results for the skin-friction coefficients of both phases and the Nusselt number of the fluid phase are shown. A parametric study of some of the physical parameters involved in the problem is conducted to elucidate interesting features of the solutions.

Transient non-Newtonian flow of a suspension with a compressible particle phase

Equations governing transient two-phase fluid-particle laminar flow over an infinite porous flat plate are developed. Both phases are assumed to behave as non-Newtonian power-law fluids. The mathematical model accounts for particle-phase viscous and diffusive effects. The particles are assumed spherical in shape and having a non-uniform density distribution. The resulting governing equations are nondimensionalized and solved numerically subject to appropriate initial and boundary conditions using an iterative, implicit, tri-diagonal finite-difference method. Graphical results for the displacement thicknesses and the skin-friction coefficients for both the fluid and particle phases are presented and discussed to illustrate special trends of the solutions.

96/05057 On MHD flow past an infinite porous plate with variable suction

96/05057 On MHD flow past an infinite porous plate with variable suction

On MHD flow past an infinite porous plate with variable suction

The two-dimensional flow of a viscous incompressible and electrically conducting fluid past an infinite porous plate in the presence of a transverse magnetic field has been considered. The plate moves with constant velocity in the direction of fluid flow. The suction velocity normal to the plate and the free stream velocity field vary exponentially with time. The expressions for the velocity field and the skin-friction have been obtained in non-dimensional form for two cases: (1) exponentially increasing small perturbation and (2) exponentially decreasing small perturbation. It has been concluded that there is a reverse type flow near the surface of the plate when it moves in the opposite direction to that of the flow. The skin-friction when the plate moves in the direction of flow is less than it is when the plate moves in the opposite direction.

Exact solutions for some simple flows of an Oldroyd-B fluid

We present two simple but elegant solutions for the flow of an Oldroyd-B fluid. First, we consider the flow past an infinite porous plate and find that the problem admits an asymptotically decaying solution in the case of suction at the plate, and that in the case of blowing it admits no such solution. Second, we study the longitudinal and torsional oscillations of an infinitely long rod of finite radius. The solutions are found in terms of Bessel functions.

Flow of non-newtonian particulate suspension with a compressible particle phase

Continuum equations for a two-phase fluid-particle flow are developed and applied to the problem of steady, laminar flow over an infinite porous flat plate. Both phases are assumed to behave as non-Newtonian power-law fluids. The effects of particle-particle interaction and diffusion of particles are taken into account in the mathematical model. In addition, the particle phase is assumed to have a non-uniform density distribution. The resulting governing equations are nondimensionalized and solved numerically subject to appropriate boundary conditions using an iterative, implicit finite-difference method. Graphical results for the displacement thicknesses and the skin-friction coefficients for both the fluid and particle phases are presented and discussed to elucidate interesting features of the solutions.

Numerical solutions for the flow of a fluid of grade three past an infinite porous plate

This paper presents a numerical study of the flow of an incompressible fluid of grade three past an infinite porous flat plate, subject to suction at the plate. This flow is governed by a non-linear differential equation that is particularly well suited to demonstrate the power and usefulness of different numerical techniques. In this work, the numerical solutions are obtained using a Runge-Kutta method of fourth order. The accuracy of the method for this problem is demonstrated.

Unsteady Flow of a Power-Law Dusty Fluid With Suction

Equations governing flow of a particulate suspension exhibiting finite volume fraction in non-Newtonian power-law fluids are developed and applied to the problem of unsteady flow past an infinite porous flat plate with suction. Numerical results for small volume fraction for the displacement thicknesses for both phases and the skin-friction coefficient for the fluid phase are obtained using an implicit finite difference scheme and presented graphically to elucidate interesting features of the solutions.

Capillary-gravity waves in the presence of infinite porous plates

The wave motion generated by a porous plate immersed in a non-wetting liquid of infinite depth is investigated. The boundary value problem for the velocity potentials is solved using Taylor's assumption on the plate and a contact-line condition that accounts for the dynamic variation of the angle of contact and the vorticity there. The amplitude of the radiated waves and the energy dissipated are calculated both when the plate is oscillating horizontally and vertically with a prescribed velocity. Also the scattering of a harmonic wave incident normally to the plate is considered and the reflexion and transmission coefficients are obtained.

A problem of a viscoelastic magnetohydrodynamic fluctuating-boundary-layer flow past an infinite porous plate

In this work we study the motion of a two-dimensional incompressible flow of an electrically conducting viscoelastic fluid past an infinite porous flat plate subject to uniform suction in the presence of a transverse uniform magnetic field. The effects of the flow on the temperature of the plate are studied when the plate is thermally insulated, and when it is kept at a constant temperature that is higher than that of the free stream. A method proposed by Lighthill and Stuart is utilized in solving the problem. The effects of various parameters such as the magnetic number, the viscoelastic parameter, and the frequency of the free-stream oscillations on the flow are studied.

Heat transfer analysis of a non-Newtonian fluid past a porous plate

The flow of an incompressible third-grade fluid past an infinite porous plate subject to suction and blowing at the plate is studied numerically. Two distinct heat transfer problems are studied. In the first case, the plate is assumed to be at a higher temperature than the fluid; and in the second case, the plate is assumed to be insulated. The non-dimensional form of the equations are presented, and the velocity and the temperature profiles for various values of the appropriate dimensionless parameters are also given.

Temperature and heat transfer solutions for aeromagnetic dusty-gas flow

Based on temperature and heat transfer solutions derived by Chamkha (1992) for aeromagnetic dusty-gas flows (such as are occurring in many industrial processes), this paper investigates the effect of a transverse magnetic field on the temperature profile, and the wall heat transfer for flow of a dusty gas past an infinite porous flat plate. The fluid phase is assumed to be incompressible and electrically conducting, and the particle phase is assumed to be incompressible and electrically nonconducing; it is also assumed that there is no radiative heat transfer from one particle to another and that the particles do not interact with each other. 6 refs.

Convective heat transfer of a particulate suspension

Exact solutions for the thermal aspect of flow of a particulate suspension past an infinite porous flat plate were obtained. It is found that the presence of particles causes an augmentation in the wall heat transfer coefficient due to thermal energy gain by the fluid phase through the thermal interaction between the two phases. 4 refs.

Pulsated hydromagnetic flow with free-convection currents and mass transfer along a vertical infinite porous plate

The influence of free-convection currents and mass transfer in the case of laminar, non-steady boundary layer is studied here. The fluid is the air, considered incompressible and electrically conductive. The free-stream velocity oscillates about a mean value. A pulsated suction is also taken into account. A second meterial lies in small concentration in the fluid and absorbs part of the radiation. The influence of various parameters (G. M. etc.) on the flow is examined.

Unsteady magnetic boundary-layer flow of power-law non-Newtonian conducting fluid through a porous medium past an infinite porous flat plate

In this paper, the nonsteady flow of non-Newtonian power-law conducting fluid through a porous medium past an infinite porous plate is investigated. The system is stressed by a constant transverse magnetic field. The velocity outside the boundary layer depends exponentially on time. The rheological effects are shown and discussed on the shear stress in terms of rheological parameter of power-law fluid. The approximate solution in a closed form were obtained by using the Galerkin method. Also the effect of the magnetic field and permeability parameter are discussed.

Unsteady hydromagnetic flow through a porous medium between two infinite parallel porous plates with time-varying suction

Unsteady two-dimensional flow of a viscous incompressible and electrical-conducting fluid through a porous medium bounded by two infinite parallel plates under the action of a transverse magnetic field is presented when there is time-varying suction at the plates. The lower plate is at rest while the upper plate is oscillating in its own plane about a constant mean velocity. Expressions for the velocity, fluctuating parts of the velocity, amplitude, and phase of the skin-friction are obtained. The flow phenomenon has been characterized by the parametersK (permeability of the porous medium),N(magnetic parameter) ω(frequency parameter), andA(variable suction parameter) and the role of these parameters on the flow characteristics has been studied.

Hall effects on oscillatory MHD boundary-layer flow under variable suction

The effects of Hall current on the oscillatory hydromagnetic boundary-layer flow under variable suction, past an infinite porous flat plate in the presence of a transverse magnetic field is discussed. The expressions for velocity and skin-friction are obtained and their variations for small and large frequency of oscillations are extensively discussed.