MHD combined free and forced convection flow through two parallel porous walls

Summary The flow of a viscous conducting fluid between two parallel plates of infinite length (one of which is at rest and the other moving parallel to itself with a linear axial temperature variation) under the influence of a uniform transverse magnetic field is considered. It is assumed that the fluid is injected into the channel through the lower wall and sucked from the channel through the upper wall with the same velocityv ₀. The velocity and temperature distributions, the coefficient of skin friction and the rate of heat transfer coefficient are evaluated. The effects of magnetic parameterM, the suction Reynolds numberR, the Grashoff numberG and Binkmann numberB on the above mentioned physical quantities are investigated.With 21 Figures     

MHD flow and heat transfer in a channel bounded by a shrinking sheet and a plate with a porous substrate

This research is concerned with heat transfer and an MHD flow of a viscous incompressible electrically conducting fluid in a channel bounded by a shrinking sheet and an impermeable plate. A fluid-saturated porous substrate of a very low permeability is attached to the impermeable plate. The flow in the channel is induced by the upper shrinking sheet, where a constant suction is imposed. By introducing the similarity transformations, the governing partial differential equations for the flow and heat transfer are transformed to ordinary differential equations which are solved analytically by using the perturbation series method for a small shrinking parameter. Expressions for the velocity distribution, temperature field, skin friction, and heat transfer rate are obtained, and numerical computations are carried out for various parameters. The results are displayed graphically and discussed.     

Start-up flow in a porous medium channel

Summary The transient fluid motion in a porous medium channel is considered. Frictional resistance induced by the solid matrix and the channel walls is accounted for by a Darcian body force and a viscous shear stress, respectively. The adopted mathematical model leads to a one-parameter problem, in which the channel half-widthh, the porosity and the permeabilityK combine into a shape parameterA=(h ²/K)^1/2. Exact analytical solutions in terms of infinite series expansions are provided both for the start-up flow following the sudden imposition of a constant pressure gradient and for the transient motion induced by an instantaneously imposed flow rate. Time histories of the centerline velocity and the wall friction are presented, together with time-varying velocity profiles. It is observed that the start-up time required to reach a steady state is significantly reduced in the less porous channels, and this reduction is more pronounced when the start-up flow is driven by a pressure gradient than if the transient motion is forced by an imposed flow rate.     

Motion of a binary gas mixture in a porous membrane with a straight channel

The diffusional baric effect at a porous barrier with a straight channel is investigated theoretically and experimentally with an arbitrary ratio of the channel and pore diameter to the free path length of molecules of the gas mixture.Notation l, R length and radius of membrane - r characteristic pore size - r₀ radius of straight channel - N, r_s number of channels of model set of capillaries per unit area of the porous medium and their radius - mean free path length - _iz ^ch, _iz ^p, _iz ^M projection of mean velocity of motion of molecules of the i-th component in the channel, porous medium, and membrane, respectively, onto the membrane axis - p, T, n pressure, temperature, and number density of mixture particles - m_i, d_i mass and diameter of molecules of the i-th component - c_i concentration of i-th component of mixture - ₁₂, _i viscosity of mixture and its i-th component, respectively - D₁₂, mutual diffusion coefficient and diffusional-slip coefficient - k Boltzmann constant - S^ch, S^P, S^M cross-sectional area of channel, porous medium, and membrane - Q^ch, Q^P, Q^M volume flow rate of gas mixture through channel, porous medium, and membrane - Q^e experimental volume flow rate of gas mixture - Kn^P, Kn^ch Knudsen number in pores and in channel - ₁₂P, ₁₂ ^ch inverse Knudsen number in pores and in channel - porosity - p_m, t_m maximum magnitude of baric effect and time for its attainment - V chamber volume Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 54, No. 5, pp. 725–732, May, 1988.     

Stokes flow through a zig-zag channel

Summary Stokes flow through a zig-zag channel is studied by the efficient method of eigenfunction expansion and collocation. The mixed boundary conditions are determined using symmetry considerations. Streamlines, velocity and pressure distributions are found. The effect of a single corner is extrapolated. In comparison with a straight channel, locally the corners increase flow, both in longitudinal and transverse directions of the corrugations.     

Investigation of MHD Go-water nanofluid flow and heat transfer in a porous channel in the presence of thermal radiation effect

In this paper, flow and heat transfer of MHD Go-water nanofluid between two parallel flat plates in the presence of thermal radiation are studied. One of plates is externally heated and cooled by coolant injection through the other plate, which also expands or contracts with time. A similarity transformation is used to transmute the governing momentum and energy equations into non-linear ordinary differential equations with the appropriate boundary conditions. The obtained non-linear ordinary differential equations are solved by Duan–Rach Approach (DRA). This method allows us to find a solution without using numerical methods to evaluate the undetermined coefficients. This method modifies the standard Adomian Decomposition Method by evaluating the inverse operators at the boundary conditions directly. The impacts of various parameters such as the Reynolds number, the expansion ratio, the magnetic parameter, the power law index, the solid volume fraction and the radiation parameter are investigated on the velocity and temperature. Furthermore, the value of the Nusselt number is calculated and presented through figures. The results indicate that the temperature profile and the Nusselt number have a direct relationship with the solid volume fraction and have an inverse relationship with the radiation parameter. In addition, the limiting cases are gained and found to be in an excellent agreement with the previous works.     

Magnetohydrodynamic poiseuille flow through a porous medium

Abstract

This paper is concerned with formulating equations for the flow of an electrically conducting fluid through a non‐conducting porous medium with non‐porous and non‐conducting boundaries. Equations are developed for the general case of the flow of a solid‐fluid suspensions; flow through a porous medium is treated as a special case by letting the velocity of the particle phase goes to zero. Two cases are considered. Exact solution is obtained for the case of flow between parallel plates, but for flow in pipes of square and circular cross sections, the equations have to be solved numerically. The numerical technique developed can treat elliptical cross sections as well. The flow in all cases is assumed to be steady, laminar, incompressible, viscous, and fully developed. The results are presented in terms of a parameter which measures the resistance of the porous medium.     

MHD rotating flow of a third-grade fluid on an oscillating porous plate

Summary The rotating flow of a third-grade fluid on an oscillating porous plate in the presence of a transverse magnetic field is considered. An analytic solution of the governing nonlinear boundary layer equation is obtained. Expressions for the velocity profile are established. It is found that an external magnetic field has the same effect on the flow as the material parameters of the fluid. Further the symmetric and asymmetric nature of the solutions is discussed.     

Effect of the aspect ratio on the flow characteristics of magnetohydrodynamic (MHD) third grade fluid flow through a rectangular channel

The magnetohydrodynamic (MHD) flow of a third grade fluid through a rectangular channel, considering the effect of aspect ratio, has been investigated. The flow considered is steady, laminar, incompressible and hydro-dynamically fully developed. The equation, describing the flow, is a highly non-linear partial differential equation (PDE) with remote possibility of having an exact solution and even numerical solution also is very difficult to obtain. A combination of the homotopy perturbation method (HPM) and integral method (IM) has been employed to solve the non-linear PDE which is scarce in open literature. The results of the present study are compared with the results obtained by the least square method (LSM) of the MHD third grade fluid flow through a rectangular channel, without the effect of aspect ratio and are found to be in close agreement. The results indicate that the flow field is significantly affected by the aspect ratio which should be considered for practical applications. In all the available literatures of the third grade fluid flow, the aspect ratio effect is neglected and this simplifying assumption reduces the highly complicated non-linear PDE to a non-linear ordinary differential equation (ODE). The novelty of the subject work lies in the inclusion of the effects of aspect ratio in the governing equation describing the flow of a third grade fluid through a channel and solving this by a combined analytical method (HPM and IM). Further, the effects of the Hartmann number and non-Newtonian third grade fluid parameter on the flow filed are discussed.     

Rarefied gas flow through a zigzag channel

A rarefied gas flow through a channel of zigzag shape is calculated over the wide range of the gas rarefaction and for several values of the aspect ratio applying the linearized kinetic equation. In the hydrodynamic flow regime, the kinetic solution is compared with that obtained from the Stokes equation. An approach to calculate a flow rate through a chain composed from an arbitrary number of zigzags is proposed. It was found that in some situations, the flow rate through a zigzag channel is higher than that trough a straight channel of the same length.     

Elastic-plastic flow through a converging conical channel

Summary The flow of an incompressible elastic-perfectly plastic solid through a rough converging conical channel is considered. A solution is obtained using theMises yield condition and thePrandtl-Reuss equations.

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Elastisch-plastische Strömung durch einen konvergierenden kegelförmigen Kanal

Zusammenfassung Es wird die Strömung eines inkompressiblen, ideal elastisch-plastischen Stoffes durch einen rauhen, sich kegelig verengenden Kanal betrachtet. Unter Benützung derMisesschen Fließbedingung und derPrandtl-Reussschen Gleichungen wird eine Lösung erhalten.

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With 6 Figures     

Stability of fluid flow in a plane channel with uniform injection or suction through porous walls

The stability of laminar flow in a channel with porous walls is analyzed within the scope of the linear theory.Notation x distance from entrance cross section - y transverse coordinate measured from axis - u_x, u_y longitudinal and transverse velocity components of main flow - h half-width of channel - kinematic viscosity coefficient - U₀ average velocity in entrance cross section - V suction or injection rate (positive for suction) - U=U₀–V_x/h local average velocity - amplitude of flow disturbances - wave number - c complex phase velocity of disturbances - c_r real propagation velocity of disturbances, =y/h - Re=Uh/ Reynolds number of main flow - R=Vh/ injection or suction Reynolds number - m=U/¦V¦ injection rate parameter Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 41, No. 3, pp. 436–440, September, 1981.     

Unsteady free convective flow through a porous medium

Unsteady 2-dimensional free-convective flow through a porous medium bounded by an infinite vertical plate is considered, when the temperature of the plate is oscillating with the time about a constant non-zero mean value. An analytical solution for the velocity field is derived and the effects of K (permeability parameter) and ω (parameter of frequency) on the velocity field are discussed.     

Mathematical modeling of heat and mass transfer effects on MHD peristaltic propulsion of two-phase flow through a Darcy-Brinkman-Forchheimer porous medium

This article deals with the combined effects of heat and mass transfer on the peristaltic propulsion of two-phase fluid flow through a Darcy-Brinkman-Forchheimer porous medium with compliant walls. The Sisko fluid model together with small particles is considered in the presence of extrinsic magnetic field and chemical reaction. It is well-known that different biological fluids behave like a Newtonian or non-Newtonian fluid depending upon the shear rates. The non-Newtonian fluid models are more complicated than Newtonian fluid and difficult to express using the single constitutive relationship between stress and strain rate. These constitutive equations provide a complex mathematical formulation and become numerous challenges to find numerical and analytical solutions. Small magnetic particles are helpful to manipulate and control the two-phase flow by magnetic force. Moreover, it is also beneficial in drug targeting for the treatment of different diseases. Further, two-phase flow plays an important role to examine the muscular expansion and contraction during the propagation of various biological fluids. An appropriate approximation is considered such as long wavelength and creeping flow regime to model the governing equations. Analytical solutions are obtained using the perturbation method. Moreover, numerical computations are performed to determine the features of peristaltic pumping. The results of different rheological properties for particle and fluid phase are discussed mathematically as well as graphically for different sundry parameters. The current analysis has an extensive amount of applications in medical engineering and also significant importance of smart fluid pumping systems in various engineering processes.     

Nonisothermal dissipative flow of viscous liquid in a porous channel

Stationary nonisothermal flow of viscous Newtonian liquid in a flat channel filled with porous material is studied. The Brinkman equation is used as a motion equation. It is assumed that viscosity depends on temperature. The energy equation is denoted using a single-temperature model. Dissipative heat emissions are accounted. The problem is solved for temperature first-order boundary conditions.     

Flow of a third grade fluid through a porous flat channel

The steady, laminar flow of a third grade fluid through a porous flat channel is considered, when the rate of injection of the fluid at one boundary is equal to the rate of suction at the other boundary. The flow is governed by a non-linear boundary value problem (BVP) in which the order of the differential equation is three, but only two boundary conditions are available. Two numerical schemes are developed to obtain the appropriate solution of the BVP. In the first scheme the dilemma is resolved by assuming that the solution is analytical in the neighborhood of K=0, where K is the non-dimensional viscoelastic fluid parameter. This scheme is practical to use only up to certain values of T, the third grade fluid parameter. The second scheme allows arbitrary values of T, but is restricted to small values of K and R, the cross-flow Reynolds number.A perturbation solution valid for small values of T is also derived. Finally two approximate solutions, based on Collatz’ iterative scheme, but with different starting trial solutions are obtained. A comparison is made of the results computed by using various methods and appropriate conclusions are drawn.