Suction Reynolds Number Research Articles

Viscoelastic Fluid Flow through a Porous Annulus

AbstractThe problem of laminar flow of a viscoelastic fluid through a porous cylindrical annulus, with walls of different permeabilities is discussed. The velocity of the fluid is given by the solution of a fifth‐order non‐linear ordinary differential equation depending on three parameters, namely, the Suction Reynolds number and the two viscoelastic parameters. Since the number of available boundary conditions is only four, we make use of the regular perturbation method to find the solution for the cases in which (i) fluid is extracted at the two walls with different constant velocities and (ii) the quantity of fluid entering one wall is nearly equal to the one being extracted at the other wall. The products of the Reynolds number with viscoelastic parameters are taken to be small in (i). A method of direct numerical integration is being treated separately. The effects of the viscoelasticity of the liquid on the velocity field, pressure distribution, skin friction are discussed for various values of the parameters involved and compared with some earlier results.

Unsteady thermal entrance heat transfer of laminar duct flows with wall suction and injection

Abstract The unsteady thermal entrance heat transfer problem is analyzed by the instant‐local similarity method for the system of fully‐developed laminar incompressible flow into the region of porous wall which permits uniform suction or injection and with a step change in wall temperature. Both the circular tube and flat duct between parallel plates are considered in this work. Numerical solutions of the transient heat transfer rates and the development of temperature profiles are presented for some selective values of suction Reynolds number, Prandtl number, and Graetz number. The numerical solutions at the asymptotic small and large time are in agreement excellently with the transient condution solution and steady‐state solution, respectively. The corresponding steady‐state heat transfer problems are also analyzed by the local similarity and local nonsimilarity methods. The numerical solutions of these methods are in agreement very closely.

Numerical solution to the flow of a micropolar fluid between porous walls of different permeability

The problem of steady laminar micropolar fluid flow through porous walls of different permeability has been discussed. At the entry of the channel, the velocity and microrotation are considered as those of Poiseuille flow. The governing nonlinear ordinary differential equations have been solved using quasilinearisation technique. The velocity and microrotation are found to involve S, the suction Reynolds number of cross flow at the upper wall. The effect of different permeability at the walls, on the longitudinal velocity and microrotation has been studied. The skin friction and the couple stress on the walls have also been calculated.

The effect of Hall currents on MHD flow and heat transfer between two parallel porous plates

The effect of Hall currents on magneto hydrodynamic (MHD) flow of an incompressible viscous electrically conducting fluid between two non-conducting porous plates in the presence of a strong uniform magnetic field is studied. The flow is generated by a small uniform suction at the plates. Solutions are obtained for suction Reynolds number R≪1, considering two cases for the imposed magnetic field, viz. (i) when the magnetic field is perpendicular to the plates (parallel to y-axis), and (ii) when the magnetic field is parallel to the plates and perpendicular to the primary flow direction (parallel to z-axis). The effect of the Hall currents on the flow as well as on the heat transfer is studied. It is observed that in the absence of Hall currents, the change of the direction of the applied magnetic field does not affect the primary flow.

Combined effect of free and forced convection on MHD flow in a rotating porous channel

This paper gives a steady linear theory of the combined effect of the free and forced convection in rotating hydromagnetic viscous fluid flows in a porous channel under the action of a uniform magnetic field. The flow is governed by the Grashof number G, the Hartmann number H, the Ekman number E, and the suction Reynolds number S. The solutions for the velocity field, temperature distribution, magnetic field, mass rate of flow and the shear stresses on the channel boundaries are obtained using a perturbation method with the small parameter S. The nature of the associated boundary layers is investigated for various values of the governing flow parameters. The velocity, the temperature, and the shear stresses are discussed numerically by drawing profiles with reference to the variations in the flow parameters.

A numerical study of magnetohydrodynamic flow between a rotating and a stationary porous coaxial discs

The magnetohydrodynamic flow of an electrically conducting viscous fluid between a rotating and a stationary disc has been studied numerically by the Newton-Raphson method and the method of continuation. The results have been calculated for a wide range of parameters involved, thus indicating the efficiency of the methods. The induced electric field has also been calculated for various values of suction Reynolds number.

Elasticoviscous flow between a rotating and a stationary disk with uniform suction at the stationary disk

The flow of an elasticoviscous fluid between a rotating and a stationary disk with uniform suction at the stationary disk is studied. The equations of motion are solved by a regular perturbation method for small suction Reynolds number and by the Runge-Kutta numerical integration method. The results from the two methods have been compared. The effects of the elasticity of the fluid and the suction parameter on the velocity components, torque on the disks, and the pressure coefficient have been studied.

Heat transfer in a rotating channel with porous walls

An attempt has been made to investigate the effects of uniform suction and injection in the temperature distribution and heat transfer, when a straight channel formed by two parallel porous walls, through which liquid is flowing under a constant pressure gradient, is rotated about an axis perpendicular to the walls. Closed form solutions for temperature θ, Nusselt numberNu are derived. It is found that for a fixed Eckert numberE and Prandtl numberPr, the temperature at any point of the fluid decreases in both cases (i) for a fixed Taylor’s number α but with an increase in suction Reynolds number β (ii) for a fixed β but with an increase in α. Also for a fixedE andPr, the Nusselt numberNu is found to decrease in either case. All other parameters remaining fixed, the effect of increasingE is to increase both the temperature at any point of the fluid and the Nusselt number.

The existence of multiple solutions for the laminar flow in a uniformly porous channel with suction at both walls

A numerical investigation is made to establish whether multiple solutions exist for laminar, incompressible, steady flow in a parallel plate porous channel with uniform suction at both walls. For values of the wall suction Reynolds number,R, greater than 12.165 three numerical solutions are observed for eachR, while forR less than 12.165 only one solution for eachR can be found. A method involving the inclusion of exponentially small terms in a perturbation series is used to find two of the solutions analytically, while an appeal to the numerical results gives an indication of how the third solution can be obtained. The series involving the exponentially small terms, as well as predicting dual solutions, gives more accurate analytic results for the skin friction at the channel walls.

Secondary Flow between Two Parallel Porous Walls in a Rotating System

When a straight channel formed by two parallel porous walls, through which liquid is flowing under a constant pressure gradient, is rotated about an axis perpendicular to the walls, secondary motion is set up. The secondary motion is analysed in detail for constant angular velocity Ω' and the suction Reynolds number β. The flow depends on the Taylor's number α, pressure gradient P and the suction Reynolds number. In a rapidly rotating system such that ( P /α 2 ) is finite, the secondary flow is confined to regions of order [α+(β/2)] -1 and a boundary layer is formed in the vicinity of both the walls. A method for setting up an experiment to test the theoretical conclusions of the paper is suggested.

A singular perturbation problem of non-newtonian flow between porous disks

The non-Newtonian flow between parallel porous stationary disks due to uniform suction at the disks is considered for both small and large suction Reynolds numbers. In the case of small suction Reynolds number the Navier-Stokes equations have been solved by a regular perturbation technique. The solution obtained is valid for both suction and injection Reynolds numbers. The velocity, pressure and shear distributions have been obtained and are compared with those of the Newtonian flow. We find, in the case of injection, that the combined effect of cross viscosity and visco-elastic co-efficients is to increase the maximum velocity at the centre of the channel and to decrease the magnitude of the velocity gradient at the disks. Whereas in the case of suction, velocity profile is flatter with higher magnitude for the velocity gradients at the disks. In the case of large suction, the Navier-Stokes equations have been solved by the method of matched asymptotic expansions. We find that the effect of large suction at the disks is to flatten the velocity profiles considerably and thereby to push the boundary layer towards the disks. The combined effect of visco-elastic and cross-viscosity terms is to decrease the radial velocity and to increase the axial velocity distributions.

Radial flow of a viscous, incompressible fluid between two stationary, uniformly porous discs

The problem of incompressible viscous laminar flow between two co-axial discs is studied when there is constant injection or suction at the discs. The resultant flow satisfies an ordinary non-linear differential equation which depends on a suction Reynolds number and this equation is solved by singular perturbation technique.

On the steady flow between a rotating and a stationary disk with a uniform suction at the stationary disk

The steady axisymmetric flow of a viscous incompressible fluid between two coaxial disks, one rotating and the other stationary, with uniform suction at the stationary disk is discussed. Similarity solutions of Navier-Stokes equations are obtained by the method of regular perturbation for small suction Reynolds number and numerically for an arbitrary suction Reynolds number by a series expansion method and also by integrating directly by a Newton-Raphson technique. It is found that for a fixed rotational Reynolds number and varying suction Reynolds number there is an overall increase in the velocity components as the suction increases.

Magnetohydrodynamic laminar flow between porous disks

The steady two-dimensional laminar flow of an incompressible conducting fluid between two parallel circular disks in the presence of a transverse magnetic field is investigated. A solution is obtained by perturbing the creeping flow solution and it is valid only for small suction or injection Reynolds numbers. Expressions for velocity, induced magnetic field, pressure, and shear stress distribution are determined and are compared with the creeping flow and hydrodynamic solutions. It is found that the overall effect of the magnetic field on the flow is the same as that in the Hartmann flow.

Flow of a Conducting Fluid between Porous Disks for Large Suction Reynolds Number

The magnetohydrodynamic laminar flow between two parallel porous disks is examined for large suction Reynolds number and arbitrary Hartmann number. The equations of motion are solved using the singular perturbation technique and the expressions for the velocity, pressure and shear stress distributions are obtained. The results of this analysis are compared with the case of large injection Reynolds number.

Laminar Non‐Newtonian Flow through a Porous Annulus

AbstractThe problem of steady laminar flow of a non‐Newtonian liquid in an annulus with porous walls of non uniform permeability is reduced to the problem of solving a fourth order differential equation depending on two parameters, namely, the suction Reynolds number and the inelastic number. For small values of the inelastic number series solutions are obtained (i) for small suction or blowing (ii) when the total flow into the channel through the walls is small and the non‐Newtonian effect of the liquid on surface‐friction and pressure coefficient is examined.Finally, the series solutions are confirmed by exact numerical solutions.

Laminar elastico-viscous flow through channels with porous walls of different permeability

The two-dimensional steady flow of an incompressible elastico-viscous fluid through a porous channel that has the fluid sucked or injected with different normal velocities V 1 and V 2 at the walls is considered. For the viscous case Terrill and Shrestha [2] have given a series solution for small suction Reynolds number. In this paper the solution of [2] is extended to include the effect of the elasticity of the fluid. It is found that the elasticity of the fluid comes into effect only when suction or blowing is present. The general expressions for the pressure distribution and the friction coefficient are given and are found to increase as the elastic parameter increases. Finally, the resulting solution is confirmed by numerical results.

A singular perturbation problem of laminar flow in a uniformly porous channel with large injection and with an applied transverse magnetic field

The problem of the steady flow of an electrically conducting viscous fluid through porous walls of a channel in the presence of an applied transverse magnetic field is considered. A solution for the case of small M2/R (where M = Hartmann number, R = suction Reynolds number) with large blowing at the walls has been given by Terrill and Shrestha [3]. Their solution, on differentiating three times, is found to become infinite at the centre of the channel. Physically this means that there must be a viscous layer at the centre of the channel and Terrill and Shrestha are neglecting the shear layer. In this paper the solution given by Terrill and Shrestha is extended by obtaining an extra term of the series of expansion and the method of inner and outer expansion is used to obtain the complete solution which includes the viscous layer. The resulting series solutions are confirmed by numerical results.

Heat transfer in laminar flow in a uniformly porous channel with an applied transverse magnetic field

The steady laminar flow of an incompressible, viscous, and electrically conducting fluid between two parallel porous plates with equal permeability has been discussed by Terrill and Shrestha [6]. In this paper, using the solution of [6] for the velocity field, the heat transfer problems of (i) uniform wall temperature and (ii) uniform heat flux at wall are solved. For small suction Reynolds numbers we find that the Nusselt number, with increasing Reynolds number, increases for case (i) and decreases for (ii).

Laminar Flow Between Porous Disks

The equation of motion for steady, incompressible, axially symmetric flow between parallel porous disks have been solved. The flow is entirely the result of either suction or injection through the disks. The solution is obtained by perturbing the creeping-flow solution. It is valid for small suction or injection Reynolds numbers. Expressions for the velocity, pressure, and shear stress are presented and compared with the creeping-flow expressions.