Permeable Cylinder Research Articles

On the Nonlinear Dynamical System of Amplitude Equations Corresponding to Intersections of Bifurcations in the Flow Between Permeable Cylinders with Radial and Axial Flows

In the present work, we study various modes that arise after a circular Couette flow loses its stability in the presence of an axial flow due to a constant axial pressure gradient and a radial flow through the permeable walls of the cylinders. The basic object of our investigation is a nonlinear system of amplitude equations describing multiple flow bifurcations between permeable cylinders. Different bifurcations will be investigated theoretically with application of numerical methods.

Unsteady Flow and Heat Transfer Characteristics of Fluid Flow Over a Shrinking Permeable Infinite Long Cylinder

The present work studies the unsteady, viscous, and incompressible laminar flow and heat transfer over a shrinking permeable cylinder. The unsteady nonlinear Navier–Stokes and energy equations are reduced, using similarity transformations, to a system of nonlinear ordinary differential equations. The boundary conditions associated with the governing equations are the time dependent surface temperature and flow conditions. The method of solution is based on a combination of the implicit Runge–Kutta method and the shooting method. The present study predicts two solutions for both the flow and heat transfer fields, and a unique solution at a specific critical unsteadiness parameter. An analysis of the results, for a specific suction parameter, suggests that the corresponding unique unsteadiness parameter does not depend on the Prandtl number. However, the unique rate of heat transfer is increasing as the Prandtl number increases. In addition, our results confirm that the unique value of heat transfer rate increases as the suction parameter increases, regardless the value of the Prandtl number.

Stagnation Point Flow of a Nanofluid Past a Permeable Cylinder with Chemical Reaction

The primary objective of the present paper is to investigate the novel aspect of nanofluid flow near the stagnation‐point past a permeable cylinder with chemical reaction. The prescribed surface heat and nanoparticle fluxes are also taken into account. The improved homotopy analysis method is introduced to obtain the recursively analytic solutions with high precision. The convergence of the obtained series solution is discussed explicitly. Besides, the effects of physically significant parameters on skin friction coefficient, local Nusselt number, local Sherwood number, as well as profiles of velocity, temperature, and nanoparticle volume fraction are examined and discussed in detail. It is found that the local Sherwood number increases when a chemical reaction occurs in the nanofluid. It is also indicated that the increase of the reaction rate parameter leads to a higher temperature and a lower nanoparticle volume fraction.

Stability of MHD Taylor–Couette Flow in a Narrow Gap with Radial Throughflow

An analysis which considers the stability of dissipative, conducting, incompressible flow between two permeable circular cylinders in presence of an axially applied magnetic field is presented. The impact of radial inflow and outflow was investigated on the Taylor–Couette flow in a narrow gap via differential transform method combined with a shooting technique. The semi analytic computations made by differential transformation method are consistent with linear instability predictions. For impermeable cylinders the critical Taylor number at the onset of instability increases with increase in Hartmann number for both conducting and non-conducting walls that establishes the stabilizing influence of the magnetic field. Radial inflow has a stabilizing effect and the stabilization is more for perfectly conducting walls, while a radial outflow destabilizes the system. Also, the critical wave number is independent of radial flow through the cylinders. For non-conducting cylinders, the asymptotes as the Hartmann numbers approaches infinity are obtained for inflow as well as outflow and found that the asymptotes increases for radial inflow and decreases for outflow.

Numerical analysis of confined flow past permeable square cylinder with CE/SE method

The unsteady flow field past a two-dimensional permeable square cylinder was predicted by an updated CE/SE method. The periodic patterns of streamline and vortex shedding were obtained. The evolution of lift and drag coefficients were analysed. Results of 2D computations were compared with the experimental data. It found that the Reynolds number dominated the magnitude and frequency of the vorticity given porosity and Darcy number. It proved that the CE/SE method was an effective tool for predicting viscous flows in porous media.

Numerical analysis of confined flow past permeable square cylinder with CE/SE method

The unsteady flow field past a two-dimensional permeable square cylinder was predicted by an updated CE/SE method. The periodic patterns of streamline and vortex shedding were obtained. The evolution of lift and drag coefficients were analysed. Results of 2D computations were compared with the experimental data. It found that the Reynolds number dominated the magnitude and frequency of the vorticity given porosity and Darcy number. It proved that the CE/SE method was an effective tool for predicting viscous flows in porous media.

Centrifugal instability and turbulence development in Taylor–Couette flow with forced radial throughflow of high intensity

A numerical simulation of the turbulent flow between coaxial permeable cylinders is performed for the case of the rotating inner cylinder and superimposed radial flow through the annular domain. Both forced inflow and outflow are considered in a wide range of the rotation rate and throughflow intensity. Two configurations of the rotating cylinder are examined with an entire permeable porous surface and with lengthwise porous slots. The stable rotational fluid motion is shown to be concentrated within a boundary layer close to the inner cylinder surface at strong enough imposed radial inflow. Under such conditions, the centrifugal stability boundary is independent on the gap width. Flow stabilization due to the forced inflow is possible at any rotation rate considered for both the configurations of the inner rotating cylinder. The stabilization by the forced outflow is feasible only in the case of the entire permeable rotating cylinder. But there are always large-scale vortices in the gap under conditions of the forced outflow through the slotted rotating cylinder except for the relatively low rotation rate. Transition to turbulence in the boundary layer at the inner rotating cylinder may occur before the centrifugal instability onset at large enough inflow intensity. The boundary layer thickness and turbulence intensity are influenced by the inflow rate and differ between the cases of the entire permeable cylinder and the slotted one.

Heat Transfer and Flow of a Casson Fluid Due to a Stretching Cylinder with the Soret and Dufour Effects

Numerical solutions of the problem on flow and heat transfer of a non-Newtonian fluid outside a stretching permeable cylinder are obtained with regard to suction or blowing and the Soret and Dufour effects. The Casson fluid model is used to characterize the non-Newtonian fluid behavior. The governing partial differential equations are reduced to a system of nonlinear ordinary differential equations by employing similarity transformations, and the obtained equations are solved numerically by using the shooting technique. The main purpose of the study is to investigate the effect of the governing parameters, namely, the Casson, Soret, and Dufour parameters, the suction/injection parameter, and the Prandtl and Reynolds numbers, on the velocity and temperature profiles, as well as on the skin friction coefficient and temperature gradient at the surface.

Cross-flow and heat transfer of porous permeable cylinder

Non-isothermal flow around the porous permeable cylinder of square cross section by a viscous incompressible fluid is considered. The motion and energy equations is solved numerically using the finite volume method. The character of the fluid flow, change of the cylinder drag coefficient and Nusselt number as a function of Reynolds and Darcy numbers is analyzed.

Effects of permeable cylinders on wake region

This paper investigates the effects of permeable cylinder on vortex shedding downstream of the permeable cylinder in deep water flow by PIV technique. In order to reveal the effect of porosity β on the vortex shedding, the permeable cylinder having four different porosities (β = 0.4, 0.5, 0.6 and 0.7) with a diameter of 45 mm have been used. During the experiments, the free-stream velocity is U∞= 156 mm/s, which corresponds to the Reynolds number of Re=5000 based on the solid cylinder diameter. The experiments show that the permeable cylinder is effective on the suppression of vortex shedding in the wake region for all porosities and in terms of the inner cylinder-outer permeable cylinder arrangement, it is understood that the inner-outer cylinder arrangement having the diameter ratio of D/d=1.5 is not effective on the attenuation of vortex shedding downstream of the inner cylinder-outer cylinder arrangement as expected. The inner and outer permeable cylinders behave like an impermeable cylinder having the diameter of D=45 mm for the porosities of β = 0.4, 0.5 and 0.6. The suppression of the large scale vortices is weak. On the other hand, for the porosity β = 0.7, the peak value of Reynolds shear stress drops to 0.0368 which is less than that of the bare cylinder. The reduction of is approximately 10%.

Numerical study of non-Newtonian Jeffreys fluid from a permeable horizontal isothermal cylinder in non-Darcy porous medium

In this article, we investigate the non-linear steady free convection heat and mass transfer of an incompressible Jeffrey’s non-Newtonian fluid from a permeable horizontal isothermal cylinder in a non-Darcy porous medium. A non-Darcy drag force model is employed to simulate the effects of linear porous media drag and second-order Forchheimer drag. The transformed conservation equations are solved numerically subject to physically appropriate boundary conditions using a versatile, implicit, finite difference technique. The numerical code is validated with previous studies. The influence of a number of emerging non-dimensional parameters, namely Deborah number (De), surface suction parameter (f w ), Prandtl number (Pr), ratio of relaxation to retardation times (λ), Darcy number (Da), Forchheimer inertial parameter (Λ) and dimensionless tangential coordinate (ξ) on velocity, temperature and concentration evolution in the boundary layer regime are examined in detail. Furthermore, the effects of these parameters on surface heat transfer rate, mass transfer rate and local skin friction are also investigated. It is observed that velocity decreases with increasing Deborah number and Forchheimer parameter, whereas temperature and concentration are enhanced. Increasing λ and Da enhances velocity but reduces temperature and concentration. The heat transfer rate and mass transfer rate are found to decrease with increasing Deborah number, De, and increase with increasing λ. Local skin friction is found to decrease with a rise in Deborah number whereas it is elevated with increasing values of relaxation to retardation time ratio (λ). Increasing suction decelerates the flow and also cools the boundary layer, i.e., reduces temperature and also concentration. With increasing tangential coordinate, the flow is decelerated; whereas, the temperature and concentration are enhanced.

Flow control downstream of a circular cylinder by a permeable cylinder in deep water

The flow characteristics of a circular cylinder surrounded by an outer permeable cylinder were experimentally investigated using Particle Image Velocimetry Technique in deep water flow. In order to consider the effects of diameter and porosity of the outer cylinder on flow structures of the inner cylinder, five different outer cylinder diameters (D=37.5, 52.5, 60, 75 and 90 mm) and eight different porosities (<TEX>${\beta}$</TEX>=0.4, 0.5, 0.6, 0.65, 0.7, 0.75, 0.8 and 0.85) were selected. During the experiments, the diameter of inner cylinder was kept constant as d=30 mm. The depth-averaged free-stream velocity was adjusted as U=0.156 m/s, which corresponds to the Reynolds number of Re=5000 based on the inner cylinder diameter. It has been concluded that both the outer permeable cylinder diameter and the porosity have important influences on the attenuation of vortex shedding in the wake region. The presence of outer permeable cylinder decreases the magnitude of Reynolds shear stress and turbulent kinetic energy compared to the bare cylinder case. Moreover, the spectral analysis of vortex shedding frequency has revealed that the dominant frequency of vortex shedding downstream of the cylinder arrangement also reduces substantially due to the weakened Karman shear layer instability.

Field and inductance of circular coils placed eccentrically inside a cylindrical screen of finite length and high permeability

For the circular coils of parallel axes eccentrically placed inside a cylinder of finite length and high permeability, the magnetic field and inductance are discussed and the analytic solutions are given by introducing a proper ansatz of the magnetic scalar potential (MSP), which is easy to satisfy the boundary conditions on the surface of the cylinder. By the separation of the total axial field into the source and secondary parts, the axial factor of the ansatz can be obtained, and the coefficients of the ansatz can be further found out by using the spring characteristics of the MSP. The results are further developed to find the self- and mutual inductance of the shielded circular rings and coils with rectangular cross section by calculating the corresponding magnetic flux. In addition, for the general case of the coils with parallel axes, the numerical results of the proposed method are compared with those of the finite element method simulations. For the special case of the rings coaxial with the cylinder, the results of our method are compared with those of the literature. Finally, the validity of our method is confirmed by the good agreement between them in the numerical calculations in all cases.

Flow and Heat Transfer of Jeffreys Non-Newtonian Fluid from Horizontal Circular Cylinder

The boundary-layer flow and heat transfer of an incompressible Jeffreys viscoelastic fluid from a permeable horizontal circular cylinder is analyzed. The surface of the cylinder is maintained at a constant temperature. The boundary-layer conservation equations, which are parabolic in nature, are normalized into nonsimilar form and then solved numerically with the well-tested, efficient, implicit, stable Keller-box finite difference scheme. The variation of the reduced Nusselt number and local skin-friction coefficient with Deborah number and suction parameter, for various values of Prandtl number, and ratio of relaxation to retardation times are tabulated and provided in graphical form. It is found that the velocity is reduced with increasing Deborah number, whereas the temperature is increased. Increasing the ratio of relaxation to retardation times enhances the velocity but decreases the temperature. Increasing the Deborah number is observed to decrease the Nusselt number (heat transfer rate) and the skin-friction coefficient. Increasing the ratio of relaxation to retardation times is found to increase the Nusselt number (heat transfer rate) and the local skin friction.

An analytical model for estimating water exchange rate in white matter using diffusion MRI.

Substantial effort is being expended on using micro-structural modeling of the white matter, with the goal of relating diffusion weighted magnetic resonance imaging (DWMRI) to the underlying structure of the tissue, such as axonal density. However, one of the important parameters affecting diffusion is the water exchange rate between the intra- and extra-axonal space, which has not been fully investigated and is a crucial marker of brain injury such as multiple sclerosis (MS), stroke, and traumatic brain injury (TBI). To our knowledge, there is no diffusion analytical model which includes the Water eXchange Rate (WXR) without the requirement of short gradient pulse (SGP) approximation. We therefore propose a new analytical model by deriving the diffusion signal for a permeable cylinder, assuming a clinically feasible pulse gradient spin echo (PGSE) sequence. Simulations based on Markov Random Walk confirm that the exchange parameter included in our model has a linear correlation (R2>0.88) with the actual WXR. Moreover, increasing WXR causes the estimated values of diameter and volume fraction of the cylinders to increase and decrease, respectively, which is consistent with our findings from histology measurements in tissues near TBI regions. This model was also applied to the diffusion signal acquired from ex vivo brains of 14 male (10 TBI and 4 normal) rats using hybrid diffusion imaging. The estimated values of axon diameter and axonal volume fraction are in agreement with their corresponding histological measurements in normal brains, with 0.96 intra-class correlation coefficient value resulting from consistency analysis. Moreover, a significant increase (p = 0.001) in WXR and diameter and decrease in axonal volume fraction in the TBI boundary were detected in the TBI rats compared with the normal rats.

Occurrence of quasiperiodic flows between two rotating permeable cylinders

This paper considers viscous incompressible fluid flows between two infinite rotating permeable concentric cylinders near the bifurcation point, which result in secondary steady flow and oscillations with azimuthal waves. Steady periodic and quasiperiodic fluid flow regimes with two, three, and four independent frequencies are obtained by methods of the theory of codimension-two bifurcations of hydrodynamic flows having cylindrical symmetry.

Dual solutions of mixed convection flow with momentum and thermal slip flow over a permeable shrinking cylinder

Axisymmetric flow of a viscous incompressible fluid over a shrinking vertical cylinder with heat transfer is investigated. The flow considered is with both, the second order momentum slip and first order thermal slip boundary condition. The governing equations of continuity, momentum and energy are transformed into the system of non-linear ordinary differential equations and solved numerically. The velocity and temperature distributions are discussed numerically and shown through graphs. The effects of various physical parameters are examined and discussed in detail. The expressions of skin-friction coefficient, Nusselt number, fluid velocity and temperature at the cylinder are discussed numerically and their variations are presented through graphs.

Magnetohydrodynamic Stagnation Flow and Heat Transfer toward a Stretching Permeable Cylinder

We perform an analysis of MHD flow and heat transfer on a stretching, permeable cylinder. We prove existence of solutions for all values of the relevant parameters and provide uniqueness results in the case of a monotonic solution. The nonlinear boundary value problem that is derived from a similarity transformation of the governing system of nonlinear partial differential equations is solved numerically and the results are presented with graphs and tables.

Computational analysis of viscous dissipation and joule-heating effects on non-Darcy MHD natural convection flow from a horizontal cylinder in porous media with internal heat generation

In the present paper we examine the effects of viscous dissipation, Joule heating and heat source/sink on non-Darcy MHD natural convection heat transfer flow over permeable horizontal circular cylinder in a porous medium. The boundary layer equations, which are parabolic in nature, are normalized into non-similar form and then solved numerically with the well-tested, efficient, implicit, stable Keller-box finite difference scheme. A parametric study illustrating the influence of Darcy parameter (Da), Forchheimer parameter (?), Grashof number(Gr), heat source/sink parameter (?) and viscous dissipation parameter (Ec) on the fluid velocity, temperature as well as local skin-friction and Nusselt numbers is conducted Increasing Forchheimer inertial drag parameter (?) retards the flow considerably but enhances temperatures. Increasing viscous dissipation parameter(Ec) is found to elevate velocities i.e. accelerate the flow and increase temperatures. Increasing heat source/sink parameter (?) is found to elevate velocities and increase temperatures. Increasing the Grashof number (Gr) is found to elevate the velocity and decrease the temperatures. Local skin friction number is found to be increases with increasing heat source/sink parameter (?) where as Local Nusselt number is found to decrease with increasing heat source/sink parameter (?).

Fluid Flow and Heat Transfer over a Permeable Stretching Cylinder

In this paper, we analyze the effects of thermo-physical properties on the axisymmetric flow of a viscous fluid induced by a stretching cylinder in the presence of internal heat generation/absorption. It is assumed that the cylinder is stretched in the axial direction with a linear velocity and the surface temperature of the cylinder is subjected to vary linearly. Here, the temperature dependent thermo-physical properties namely, the fluid viscosity and the fluid thermal conductivity are respectively assumed to vary as an inverse function of the temperature and a linear function of the temperature. The governing system of partial differential equations is converted into a system of coupled non-linear ordinary differential equations with variable coefficients. The resulting system is solved numerically using a second order finite difference scheme known as the Keller-box method. The governing equations of the problem show that the flow and heat transfer characteristics depend on six parameters, namely the curvature parameter, fluid viscosity parameter, injection/suction parameter, variable thermal conductivity parameter, heat source/sink parameter and the Prandtl number. The numerical values obtained for the velocity, temperature, skin friction, and the Nusselt number are presented through graphs and tables for several sets of values of the pertinent parameters. The results obtained for the flow and heat transfer characteristics reveal many interesting behaviors that warrant further study on the axisymmetric flow phenomena. Comparisons with the available results in the literature are presented as special cases.