Flow In Porous Tube Research Articles

Mathematical Analysis of Blood Flow in Porous Tubes: A Comparative Study

The steady flow of Herschel-Bulkley and Casson fluids for blood flow in tubes filled with homogeneous porous medium with (i) constant and (ii) variable permeability is analyzed. The expression for the shear stress is obtained first by general iteration method and then using numerical integration; the solutions for velocity and flow rate are obtained. It is noticed that the shear stress and plug core radius are considerably higher in the case of variable permeability than those of the constant permeability case. The velocity and flow rate of both the fluids increase considerably with the increase in the permeability factor and they decrease with the increase in the yield stress of the fluids. The velocity and flow rate of Herschel-Bulkley fluid are considerably higher than those of Casson fluid. Aforesaid flow quantities are significantly higher for flow in tubes with variable permeability than for flow in tubes with constant permeability.

CFD modeling of porous membranes

Membrane filtration has become firmly established as a primary technology for ensuring the purity, safety and efficiency of treatment of water or effluents. Water desalination is one of the major applications of this technology around the world. Several researches have been performed to develop and design membrane systems in order to increase the process accuracy and performance. In this research, the laminar fluid flow in porous tubes, a mode of crossflow filtration tubular membrane, is simulated numerically using the computational fluid dynamics (CFD) techniques. A two-dimensional numerical solution of the coupled Navier–Stokes, Darcy's law and mass transfer equation has been developed using control volume based finite difference method. Case study was performed for a microfiltration process. Prediction of the growth rate of the concentration polarization boundary layer along the length of tubular membranes has been performed. Effects of various operating conditions (e.g. geometrical dimension, required membrane surface area, Reynolds number and fouling) on the performance of membrane are studied and some comments on designing of such membranes are suggested.

Effect of slip on existence, uniqueness, and behavior of similarity solutions for steady incompressible laminar flow in porous tubes and channels

The existence and multiplicity of similarity solutions for steady, fully developed, incompressible laminar flow in uniformly porous tubes and channels with one or two permeable walls is investigated from first principles. A fourth-order ordinary differential equation obtained by simplifying the Navier-Stokes equations by introducing Berman’s stream function [A. S. Berman, J. Appl. Phys. 24, 1232 (1953)] and Terrill’s transformation [R. M. Terrill, Aeronaut. Q. 15, 299 (1964)] is probed analytically. In this work that considers only symmetric flows for symmetric ducts; the no-slip boundary condition at porous walls is relaxed to account for momentum transfer within the porous walls. By employing the Saffman [P. G. Saffman, Stud. Appl. Math. 50, 93 (1971)] form of the slip boundary condition, the uniqueness of similarity solutions is investigated theoretically in terms of the signs of the guesses for the missing initial conditions. Solutions were obtained for all wall Reynolds numbers for channel flows whereas no solutions existed for intermediate values for tube flows. Introducing slip did not fundamentally change the number or the character of solutions corresponding to different sections. However, the range of wall Reynolds numbers for which similarity solutions are theoretically impossible in tube flows was found to be a weak function of the slip coefficient. Slip also weakly influenced the transition wall Reynolds number corresponding to flow in the direction of a favorable axial pressure gradient to one in the direction of an adverse pressure gradient. Momentum transfer from the longitudinal axis to the walls appears to occur more efficiently in porous channels compared to porous tubes even in the presence of slip.

An approximate analytical solution for the fluid dynamics of laminar flow in a porous tube

An approximate solution for the fluid dynamics of flow through a porous tube, such as encountered in the cross-flow filtration process, is presented. Conservation of mass for the entire unit combined with the assumptions of quadratic variation of pressure along the length of the unit and local validity of the Hagen–Poiseuille law results in simplified expressions for the pressure and axial and radial velocity profiles. A finite element solution to the Navier–Stokes equations is used to compare the resulting expressions to the only other approximate analytical solution found in the literature. The results indicate that all three analyses are within 0.5% of each other for laminar flow in a long porous tube.

Magnetic resonance imaging of laminar flow in porous tube and shell systems

Abstract Magnetic resonance imaging (MRI) was used to measure noninvasively the steady, incompressible, laminar fluid flow in an inorganic porous tube and shell module. The porous tube module was operated in closed-end or “dead-end” mode for Reynolds numbers of 100 and 200, based on the tube radius. An MIR spin-echo, time-of-flight (TOF) technique was implemented and the results were compared to those of St»hlberg (1986) and Pangrle (1991). St»hlberg (1986) predicted the signal intensity generated by flowing protons using the TOF technique and Pangrle (1991) presented a theoretically based, numerical method for predicting fluid velocities and pressures in porous tube and shell systems. The experimental measurements agreed favorably with both the values predicted by the MRI, TOF theory and the axial velocity values from the numerical method.

An analysis of laminar fluid flow in porous tube and shell systems

The finite element method was used to study steady, incompressible, laminar flow in porous tube systems. The Navier-Stokes equations were used to describe the flow phenomena in the tube and shell space while the continuum theory of Brinkman was used to describe flow in the porous tube wall. The solution method, based on the Galerkin finite element and Newton iteration techniques, provided velocities and pressures for a wide range of Reynolds numbers and operational modes. the Darcy permeability was the only adjustable parameter used in the model and it was calculated a priori. The approach was justified by a comparison to previous experimental results for flow in a porous ceramic tube and shell system. The model was then used to investigate the effect of shell diameter and tube length on the flow field for closed shell, closed end, and cross flow operation.

Turbulence transport phenomena of air flow in porous tube with permeate flux of carbon dioxide gas injection.

Turbulence transport phenomena of air flow in porous tube with permeate flux of carbon dioxide gas injection.

Fluid mechanics and cross-flow filtration: some thoughts

Most mass transfer models for describing polarization and fouling in porous membrane ducts require some knowledge of the fluid mechanics. Mass transfer correlations for porous membrane systems are usually borrowed from studies of flow in non-porous ducts. In this paper we show that friction coefficients are higher for flow in a duct with wall suction than without. We also show that the onset of turbulence is delayed from 2100 to about 4000 Reynolds number for flow in porous tubes with suction when compared to flow in non-porous tubes. In the laminar regime at a given axial Reynolds number increased suction results in a maximum value for the friction coefficient. Using a trajectory analysis, we have compared the performance of several commercial modules for capturing suspended particles from dilute solution. Under the assumptions of the theoretical models, and all things being equal (besides fractional recovery per unit length), tubular systems will capture more particles from dilute suspensions than slits with two porous walls.

Entrance-region heat transfer for laminar flow in porous tubes

Entrance-region heat transfer for laminar flow in porous tubes

Fully developed frictional and heat-transfer characteristics of laminar flow in porous tubes

The frictional and heat-transfer characteristics of fully developed laminar flow in porous tubes have been examined utilizing numerical solutions to the flow and energy equations. Based on the assumption of a constant-property fluid and uniform wall mass transfer, universal wall-friction and heat-transfer results for flow in constant temperature tubes are obtained. These are presented in the form of friction-coefficient and Nusselt-number curves spanning the continuous range of injection and extraction wall Reynolds numbers for which fully developed conditions exist.