Laminar Pipe Flow With Injection and Suction Through a Porous Wall

Yuan, Shao

doi:10.21236/ad0058831

Cited by 100 publications

(98 citation statements)

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“…A rigorous asymptotic analysis of solutions of type I for large negative R appears in [8]. Included there are proofs of several conjectures based on numerical evidence obtained by Yuan and Finkelstein [21]. Recently, McLeod [10] has proved the validity of the asymptotic +*■ T) FIGURE 1.…”

Section: Type I and Type Ii Solutionsmentioning

confidence: 99%

“…In particular, the case 0 < e <C 1, which corresponds to large suction, (i.e., R > 1) leads to three such problems, one of which is the subject of this paper. This problem and related problems have been studied by Berman [3], Proudman [12], Yuan and Finkelstein [21], Terrill [16], Terrill and Thomas [17], Robinson [13], Skalak and Wang [15], and Zaturska et al [22]. The importance of exponentially small terms in some of the analyses was commented on by Van Dyke [18].…”

Section: Introductionmentioning

confidence: 99%

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Asymptotic solution of a laminar flow in a porous channel with large suction: A nonlinear turning point problem

MacGillivray¹,

Lu²

1994

Methods and Applications of Analysis

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Section: Type I and Type Ii Solutionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Asymptotic solution of a laminar flow in a porous channel with large suction: A nonlinear turning point problem

MacGillivray¹,

Lu²

1994

Methods and Applications of Analysis

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“…Berman [7] attempted a solution to the problem of twodimensional laminar flow in channels having porous walls based on the assumption of uniform wall suction. On similar grounds, Yuan and Finkelstein [43] came up with the solution for axisymmetric channels. Both these solutions are reported to be valid at values of Reynolds number nearing one.…”

Section: Introductionmentioning

confidence: 93%

Development of a predictive mathematical model for coupled stokes/Darcy flows in cross-flow membrane filtration

Hanspal

Waghode

Nassehi

et al. 2009

Chemical Engineering Journal

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a b s t r a c tFree flow regimes accompanied by porous walls feature commonly in a variety of natural processes and industrial applications such as groundwater flows, packed beds, arterial blood flows and cross-flow and dead-end filtrations. Cross-flow microfiltration or ultrafiltration processes are generally employed in a range of industrial situations ranging from oil to medical applications. The coupled free/porous fluid transport phenomenon plays an equally important role along with the particle transport mechanisms concerning the separation efficiency of cross-flow membrane filtration. To provide a theoretical background for the experimental outcomes of cross-flow filtration, a mathematically sound model is desired which can reliably represent the interfacial boundary whilst maintaining the continuity of flow field variables across the interface between the free and porous flow regimes. Notwithstanding the numerous attempts reported in the literature, the development of a generic mathematical model for coupled flows has been prohibited by the complexities of interactions between the free and the porous flow systems. Henceforth, the aim of present work is to gain a better mathematical understanding of the interfacial phenomena encountered in coupled free and porous flow regimes applicable to cross-flow filtration systems. The free flow dynamics can be justifiably represented by the Stokes equation whereas the non-isothermal, non-inertial and incompressible flow in a low permeability porous medium can be handled by the Darcy equation. Solutions to the system of partial differential equations (PDEs) are obtained using the finite element method employing mixed interpolations for the primary field variables which are velocity and pressure. A nodal replacement scheme previously developed by the same authors has been effectively enforced as the boundary constraint at the free/porous interface for coupling the two physically different flow regimes in a single mathematical model. A series of computational experiments for permeability values of the porous medium ranging between 10 −6 and 10 −12 m 2 have been performed to examine the susceptibility of the developed model towards complex and irregular shaped geometries. Our results indicate that at high permeability values, the discrepancy in mass balance calculations is observed to be significant for a curved porous surface, which may be attributed to the inability of the Darcy equation to represent the flow dynamics in a highly permeable medium. At a low permeability, a very small amount of fluid permeated through the free/porous interface as most of the fluid leaves the domain through the free flow exit. The geometry and permeability of the free/porous interface are found to affect the amount of fluid passing through the porous medium significantly. All the numerical solutions that are presented have been theoretically validated for their accuracy by computing the overall mass continuity across the computational domains.

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“…1) giving: (9) Upon integration of Eq. (9) from the wall of the tube (r = R; u = 0) to a distance r from the center where the axial velocity u is to be evaluated, gives: (10) Now, the overall volumetric fl ow rate of the fl uid can be obtained by integrating Eq.…”

Section: Modeling Flow Through Tubular Hollow--fibersmentioning

confidence: 99%

Flow behavior in weakly permeable micro-tube with varying viscosity near the wall

Gupta

Kumar

Chand

2017

Polish Journal of Chemical Technology

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Weakly permeable micro-tubes are employed in many applications involving heat and/or mass transfer. During these processes, either solute concentration builds up (mass transfer) or steep change in temperature (heat transfer) takes place near the permeable wall causing a change in the viscosity of the fl uid. Results of the present work suggest that such change in viscosity leads to a considerable alteration in the fl ow behavior, and the commonly assumed parabolic velocity profi le no longer exists. To solve the problem numerically, the equation of motion was simplifi ed to represent permeation of incompressible, Newtonian fl uid with changing viscosity through a micro-tube. Even after considerable simplifi cation, the accuracy of the results was the same as that obtained by previously reported results for some specifi c cases using rigorous formulation. The algorithm developed in the present work is found to be numerically robust and simple so that it can be easily integrated with other simulations.

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Laminar Pipe Flow With Injection and Suction Through a Porous Wall

Cited by 100 publications

References 0 publications

Asymptotic solution of a laminar flow in a porous channel with large suction: A nonlinear turning point problem

Asymptotic solution of a laminar flow in a porous channel with large suction: A nonlinear turning point problem

Development of a predictive mathematical model for coupled stokes/Darcy flows in cross-flow membrane filtration

Flow behavior in weakly permeable micro-tube with varying viscosity near the wall

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