Laminar Flow With Large Injection Through Parallel and Uniformly Porous Walls of Different Permearility

Shrestha, G. M.; Terrill, R. M.

doi:10.1093/qjmam/21.4.413

Cited by 37 publications

(18 citation statements)

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“…Excellent comparison validates our numerical computation and the use of extrapolation to improve the accuracy of the results. Another source of validity of our results is Table 3 in which present results have been compared with the literature results [4]. Shrestha and Terrill [4] computed values of shear stresses at the walls and the position of viscous layer across the channel using numerical technique and the series method.…”

Section: Resultsmentioning

confidence: 55%

“…Another source of validity of our results is Table 3 in which present results have been compared with the literature results [4]. Shrestha and Terrill [4] computed values of shear stresses at the walls and the position of viscous layer across the channel using numerical technique and the series method. An excellent comparison of our numerical results for the case of Newtonian fluid flow with the literature results may be seen in Table 3 for three sets of values of R and A.…”

Section: Resultsmentioning

confidence: 55%

“…We observe that the Eq. (19) reduces to the corresponding governing equation for the Newtonian fluid as given in [4][5][6] whereas the Eq. (20) becomes identically zero for vanishing microrotation and j = 0.This validates our model for the micropolar fluid motion.…”

Section: Problem Formulationmentioning

confidence: 99%

“…This exact solution was developed and generalized by Cox [2], Brady [3], Terrill and Shrestha [4,5], Terrill [6], Waston et al [7] and Robinson [8]. Cox [2] examined the flow by considering channel with one porous wall and other non-porous but was accelerating.…”

Section: Introductionmentioning

confidence: 99%

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Numerical study of asymmetric laminar flow of micropolar fluids in a porous channel

2009

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Section: Resultsmentioning

confidence: 55%

Section: Resultsmentioning

confidence: 55%

Section: Problem Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Numerical study of asymmetric laminar flow of micropolar fluids in a porous channel

2009

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“…He used similarity transformations to reduce the coupled system of partial differential equations to a fourth-order nonlinear ordinary differential equation (ODE) and found its exact solution subject to the transformed boundary conditions. This exact solution was further extended and generalized by Cox [2], Brady [3], Terrill and Shrestha [4,5], Terrill [6], Waston et al [7], and Robinson [8] for various conditions on the channel walls.…”

Section: Introductionmentioning

confidence: 97%

Numerical simulation of flow of micropolar fluids in a channel with a porous wall

Ashraf

Syed

Kamal

2011

Numerical Methods in Fluids

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SUMMARYTwo-dimensional steady, laminar, and incompressible flow of a micropolar fluid in a channel with no-slip at one wall and constant uniform injection through the other wall is considered for different values of the Reynolds number R. The main flow stream is superimposed by constant injection velocity at the porous wall. The micropolar model introduced by Eringen is used to describe the working fluid. An extension of Berman's similarity transformations is used to reduce governing equations to a set of nonlinear coupled ordinary differential equations (ODEs) in dimensionless form. An algorithm based on finite difference method is employed to solve these ODEs and Richardson's extrapolation is used to obtain higher order accuracy. It has been found that the magnitude of shear stress increases strictly at the impermeable wall whereas it decreases steadily at the permeable wall, by increasing the injection velocity. The maximum value of streamwise velocity and that of the microrotation both increase with increasing the magnitude of R.

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Moderate‐to‐large injection and suction driven channel flows with expanding or contracting walls

2003

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We consider in this paper the incompressible laminar flow in a porous channel with expanding or contracting walls. While the head-end is closed by a compliant membrane, the downstream end is left unobstructed. For symmetric injection or suction along the uniformly expanding porous walls, the Navier-Stokes equations are reduced to a single, nonlinear, ordinary differential equation. The latter is obtained via similarity transformations in both time and space. The resulting equation is then solved both numerically and asymptotically, using perturbations in the crossflow Reynolds number R. Two separate approaches are presented for each of the injection and suction cases, respectively. For the large injection case, the governing equation is first integrated and the resulting third-order differential equation is solved using the method of variation of parameters. For the large suction case, the governing equation is first simplified near the wall and then solved using successive approximations. Results are then correlated and compared for variations in R and the dimensionless wall expansion rate α. For injection-induced flow, the asymptotic solution becomes more accurate when R/α is increased. Its deviation from the classic sinusoidal profile arising in nonexpanding channels becomes less significant with successive increases in R. For suction-induced flows, faster wall contractions increase the effective Reynolds number −(α + R), thus leading to more precise approximations. For the same absolute value of R, the suction-flow approximation tends to be the most accurate of the two and the least sensitive to variations in α. As −(α + R) is increased, the suction profile approaches the linear form anticipated in nonexpanding channels. By comparison with the injection-induced flow, suction is characterized by improved accuracy, sharper flow turning, and larger

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Laminar Flow With Large Injection Through Parallel and Uniformly Porous Walls of Different Permearility

Cited by 37 publications

References 0 publications

Numerical study of asymmetric laminar flow of micropolar fluids in a porous channel

Numerical study of asymmetric laminar flow of micropolar fluids in a porous channel

Numerical simulation of flow of micropolar fluids in a channel with a porous wall

Moderate‐to‐large injection and suction driven channel flows with expanding or contracting walls

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