Three-dimensional flow near a two-dimensional stagnation point

Davey, A.; Schofield, Damian

doi:10.1017/s0022112067001958

Cited by 41 publications

(26 citation statements)

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“…Full numerical solution of the system also confirms the restriction on α , ie, solutions do exist only in the range −1< α < ∞ . This is also reported in the studies of Davey and Schofield . These numerical solutions always compliment the asymptotic solutions qualitatively, and hence the same results have not been reproduced.…”

Section: Resultssupporting

confidence: 63%

“…This is also reported in the studies of Davey and Schofield. 3 These numerical solutions always compliment the asymptotic solutions qualitatively, and hence the same results have not been reproduced. Also, in Figures 5 and 6, the wall shear stresses ′′ (0) and g ′′ (0) are compared with the asymptotic solutions and found that results are agreeing well.…”

Section: Resultsmentioning

confidence: 90%

“…Since there is an additional flow component, the shear‐to‐strain‐rate or 3‐dimensionality parameter ( α ) appears in the differential equations (Banks). Davey and Davey and Schofield have analyzed self‐similar solutions of the 3‐dimensional boundary‐layer flows in which the outer mainstream irrotational flows are considered in linear forms U = U ∞ x and V = V ∞ y (where U ∞ and V ∞ , in our notations, are strain rates and x and y are distances along the surface from the leading edge) in both directions and have reported a wide range of boundary‐layer flows including the 2‐dimensional case. The solutions exist only in the range −1≤ α ≤0.…”

Section: Introductionmentioning

confidence: 99%

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Asymptotic and numerical solutions of three‐dimensional boundary‐layer flow past a moving wedge

Kudenatti

Bujurke

2018

Math Methods in App Sciences

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We consider a laminar boundary‐layer flow of a viscous and incompressible fluid past a moving wedge in which the wedge is moving either in the direction of the mainstream flow or opposite to it. The mainstream flows outside the boundary layer are approximated by a power of the distance from the leading boundary layer. The variable pressure gradient is imposed on the boundary layer so that the system admits similarity solutions. The model is described using 3‐dimensional boundary‐layer equations that contains 2 physical parameters: pressure gradient (β) and shear‐to‐strain‐rate ratio parameter (α). Two methods are used: a linear asymptotic analysis in the neighborhood of the edge of the boundary layer and the Keller‐box numerical method for the full nonlinear system. The results show that the flow field is divided into near‐field region (mainly dominated by viscous forces) and far‐field region (mainstream flows); the velocity profiles form through an interaction between 2 regions. Also, all simulations show that the subsequent dynamics involving overshoot and undershoot of the solutions for varying parameter characterizing 3‐dimensional flows. The pressure gradient (favorable) has a tendency of decreasing the boundary‐layer thickness in which the velocity profiles are benign. The wall shear stresses increase unboundedly for increasing α when the wedge is moving in the x‐direction, while the case is different when it is moving in the y‐direction. Further, both analysis show that 3‐dimensional boundary‐layer solutions exist in the range −1<α<∞. These are some interesting results linked to an important class of boundary‐layer flows.

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Section: Resultssupporting

confidence: 63%

Section: Resultsmentioning

confidence: 90%

Section: Introductionmentioning

confidence: 99%

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Asymptotic and numerical solutions of three‐dimensional boundary‐layer flow past a moving wedge

Kudenatti

Bujurke

2018

Math Methods in App Sciences

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“…for Y † = O(1), with θ and A given asymptotically by (27), we are in a position to calculate the required exponentially small correction term , which satisfies…”

Section: Analysis For γ → ∞ (Small Suction or Injection)mentioning

confidence: 99%

“…Coefficients in the Series θ ∼ N 0 θ n µ n and A ∼ N 0 A n µ n , Whose First Few Terms are Given in (27), and Coefficients ψ n in (42) n θ n A n ψ n…”

Section: Tablementioning

confidence: 99%

Self‐Similar “Stagnation Point” Boundary Layer Flows with Suction or Injection

King

Cox

2005

Stud Appl Math

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Multiple solutions are reported for the two-dimensional boundary layer flow of a viscous fluid near a permeable wall through which fluid is uniformly withdrawn. In the limit of large wall suction, three flows of similarity form are found: the first is the well-known monotonic solution of Terrill; the second exhibits flow reversal, with the streamlines being separated into three distinct cells; the third also exhibits flow reversal, but has multiple cells only when the fluid withdrawal speed is less than some threshold. The wall injection problem is also briefly studied, only Terrill's branch of solutions being found. Numerical and asymptotic solutions are presented and compared; the large-suction asymptotics of the third solution branch are found to be rather subtle.

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References

2013

Incompressible Flow

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Three-dimensional flow near a two-dimensional stagnation point

Abstract: This paper shows the existence of a three-dimensional solution of the boundary-layer equations of viscous incompressible flow in the immediate neighbourhood of a two-dimensional stagnation point of attachment. The numerical solution has been obtained.

Cited by 41 publications

References 1 publication

Asymptotic and numerical solutions of three‐dimensional boundary‐layer flow past a moving wedge

Asymptotic and numerical solutions of three‐dimensional boundary‐layer flow past a moving wedge

Self‐Similar “Stagnation Point” Boundary Layer Flows with Suction or Injection

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