### Abstract

In this paper we investigate a boundary value problem resulting from a similarity transformation of the Navier-Stokes equations governing radial stagnation ow toward a permeable stretching infinite cylinder with superimposed suction or blowing on the cylinder surface. A steady, laminar, viscous, and incompressible uid impinges normally onto the cylindrical surface and spreads out axially away from a stagnation circle. The boundary value problem governing the ow is given by ηf′″ + f″ + R(ff″ + 1 - f′2) = 0, f(1) = γ, f′(1) = λ, f′(∞) = 1, where R is the Reynolds number, γ represents wall suction (γ > 0) or blowing (γ < 0), and γ > 0 represents the stretching rate of the cylinder. Here we prove existence of solutions with monotonic derivatives for all λ ≥ 0 and for all γ ϵ ℝ. We also prove that if 0 < λ < 1 and γ ≤ -1/R, then the boundary value problem has a unique solution. If λ > 1, we show that any further solution cannot have a monotonically decreasing derivative. Finally, an a priori bound on the skin friction coefficient is obtained for all λ ≥ 0.

Original language | English (US) |
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Pages (from-to) | 125-141 |

Number of pages | 17 |

Journal | Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis |

Volume | 23 |

Issue number | 2 |

State | Published - 2016 |

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### All Science Journal Classification (ASJC) codes

- Applied Mathematics
- Analysis
- Discrete Mathematics and Combinatorics

### Cite this

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**Existence and a priori bounds for radial stagnation flow on a stretching cylinder with wall transpiration.** / Sadhu, Susmita; Paullet, Joseph E.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Existence and a priori bounds for radial stagnation flow on a stretching cylinder with wall transpiration

AU - Sadhu, Susmita

AU - Paullet, Joseph E.

PY - 2016

Y1 - 2016

N2 - In this paper we investigate a boundary value problem resulting from a similarity transformation of the Navier-Stokes equations governing radial stagnation ow toward a permeable stretching infinite cylinder with superimposed suction or blowing on the cylinder surface. A steady, laminar, viscous, and incompressible uid impinges normally onto the cylindrical surface and spreads out axially away from a stagnation circle. The boundary value problem governing the ow is given by ηf′″ + f″ + R(ff″ + 1 - f′2) = 0, f(1) = γ, f′(1) = λ, f′(∞) = 1, where R is the Reynolds number, γ represents wall suction (γ > 0) or blowing (γ < 0), and γ > 0 represents the stretching rate of the cylinder. Here we prove existence of solutions with monotonic derivatives for all λ ≥ 0 and for all γ ϵ ℝ. We also prove that if 0 < λ < 1 and γ ≤ -1/R, then the boundary value problem has a unique solution. If λ > 1, we show that any further solution cannot have a monotonically decreasing derivative. Finally, an a priori bound on the skin friction coefficient is obtained for all λ ≥ 0.

AB - In this paper we investigate a boundary value problem resulting from a similarity transformation of the Navier-Stokes equations governing radial stagnation ow toward a permeable stretching infinite cylinder with superimposed suction or blowing on the cylinder surface. A steady, laminar, viscous, and incompressible uid impinges normally onto the cylindrical surface and spreads out axially away from a stagnation circle. The boundary value problem governing the ow is given by ηf′″ + f″ + R(ff″ + 1 - f′2) = 0, f(1) = γ, f′(1) = λ, f′(∞) = 1, where R is the Reynolds number, γ represents wall suction (γ > 0) or blowing (γ < 0), and γ > 0 represents the stretching rate of the cylinder. Here we prove existence of solutions with monotonic derivatives for all λ ≥ 0 and for all γ ϵ ℝ. We also prove that if 0 < λ < 1 and γ ≤ -1/R, then the boundary value problem has a unique solution. If λ > 1, we show that any further solution cannot have a monotonically decreasing derivative. Finally, an a priori bound on the skin friction coefficient is obtained for all λ ≥ 0.

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UR - http://www.scopus.com/inward/citedby.url?scp=84963804668&partnerID=8YFLogxK

M3 - Article

VL - 23

SP - 125

EP - 141

JO - Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis

JF - Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis

SN - 1201-3390

IS - 2

ER -