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

Susmita Sadhu, Joseph E. Paullet

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)125-141
Number of pages17
JournalDynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis
Volume23
Issue number2
StatePublished - 2016

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Transpiration
Radial flow
A Priori Bounds
Blow molding
Boundary value problems
Stretching
Suction
Derivatives
Skin friction
Boundary Value Problem
Navier Stokes equations
Derivative
Reynolds number
Skin Friction
Similarity Transformation
Friction Coefficient
Monotonic
Existence of Solutions
Navier-Stokes Equations
Circle

All Science Journal Classification (ASJC) codes

  • Applied Mathematics
  • Analysis
  • Discrete Mathematics and Combinatorics

Cite this

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title = "Existence and a priori bounds for radial stagnation flow on a stretching cylinder with wall transpiration",
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.",
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AU - Paullet, Joseph E.

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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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