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 journalArticlepeer-review

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 - Jan 1 2016

All Science Journal Classification (ASJC) codes

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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