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

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.