On boundary layer growth past a spinning body

Summary The incompressible boundary layer growth on a body of revolution in spinning motion when the outer flow and the angular velocity of the body are expressed in powers series of √t is studied. Series at small time are established for the velocity. A simple application is presented in the case of a sphere and the separation characteristics are studied. Entrata in Redazione il 23 novembre 1970.     

Analysis of boundary conditions for approximate solution of problems of viscous incompressible flow past a body

Translated from Aktual'nye Voprosy Prikladnoi Matematiki, pp. 49–54, 1989.     

Transition of MHD boundary layer flow past a stretching sheet

In this paper a study is carried out to understand the transition effect of boundary layer flow: (1) due to a suddenly imposed magnetic field over a viscous flow past a stretching sheet and (2) due to sudden withdrawal of magnetic field over a viscous flow past a stretching sheet under a magnetic field. In both the cases the sheet stretches linearly along the direction of the fluid flow. Governing equations have been non-dimensionalised and the non-dimensionalised equations have been solved using the implicit finite difference method of Crank–Nicholson type. Comparison between the steady state exact solutions and the steady state computed solutions has been carried out. Graphical representation of the dimensionless horizontal velocity, vertical velocity and local skin friction profiles of the steady state and unsteady state has been presented. Computation has been carried out for various values of the magnetic parameter M. The obtained results has been interpreted and discussed.     

A univalent spiral-vortex model for separated flow past a polygonal obstacle

Summary A free-streamline flow model for flow past a polygonal obstacle with a near-wake terminating in Tulin's double spiral vortices is constructed. The flows are univalent for a large class of geometries. In addition a criterion is given for determining the underpressure as function of the Reynolds number using the Stokes solution for diffusion of a vortex sheet, and an extension of Tulin and Hsu's matching theory to transitional flows.

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Sunto Si costruisce un modello di flusso con scia e vortici a doppia spirale alla Tulin per un ostacolo poligonale arbitrario. Il flusso risulta univalente per un' ampia classe di geometrie. Inoltre viene proposto un criterio per correlare il parametro del modello al numero di Reynolds del corrispondente flusso viscoso, combinando la soluzione di Stokes per la diffusione di uno strato di vortici con la teoria di Tulin e Hsu (1980).

     

Visco-elastic boundary layer flow past a stretching plate and heat transfer

In the present paper, we study the temperature profile in the case of a linear stretching plate for large Prandtl numberP by an asymptotic approach. Also, we evaluate the Nusselt number and the order of magnitude of Prandtl number for variable Nusselt numbers.     

Falkner-Skan boundary layer flow of a power-law fluid past a stretching wedge

The steady two-dimensional laminar boundary layer flow of a power-law fluid past a permeable stretching wedge beneath a variable free stream is studied in this paper. Using appropriate similarity variables, the governing equations are reduced to a single third order highly nonlinear ordinary differential equation in the dimensionless stream function, which is solved numerically using the Runge-Kutta scheme coupled with a conventional shooting procedure. The flow is governed by the wedge velocity parameter λ, the transpiration parameter f₀, the fluid power-law index n, and the computed wall shear stress is f″(0). It is found that dual solutions exist for each value of f₀, m and n considered in λ − f″(0) parameter space. A stability analysis for this self-similar flow reveals that for each value of f₀, m and n, lower solution branches are unstable while upper solution branches are stable. Very good agreements are found between the results of the present paper and that of Weidman et al. [28] for n = 1 (Newtonian fluid) and m = 0 (Blasius problem [31]).     

A second order solution for the non-equilibrium flow of a relaxing gas in a plane expansion

Zusammenfassung Um eine analytische Lösung zu erhalten, welche Effekte der endlichen Entropie- und Wirbelstärkeerzeugung berücksichtigt, ist die linearisierte Theorie formell durch Einbeziehung von Grössen zweiter Ordnung erweitert worden. Anwendungen sind gegeben für den Fall einer ebenen Expansionsströmung eines harmonisch relaxierenden Gases, das sich nicht im Gleichgewicht befindet. Die Theorie zweiter Ordnung zeigt eine Verbesserung gegenüber der ersten Ordnung in der Voraussage der Zustandsgrössen entlang der Wand. Insbesondere wird eine Abschätzung der Abweichungen der asymptotischen Wandwerte des Druckes, der Temperatur usw. vom entsprechenden Gleichgewichtswert für unendliche Reaktionsgeschwindigkeiten ermöglicht.     

Free convection flow of a second order fluid past a hot vertical plate

Laminar free convection flow of a second order fluid past a hot vertical plate with varying wall temperature has been studied in this paper. Exact solutions for the velocity and temperature fields have been obtained. The effects of elastic coefficient on the velocity and temperature fields, rate of heat transfer and the skin-friction have been studied.     

Deficient discrete cubic spline solution for a system of second order boundary value problems

In this paper we use deficient discrete cubic spline to obtain approximate solution of a system of second order boundary value problems. It is shown that the method is of order 2 when a parameter takes a specific value. A well known numerical example is presented to illustrate our method as well as to compare the performance with other numerical methods proposed in the literature.     

A boundary value problem for a differential equation of second order

We find the spectrum and prove a theorem on the expansion of an arbitrary function satisfying certain smoothness conditions in terms of the root functions of a boundary value problem of the type ?y″+q(x)+a/x²y=λy, y(0)=0, M(λ) y(a)+N(λ) y(b)=0, where 0   

A two-parameter boundary problem for second order differential system

Summary This paper is concerned with second order differential systems involving two parameters with boundary conditions specified at three points. In particular, we consider the system y' = k(x, λ, μ)z, z' = -g(x, λ, μ)y, where k and g are real-valued junctions defined on X: a ≤ x ≤ c, L: L₁ < λ < L₂, and M: M₁ < μ < M₂. This system is studied together with the boundary conditions α(λ, μ)y(a) - β(λ, μ)z(a)=0, γ(λ, μ)y(b) - δ(λ, μ)z(b)=0, ε₁(μ)y(b) - φ₁(μ)z(b)=ε₂(μ)y(c) - φ₂(μ)z(c), where α, β, δ, γ, ε_i, φ_i, i=1, 2, are continuous functions of the parameters. This work establishes the existence of eigenvalue pairs for the boundary problem and the oscillatory behavior of the associated solutions. These results complement those previously obtained by the authors and B. D. Sleeman, where boundary conditions of the ? Sturm-Liouville ? type were studied. Entrata in Redazione il 5 dicembre 1977. The research for this paper was supported by a University College Reasearch Grant, University of Alabama in Birmingham.     

A free boundary problem of elliptic equation arising in supersonic flow past a conical body

We study free boundary value problems of elliptic equation caused by a supersonic flow past a non-symmetric conical body. The flow is described by the potential flow equation. In the self-similar coordinate system the problem can be reduced to a boundary value problem of second order nonlinear elliptic equation with a free boundary. Applying the partial hodograph transformation and the method of nonlinear alternative iteration we proved the existence of solution to this boundary value problem. Consequently, we also proved the conclusion that for the problem of supersonic flow past a conical body, if the conical body is slightly different from a circular cone with its vertex angle less than a given value determined by the parameters of the coming flow, then there exists a weak entropy solution with an attached conical shock.     

Coherent structure in flow over a slitted bluff body

The focus of the present investigation is resolution of the coherent structure in the near wake behind a slitted bluff body. The bluff body is two-dimensional with gap ratio from 0.12 to 0.48. The evolution of the structure was numerically investigated using the renormalization group (RNG) k–ε model at Reynolds number of 470,000. Two types of coherent structure are identified: At low gap ratio 0.12, the structure is characterized by a flip–flopping gap flow; at high ratio 0.22–0.48, the gap flow deflects to one side with an asymmetrical wake. The coherent structure is divided by the gap flow into two zones called the primary recirculation zone and the secondary recirculation zone. The coherent structure is intimately related to the gap ratio, and the structure of small gap ratio is different from that of large gap ratio because the interaction between two zones relates to the gap ratio. To explain the vortex shedding, a mechanism that single vortex of large size suddenly immerses between two shear layers was proposed. Experimental results using point-to-point method and particle-image velocimetry (PIV) measurements in a close wind tunnel were also carried out to confirm the observation from the numerical study. The evidence shows that the numerical results are of good agreement with the experiments. The comparison between the RNG k–ε model and the large eddy simulation also indicates that the RNG k–ε model is adequate in computing the bluff body flow.     

A boundary value problem for second order fuzzy differential equations

In this paper, we interpret a two-point boundary value problem for a second order fuzzy differential equation by using a generalized differentiability concept. We present a new concept of solutions and, utilizing the generalized differentiability, we investigate the problem of finding new solutions. Some examples are provided for which the new solutions are found.     

The probabilistic solution of the third boundary value problem for second order elliptic equations

Using standard reflected Brownian motion (SRBM) and martingales we define (in the spirit of Stroock and Varadhan-see [S-V]) the probabilistic solution of the boundary value problem

Positive solution of singular Dirichlet boundary value problems for second order differential equation system

This paper investigates the existence of positive solutions of singular Dirichlet boundary value problems for second order differential system. A necessary and sufficient condition for the existence of C[0,1]×C[0,1] positive solutions as well as C¹[0,1]×C¹[0,1] positive solutions is given by means of the method of lower and upper solutions and the fixed point theorems. Our nonlinearity fi(t,x₁,x₂) may be singular at x₁=0, x₂=0, t=0 and/or t=1, i=1,2.