A “Boundary Layer” Method of Obtaining an Approximate Solution to the Infinite Fin Problem

2002 ◽  
Author(s):  
William S. Janna ◽  
John I. Hochstein
Keyword(s):  
Boundary Layer ◽  
Exact Solution ◽  
Approximate Solutions ◽  
Third Order ◽  
Fin Efficiency ◽  
Layer Method ◽  
Boundary Layer Method ◽  
Layer Flow ◽  
Alternative Solutions ◽  
Good Agreement

The classical infinite fin problem is considered in this study. First the exact solution is stated in which temperature, heat transfer rate, effectiveness and fin efficiency are all given. Then the boundary layer method is used to obtain alternative solutions in polynomial form. Boundary conditions are written for this method, and applied in various combinations to an assumed temperature profile. First, second, and third order approximate solutions are derived. Temperature profiles obtained from these solutions are compared to that calculated from the exact solution. It is shown that as more terms are included in the assumed profile, the resultant expression better fits the exact solution. Very good agreement between the third order and exact solution was obtained. Also derived from the approximate solutions was a distance along the fin beyond which the temperature difference between the fin and the surroundings is negligible. This arbitrary distance is analogous to the boundary layer thickness for boundary layer flow over a flat plate.

IACC Appendage Studies

1993 ◽  
Author(s):  
E. N. Tinoco ◽  
A. E. Gentry ◽  
P. Bogataj ◽  
E. G. Sevigny ◽  
B. Chance
Keyword(s):  
Boundary Layer ◽  
Wind Tunnel ◽  
Computational Models ◽  
Ground Plane ◽  
Induced Drag ◽  
Layer Method ◽  
Boundary Layer Method ◽  
Wind Tunnel Data ◽  
Constant Section ◽  
Good Agreement

Experimental and computational studies of several representative IACC appendage geometries were carried out to establish baseline data and verify computational models and methods. Wind tunnel tests of an unheeled, unswept, constant section, rectangular planform keel mounted on a ground plane included force and moment measurements, and wake surveys at various angles of attack. Test configurations (all at constant draft) included the addition of ballast bulbs and winglets. Correlations of computational results with experimental wind tunnel data were made. A502/PAN AIR potential flow induced drag predictions proved to be in good agreement with the wind tunnel data. Comparisons are also presented between A598 (A502 + boundary layer), wind tunnel results and empirical predictions. Again good agreement was shown for cases within the limitations of the boundary layer method.

Compressible Conical Diffuser Flow Using the Energy Deficit Boundary Layer Method

1975 ◽  
Vol 17 (4) ◽  
pp. 206-213
Author(s):  
J. L. Livesey ◽  
A. O. Odukwe ◽  
W. A. Kamal
Keyword(s):  
Boundary Layer ◽  
Performance Prediction ◽  
Prediction Method ◽  
Energy Deficit ◽  
Layer Method ◽  
Diffuser Flow ◽  
Conical Diffuser ◽  
Boundary Layer Method ◽  
Incompressible Boundary ◽  
Good Agreement

A performance prediction method for high inlet Mach number conical diffusers is developed, which uses the kinetic energy deficit equation in the calculation of the compressible turbulent boundary layer. A power law velocity profile is assumed together with Crocco's relation for the temperature distribution. Following Green, Morkovin's hypothesis is invoked to extend to the compressible flow the existing relations for the shear work integral originally developed for incompressible boundary layers. Comparison of the predicted results with available experimental results shows good agreement.

Equilibrium Temperatures in a Boundary-Layer Flow Over a Flat Plate of Absorbing-Emitting Gas

1968 ◽  
Vol 90 (2) ◽  
pp. 257-266 ◽  
Author(s):  
Yehuda Taitel ◽  
J. P. Hartnett
Keyword(s):  
Boundary Layer ◽  
Exact Solution ◽  
Flat Plate ◽  
Interaction Mechanism ◽  
Approximate Solutions ◽  
Equilibrium Temperature ◽  
Constant Heat Flux ◽  
Adiabatic Wall ◽  
Approximate Methods ◽  
Layer Flow

The effect of radiation on the equilibrium temperature for a flow of emitting-absorbing gas over a flat plate is studied. Three methods of solution are formulated: An approximate solution for a thin boundary layer, a similarity solution for the limiting case when the boundary layer is optically thick, and an exact solution. Emphasis is put on the study of the recovery or adiabatic wall case, where conduction to the wall is balanced by the net radiation away from the wall. Results are reported for the limiting cases of a black plate and completely reflective plate and for a unit Prandtl number. The exact solution reflects very favorably on the use of the approximate methods and points out clearly the conditions for which the approximate solutions are applicable. Results are also reported for the equilibrium wall temperature for the case of constant heat flux and for the recovery factor in the case of blowing and suction; both for optically thin boundary layers. Special attention is put on the interaction mechanism and the role of the emitting-absorbing coefficient on this process. It is shown that, for small absorption coefficient, high wall emissivity, and Mach number, the results approach the case where the gas is transparent.

Comparison of the Triple-Deck Theory, Interactive Boundary Layer Method, and Navier-Stokes Computation for Marginal Separation

1994 ◽  
Vol 116 (1) ◽  
pp. 22-28 ◽  
Author(s):  
Chao-Tsung Hsiao ◽  
Laura L. Pauley
Keyword(s):  
Boundary Layer ◽  
Separation Bubble ◽  
Physical Phenomenon ◽  
Navier Stokes ◽  
Gradient Distribution ◽  
Layer Method ◽  
Boundary Layer Method ◽  
Incompressible Boundary ◽  
Layer Flow ◽  
Comparison Of The Results

The steady two-dimensional marginal separation of an incompressible boundary layer flow within a channel was solved independently by three different methods: the triple-deck method of marginal separation, the interactive boundary layer method, and the full Navier-Stokes computation. From comparison of the results between these three methods, the accuracy and appropriateness of each method was determined. The critical condition beyond which the steady marginal separation solution of triple-deck method does not exist was related to a physical phenomenon in which the separation bubble becomes unsteady. Factors such as Reynolds number and pressure gradient distribution which might influence the accuracy of the marginal separation solution were also investigated.

Boundary layer method in the problem of far propagation of surface SV-waves

2011 ◽  
Vol 175 (6) ◽  
pp. 651-671
Author(s):  
N. Ya. Kirpichnikova ◽  
A. S. Kirpichnikova
Keyword(s):  
Boundary Layer ◽  
Layer Method ◽  
Boundary Layer Method

A Simple and Robust Subsonic Boundary Layer Method to Be Used with the Panel Method for Wing Calculations Using a Wing Strip Approach

2015 ◽  
Vol 798 ◽  
pp. 596-601
Author(s):  
R.F. Francisco Reis ◽  
Guilherme A. Santana ◽  
Paulo Iscold ◽  
Carlos A. Cimini
Keyword(s):  
Boundary Layer ◽  
Lift Coefficient ◽  
Aircraft Design ◽  
Aerodynamic Characteristics ◽  
Viscous Drag ◽  
Layer Method ◽  
Boundary Layer Method ◽  
Dimensional Boundary ◽  
Classical Integral ◽  
Empirical Corrections

This paper will present the development of a simple subsonic boundary layer method suitable to be used coupled with panel methods in order to estimate the aerodynamic characteristics, including viscous drag and maximum lift coefficient, of 3D wings. The proposed method does not require viscous-inviscid iterations and is based on classical integral bi-dimensional boundary layer theory using Thwaites and Head ́s models with bi-dimensional empirical corrections applied to each wing strip being therefor robust and efficient to be used in the early conceptual stage of aircraft design. Presented results are compared to the Modified CS Method in an IBL scheme and experimental data and are shown to provide good results.

scholarly journals THIRD-ORDER GENERALIZED DISCONTINUOUS IMPULSIVE PROBLEMS ON THE HALF-LINE

2021 ◽  
Vol 26 (4) ◽  
pp. 548-565
Author(s):  
Feliz Minhós ◽  
Rui Carapinha
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Boundary Layer Flow ◽  
Stretching Sheet ◽  
Flow Problem ◽  
Sufficient Conditions ◽  
Half Line ◽  
Third Order ◽  
Impulsive Problems ◽  
Layer Flow

In this paper, we improve the existing results in the literature by presenting weaker sufficient conditions for the solvability of a third-order impulsive problem on the half-line, having generalized impulse effects. More precisely, our nonlinearities do not need to be positive nor sublinear and the monotone assumptions are local ones. Our method makes use of some truncation and perturbed techniques and on the equiconvergence at infinity and the impulsive points. The last section contains an application to a boundary layer flow problem over a stretching sheet with and without heat transfer.

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