On the analogy between the transport of vorticity and heat in laminar boundary layers

1962 ◽  
Vol 14 (3) ◽  
pp. 399-404 ◽  
Author(s):  
N. Riley
Keyword(s):  
Boundary Layer ◽  
Prandtl Number ◽  
Boundary Layers ◽  
Energy Equation ◽  
Plane Flow ◽  
Laminar Boundary Layers

The analogy between the transport of heat and vorticity when the Prandtl number is unity is used to provide a simple complementary solution of the boundary-layer energy equation for plane flow. The solution is extended to apply to axisymmetric boundary layers by suitably stretching the co-ordinate normal to the wall. Several applications of the solution are discussed.

scholarly journals On a Simple Method for Calculating Laminar Boundary Layers

1954 ◽  
Vol 5 (1) ◽  
pp. 25-38 ◽  
Author(s):  
K. E. G. Wieghardt
Keyword(s):  
Boundary Layers ◽  
Parametric Method ◽  
Symmetric Flow ◽  
Numerical Constant ◽  
Simple Method ◽  
Plane Flow ◽  
Laminar Boundary Layers ◽  
Energy Equations

SummaryA simple one parametric method, due to A. Walz and based on the momentum and energy equations, for calculating approximately laminar boundary layers is extended to cover axi-symmetric flow as well as plane flow. The necessary computing work is reduced a little.Another known method which requires still less computing work is also extended for axi-symmetric flow and, with the amendment of a numerical constant, proves adequate for practical purposes.

Laminar boundary layers behind detonation waves

1983 ◽  
Vol 387 (1793) ◽  
pp. 331-349 ◽  
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Boundary Layers ◽  
Flow Analysis ◽  
Time Dependent ◽  
Detonation Waves ◽  
Planar Geometry ◽  
Laminar Boundary Layers ◽  
Spherical Detonation ◽  
Layer Flow

New solutions are presented for non-stationary boundary layers induced by planar, cylindrical and spherical Chapman-Jouguet (C-J) detonation waves. The numerical results show that the Prandtl number ( Pr ) has a very significant influence on the boundary-layer-flow structure. A comparison with available time-dependent heat-transfer measurements in a planar geometry in a 2H 2 + O 2 mixture shows much better agreement with the present analysis than has been obtained previously by others. This lends confidence to the new results on boundary layers induced by cylindrical and spherical detonation waves. Only the spherical-flow analysis is given here in detail for brevity.

Effects of Curvature on Laminar Boundary Layers in Sink-Type Flows

1969 ◽  
Vol 91 (3) ◽  
pp. 353-358 ◽  
Author(s):  
W. A. Gustafson ◽  
I. Pelech
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Momentum Equation ◽  
Similarity Solutions ◽  
Momentum Thickness ◽  
Two Dimensional ◽  
Thickness Increase ◽  
Laminar Boundary Layers ◽  
Converging Channel ◽  
Special Case

The two-dimensional, incompressible laminar boundary layer on a strongly curved wall in a converging channel is investigated for the special case of potential velocity inversely proportional to the distance along the wall. Similarity solutions of the momentum equation are obtained by two different methods and the differences between the methods are discussed. The numerical results show that displacement and momentum thickness increase linearly with curvature while skin friction decreases linearly.

A Reference Temperature Method for Compressible Laminar Boundary Layers

1973 ◽  
Vol 2 (4) ◽  
pp. 201-204
Author(s):  
R. Camarero
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Wall Temperature ◽  
Reference Temperature ◽  
Integral Approach ◽  
Pressure Gradients ◽  
Two Dimensional ◽  
Laminar Boundary Layers ◽  
Temperature Method ◽  
Compressibility Effects

A calculation procedure for the solution of two-dimensional and axi-symmetric laminar boundary layers in compressible flow has been developed. The method is an extension of the integral approach of Tani to include compressibility effects by means of a reference temperature. Arbitrary pressure gradients and wall temperature can be specified. Comparisons with experiments obtained for supersonic flows over a flat plate indicate that the method yields adequate results. The method is then applied to the solution of the boundary layer on a Basemann inlet.

A Method for the Calculation of 3D Boundary Layers on Practical Wing Configurations

1981 ◽  
Vol 103 (1) ◽  
pp. 104-111 ◽  
Author(s):  
J. P. F. Lindhout ◽  
G. Moek ◽  
E. De Boer ◽  
B. Van Den Berg
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Boundary Layer Flow ◽  
Eddy Viscosity ◽  
Separated Flow ◽  
Laminar Boundary Layers ◽  
Eddy Viscosity Model ◽  
Airplane Wing ◽  
Turbulent Boundary Layer Flow ◽  
Layer Flow

This paper gives a description of a calculation method for 3D turbulent and laminar boundary layers on nondevelopable surfaces. A simple eddy viscosity model is incorporated in the method. Special attention is given to the organization of the computations to circumvent as much as possible stepsize limitations. The method is also able to proceed the computation around separated flow regions. The method has been applied to the laminar boundary layer flow over a flat plate with attached cylinder, and to a turbulent boundary layer flow over an airplane wing.

Closed-Form Analytical Solutions for Laminar Natural Convection on Horizontal Plates

2013 ◽  
Vol 135 (10) ◽  
Author(s):  
Abhijit Guha ◽  
Subho Samanta
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Heat Flux ◽  
Natural Convection ◽  
Prandtl Number ◽  
Boundary Layers ◽  
Wall Temperature ◽  
Temperature Profiles ◽  
Integral Analysis ◽  
Laminar Natural Convection

A boundary layer based integral analysis has been performed to investigate laminar natural convection heat transfer characteristics for fluids with arbitrary Prandtl number over a semi-infinite horizontal plate subjected either to a variable wall temperature or variable heat flux. The wall temperature is assumed to vary in the form T¯w(x¯)-T¯∞=ax¯n whereas the heat flux is assumed to vary according to qw(x¯)=bx¯m. Analytical closed-form solutions for local and average Nusselt number valid for arbitrary values of Prandtl number and nonuniform heating conditions are mathematically derived here. The effects of various values of Prandtl number and the index n or m on the heat transfer coefficients are presented. The results of the integral analysis compare well with that of previously published similarity theory, numerical computations and experiments. A study is presented on how the choice for velocity and temperature profiles affects the results of the integral theory. The theory has been generalized for arbitrary orders of the polynomials representing the velocity and temperature profiles. The subtle role of Prandtl number in determining the relative thicknesses of the velocity and temperature boundary layers for natural convection is elucidated and contrasted with that in forced convection. It is found that, in natural convection, the two boundary layers are of comparable thickness if Pr ≤ 1 or Pr ≈ 1. It is only when the Prandtl number is large (Pr > 1) that the velocity boundary layer is thicker than the thermal boundary layer.

Three-dimensional laminar boundary layers in crosswise pressure gradients

1974 ◽  
Vol 66 (4) ◽  
pp. 641-655 ◽  
Author(s):  
J. H. Horlock ◽  
A. K. Lewkowicz ◽  
J. Wordsworth
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Boundary Layers ◽  
Free Stream ◽  
Three Dimensional ◽  
Cross Flow ◽  
Free Stream Velocity ◽  
Stream Velocity ◽  
Laminar Boundary Layers ◽  
The Cross

Two attempts were made to develop a three-dimensional laminar boundary layer in the flow over a flat plate in a curved duct, establishing a negligible streamwise pressure gradient and, at the same time, an appreciable crosswise pressure gradient.A first series of measurements was undertaken keeping the free-stream velocity at about 30 ft/s; the boundary layer was expected to be laminar, but appears to have been transitional. As was to be expected, the cross-flow in the boundary layer decreased gradually as the flow became progressively more turbulent.In a second experiment, at a lower free-stream velocity of approximately 10 ft/s, the boundary layer was laminar. Its streamwise profile resembled closely the Blasius form, but the cross-flow near the edge of the boundary layer appears to have exceeded that predicted theoretically. However, there was a substantial experimental scatter in the measurements of the yaw angle, which in laminar boundary layers is difficult to obtain accurately.

The Interaction of Thermal Radiation in Optically Thick Boundary Layers

1967 ◽  
Vol 89 (4) ◽  
pp. 309-312 ◽  
Author(s):  
J. L. Novotny ◽  
Kwang-Tzu Yang
Keyword(s):  
Boundary Layer ◽  
Flow Field ◽  
Boundary Layers ◽  
Optical Thickness ◽  
Asymptotic Expansions ◽  
Energy Equation ◽  
Two Dimensional ◽  
Small Temperature ◽  
Dimensional Boundary

An analysis is presented to examine the role of the Rosseland or optically thick approximation in convection-radiation interaction situations. The analysis is formulated for the flow of a gray gas in a laminar two-dimensional boundary layer under the restriction of small temperature differences within the flow field. The boundary-layer energy equation is treated using the method of matched asymptotic expansions based on a parameter which characterizes the optical thickness of the gas. Two illustrative examples of the resulting equations are presented.

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