Approximate Methods for Calculating Heated Water Laminar Boundary-Layer Properties

1979 ◽  
Vol 46 (1) ◽  
pp. 9-14 ◽  
Author(s):  
G. M. Harpole ◽  
S. A. Berger ◽  
J. Aroesty
Keyword(s):  
Boundary Layers ◽  
Integral Method ◽  
Numerical Solutions ◽  
Approximate Methods ◽  
Laminar Boundary Layers ◽  
Heated Water ◽  
Nusselt Numbers ◽  
Variable Fluid Properties ◽  
Fluid Properties ◽  
High Prandtl Number

The integral method of Thwaites, for computing the primary parameters of laminar boundary layers with constant fluid properties, is extended to heated boundary layers in water, taking into account variable fluid properties. Universal parameters are correlated from numerical solutions of heated water wedge flows for use with the integral method. The method shows good accuracy in a test with the Howarth retarded flow. The Lighthill high Prandtl number approximation is extended to permit computation of the Nusselt number for boundary layers with variable fluid properties. Nusselt numbers computed for the Howarth flow are close to the exact numerical solutions, except near separation.

Approximate Methods of Solving the Laminar Boundary-Layer Equations

1962 ◽  
Vol 13 (3) ◽  
pp. 285-290 ◽  
Author(s):  
R. M. Terrill
Keyword(s):  
Boundary Layer ◽  
Circular Cylinder ◽  
Skin Friction ◽  
Boundary Layers ◽  
Laminar Boundary Layer ◽  
Numerical Solutions ◽  
Approximate Methods ◽  
Boundary Layer Equations ◽  
Laminar Boundary Layers ◽  
Remarkable Agreement

SummaryCurie and Skan have modified the approximate methods of Thwaites and Stratford to predict separation properties of laminar boundary layers for flow over an impermeable surface. The work of Curie and Skan has been extended by Curle to include the estimation of laminar skin friction for the whole flow. The purpose of the following note is to compare the approximate methods of Curie and Skan and Curle with the numerical results given by the author for flow past a circular cylinder. It is found that there is remarkable agreement between these approximate methods and the exact numerical solutions. This indicates that these methods can be used widely, both on account of their simplicity and their accuracy.

An Approximate Solution of the Laminar Boundary Layer on a Flat Plate with Uniform Suction

1955 ◽  
Vol 59 (538) ◽  
pp. 697-698
Author(s):  
S. J. Peerless ◽  
D. B. Spalding
Keyword(s):  
Boundary Layer ◽  
Boundary Conditions ◽  
Present Method ◽  
Integral Method ◽  
Boundary Layer Thickness ◽  
Numerical Solutions ◽  
Approximate Methods ◽  
Boundary Layer Problems ◽  
Momentum Integral ◽  
Similar Solutions

Boundary layer problems may be divided into two classes: (a) those for which similar solutions can be found, i.e. where the boundary conditions are such that similar profiles differing only in scale factor exist at different sections; and (b) those where the boundary conditions do not effect similarity, so that the development of the boundary layer must be calculated in stages. The latter class are known as “continuation problems,” and very few numerical solutions have been obtained because of the labour involved.Approximate methods of solving continuation problems are known, using the Karman momentum integral method (e.g. Ref. 1) or variants. Some of these methods make use of velocity profiles calculated for “similar” boundary layers. This note presents a new approximate method which uses “similar” profiles but avoids using the momentum integral. Instead of characterising the boundary layer thickness by the “momentum thickness,” which needs to be calculated yet is of less direct interest, the wall shear stress is used; this stress usually has to be calculated in any case and the present method is therefore comparatively simple.

Triple-deck solutions for supersonic flows past flared cylinders

1987 ◽  
Vol 179 ◽  
pp. 469-487 ◽  
Author(s):  
Ph. Gittler ◽  
A. Kluwick
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Asymptotic Expansions ◽  
Numerical Solutions ◽  
Reynolds Numbers ◽  
Hysteresis Phenomenon ◽  
Two Dimensional ◽  
Planar Flow ◽  
Laminar Boundary Layers ◽  
External Flows

Using the method of matched asymptotic expansions, the interaction between axisymmetric laminar boundary layers and supersonic external flows is investigated in the limit of large Reynolds numbers. Numerical solutions to the interaction equations are presented for flare angles α that are moderately large. If α > 0 the boundary layer separates upstream of the corner and the formation of a plateau structure similar to the two-dimensional case is observed. In contrast to the case of planar flow, however, separation can occur also if α < 0, owing to the axisymmetric effect of overexpansion and recompression. The separation point then is located downstream of the corner and, most remarkable, a hysteresis phenomenon is observed.

An integral method for two‐temperature ionizing laminar boundary layers

1988 ◽  
Vol 31 (1) ◽  
pp. 193-200
Author(s):  
V. V. Subramaniam ◽  
J. L. Lawless
Keyword(s):  
Boundary Layers ◽  
Integral Method ◽  
Laminar Boundary Layers ◽  
Two Temperature
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