The Laminar Boundary Layer on a Hot Cylinder Fixed in a Fluctuating Stream

1961 ◽  
Vol 28 (3) ◽  
pp. 339-346 ◽  
Author(s):  
R. J. Gribben
Keyword(s):  
Boundary Layer ◽  
Mach Number ◽  
Laminar Boundary Layer ◽  
Small Amplitude ◽  
External Flow ◽  
Low Speed ◽  
Boundary Layer Equations ◽  
Special Cases ◽  
Exact Calculations ◽  
Small Amplitude Oscillation

The equations for nonsteady, two-dimensional low-speed compressible flow in the laminar boundary layer are solved approximately by use of the Pohlhausen technique with the assumption of quartic profiles for the velocity and temperature. The external flow considered is of the form of a steady basic velocity with a superimposed small amplitude oscillation such as may arise, for example, when a sound wave is present in a uniform incident stream. The analysis is then applicable to the case of a hot cylinder fixed in such a stream. Terms of the order of the incident stream Mach number are neglected in the expressions for external flow quantities (whereas the low-speed boundary-layer equations involve errors of the order of only the square of this Mach number). Two special cases are worked out—the flow over a flat plate for which there is fair agreement with available exact calculations, and the flow over a circular cylinder.

Supersonic laminar boundary layer near the plane of symmetry of a cone at incidence

1972 ◽  
Vol 51 (1) ◽  
pp. 1-14 ◽  
Author(s):  
Bernard Roux
Keyword(s):  
Boundary Layer ◽  
Mach Number ◽  
Laminar Boundary Layer ◽  
External Flow ◽  
Leeward Side ◽  
Detailed Consideration ◽  
Boundary Layer Equations ◽  
Similarity Method ◽  
Supersonic Laminar ◽  
Critical Incidence

Supersonic laminar boundary-layer equations near the plane of symmetry of a cone at incidence are treated by the similarity method. Numerical integration of differential equations governing such a flow is performed, taking into consideration the temperature dependence of the Prandtl numberPrand viscosity μ throughout the boundary layer. On the leeward side, a detailed consideration of the solutions shows the existence of two solutions up to a critical incidence beyond which it appears that no solution may be found. Calculations carried out for a set of values of the external flow Mach number show up a significant effect of this parameter on the behaviour of the boundary layer.

On a Convergent Multi-Moment Method for the Laminar Boundary Layer Equations

1967 ◽  
Vol 18 (4) ◽  
pp. 332-353 ◽  
Author(s):  
Howard E. Bethel
Keyword(s):  
Boundary Layer ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Laminar Boundary Layer ◽  
Difference Method ◽  
Moment Method ◽  
External Flow ◽  
Higher Moments ◽  
Type Method ◽  
Boundary Layer Equations

SummaryThis paper presents a summary of a multi-moment method for solving the laminar boundary layer equations. Results obtained with the method tend to converge to the exact values as higher moments are used. Both similar and non-similar external flow fields are considered. The present results are compared with those obtained by another multi-moment method, a finite-difference method and a refined Pohlhausen-type method.

On solutions of the compressible laminar boundary-layer equations and their behaviour near separation

1977 ◽  
Vol 80 (2) ◽  
pp. 279-292 ◽  
Author(s):  
T. Davies ◽  
G. Walker
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Mach Number ◽  
Skin Friction ◽  
Laminar Boundary Layer ◽  
Numerical Solutions ◽  
Free Stream ◽  
Suction Velocity ◽  
Boundary Layer Equations ◽  
Free Stream Mach Number

A numerical solution of the two-dimensional compressible laminar boundary-layer equations up to the point of separation is presented. For a particular mainstream velocity distribution it is necessary to specify the surface temperature (or the heat flux across the surface), the suction velocity, the free-stream Mach number and the viscosity-temperature relationship for a solution to be generated. The effect upon the position of separation of a hot or cold wall and of varying the free-stream Mach number is given special emphasis. The variations of the skin friction, heat transfer and various boundary-layer thicknesses for compressible flow past a circular cylinder and for flow with a linearly retarded mainstream were found. The behaviour of the solutions close to separation is investigated. Known functions which model the skin friction and heat transfer are introduced and are used to match the numerical solutions with the Buckmaster (1970) expansions.

scholarly journals Analysis of a Chemically Reactive Mhd Flow With Heat and Mass Transfer Over a Permeable Surface

2019 ◽  
Vol 24 (1) ◽  
pp. 53-66
Author(s):  
O.J. Fenuga ◽  
S.J. Aroloye ◽  
A.O. Popoola
Keyword(s):  
Boundary Layer ◽  
Mass Transfer ◽  
Heat And Mass Transfer ◽  
Mhd Flow ◽  
Skin Friction Coefficient ◽  
Permeable Surface ◽  
Physical Parameters ◽  
Boundary Layer Equations ◽  
Special Cases ◽  
Momentum Boundary Layer

Abstract This paper investigates a chemically reactive Magnetohydrodynamics fluid flow with heat and mass transfer over a permeable surface taking into consideration the buoyancy force, injection/suction, heat source/sink and thermal radiation. The governing momentum, energy and concentration balance equations are transformed into a set of ordinary differential equations by method of similarity transformation and solved numerically by Runge- Kutta method based on Shooting technique. The influence of various pertinent parameters on the velocity, temperature, concentration fields are discussed graphically. Comparison of this work with previously published works on special cases of the problem was carried out and the results are in excellent agreement. Results also show that the thermo physical parameters in the momentum boundary layer equations increase the skin friction coefficient but decrease the momentum boundary layer. Fluid suction/injection and Prandtl number increase the rate of heat transfer. The order of chemical reaction is quite significant and there is a faster rate of mass transfer when the reaction rate and Schmidt number are increased.

The Critical Height of Distributed Roughness to Cause Boundary Layer Transition

1959 ◽  
Vol 63 (588) ◽  
pp. 722-722
Author(s):  
R. L. Dommett
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Laminar Boundary Layer ◽  
Boundary Layer Transition ◽  
Critical Height ◽  
Layer Transition ◽  
Local Conditions ◽  
Additional Advantage ◽  
Boundary Layer Equations ◽  
General Method

It has been found that there is a critical height for “sandpaper” type roughness below which no measurable disturbances are introduced into a laminar boundary layer and above which transition is initiated at the roughness. Braslow and Knox have proposed a method of predicting this height, for flow over a flat plate or a cone, using exact solutions of the laminar boundary layer equations combined with a correlation of experimental results in terms of a Reynolds number based on roughness height, k, and local conditions at the top of the elements. A simpler, yet more general, method can be constructed by taking additional advantage of the linearity of the velocity profile near the wall in a laminar boundary layer.

scholarly journals Integration of the boundary-layer equations for a plane in a compressible fluid

1948 ◽  
Vol 195 (1041) ◽  
pp. 180-188 ◽  
Keyword(s):  
Boundary Layer ◽  
Mach Number ◽  
Prandtl Number ◽  
Incompressible Fluid ◽  
Satisfactory Agreement ◽  
Asymptotic Method ◽  
Compressible Fluid ◽  
Boundary Layer Equations ◽  
Rapid Calculation ◽  
Elementary Methods

The aim of this paper is to integrate Emmons & Brainerd’s equations analytically for arbitrary values of the Prandtl number and the Mach number, using the powerful asymptotic method of integration developed by the author in a previous paper (Meksyn 1948), dealing with the boundary layer in an incompressible fluid. It is shown here that in the first approximations the asymptotic integration gives ample accuracy and that it can be determined by simple and elementary methods. The results of this comparatively rapid calculation are in very satisfactory agreement with the results of the lengthy numerical calculations made by Emmons & Brainerd for certain specific values of Prandtl number and Mach number.

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