Effects of a sharp pressure rise on a compressible laminar boundary layer, when the Prandtl number is σ = 0.72

1979 ◽  
Vol 84 (1-2) ◽  
pp. 153-171 ◽  
Author(s):  
N. Curle
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Prandtl Number ◽  
Laminar Boundary Layer ◽  
Pressure Rise ◽  
Adverse Pressure Gradient ◽  
Absolute Temperature ◽  
Stagnation Temperature ◽  
Constant Wall Temperature ◽  
Displacement Thickness

SynopsisFollowing an earlier paper (Curle 1978) we consider a compressible laminar boundary layer with uniform pressure when the distance x along the wall satisfies x < x0 and a prescribed large adverse pressure gradient when x > x0. The viscosity and absolute temperature are again taken to be proportional, but the Prandtl number is no longer assumed to be unity. After applying the Illingworth-Stewartson transformation, the transformed external velocity u1(x) is chosen so thatis large and constant, where Ts is the stagnation temperature, Tw is the (constant) Wall temperature and u0 is the upstream value of u1(x).The flow reacts to this sharp pressure rise mainly in a thin inner sublayer, so inner and outer asymptotic expansions are derived and matched for functions F and S which determine the stream function and the temperature.The skin friction, heat transfer, displacement thickness and momentum thickness are determined as functions of , andinvolve two parameters B1, B2, which depend upon the Mach number and the walltemperature. Detailed numerical calculations are presented here for σ = 0.72. In particular, it is seen that the heat transfer rate varies roughly like σ⅓ except near to separation, where it varies like σ¼.

Some Aspects of Laminar Boundary Layer Separation in Compressible Flow with no Heat Transfer to the Wall

1953 ◽  
Vol 4 (2) ◽  
pp. 123-150 ◽  
Author(s):  
G. E. Gadd
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Prandtl Number ◽  
Pressure Distribution ◽  
Compressible Flow ◽  
Laminar Boundary Layer ◽  
Free Stream ◽  
Boundary Layer Separation ◽  
Absolute Temperature ◽  
Laminar Separation

SummaryAn analysis has been made which suggests that, with the types of pressure distribution most usual in practice and free stream Mach numbers up to 10, no serious errors would be introduced into the calculation of the laminar separation point by the assumption that σ, the Prandtl number, and ω, the index of variation of viscosity with absolute temperature, are equal to unity. (Typical actual values of σ and ω for air are 0.72 and 0.89 respectively).

Mass Transfer Cooling in a Boundary Layer

1961 ◽  
Vol 12 (2) ◽  
pp. 165-188 ◽  
Author(s):  
D. G. Hurley
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Mass Transfer ◽  
Stagnation Point ◽  
Theoretical Work ◽  
Absolute Temperature ◽  
Analogue Computer ◽  
Constant Wall Temperature ◽  
Dimensional Boundary ◽  
Similar Solutions

SummaryPrevious theoretical work on mass transfer cooling is reviewed and it is shown that this may be complemented by similar solutions that occur when the velocity outside a two-dimensional boundary layer varies as some power of the distance from the front stagnation point. The case of stagnation point flow with constant wall temperature is investigated in some detail, under the assumption that the temperature differences are everywhere small compared with the absolute temperature. Calculations on an analogue computer, supplemented by an investigation of the asymptotic behaviour, are used to determine the boundary layer development and heat transfer rates when the coolant is hydrogen, helium, steam or carbon dioxide. It is found that, on a mass flow basis, hydrogen reduces the heat transfer rate most and that steam is the next most effective of the substances investigated.

Skin Friction and Heat Transfer for Laminar Boundary-Layer Flow With Variable Properties and Variable Free-Stream Velocity

1953 ◽  
Vol 20 (3) ◽  
pp. 415-421
Author(s):  
S. Levy ◽  
R. A. Seban
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Prandtl Number ◽  
Skin Friction ◽  
Laminar Boundary Layer ◽  
Boundary Layer Flow ◽  
Free Stream ◽  
Free Stream Velocity ◽  
Stream Velocity ◽  
Layer Flow

Abstract Numerical solutions of the momentum and energy equations are presented for particular types of laminar boundary-layer flow analogous to the Hartree “wedge flows.” Variation of the viscosity and of the thermal conductivity is considered under the circumstances of no dissipation, favorable pressure gradient, and the product of conductivity and density a constant. The solution is based on approximate representations of the velocity and temperature profiles in the boundary layer and these are of such character that the labor of calculation is minimized and the accuracy of the results preserved. The differential equations are reduced to two algebraic equations which rapidly yield the skin friction and the heat transfer in terms of the wall to free-stream temperature ratio for the desired value of Prandtl number. Numerical results are given for a range of wedge flows with gases of Prandtl number 0.70 and 1.0. These results reveal that when the free-stream velocity is variable the temperature difference between the wall and the free stream exerts a substantial effect on the velocity distribution in the boundary layer and on the skin-friction coefficient. Alternatively, the heat-transfer coefficient is not affected radically. A calculation method is presented for the determination of the heat transfer and skin friction for a flow with an arbitrary variation of velocity over an isothermal surface. This method utilizes the results of the present analysis for the variable property wedge flows.

Heat Transfer in a Laminar Boundary Layer with Constant Fluid Properties and Constant Wall Temperature

1958 ◽  
Vol 62 (565) ◽  
pp. 60-64 ◽  
Author(s):  
A. G. Smith ◽  
D. B. Spalding
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Laminar Flow ◽  
Laminar Boundary Layer ◽  
Wall Temperature ◽  
Two Dimensional ◽  
Constant Wall Temperature ◽  
Simple Method ◽  
Flow Surface ◽  
Fluid Properties

A simple method is given for the calculation of the heat transfer from a laminar flow surface. Computation is by a quadrature. The method is essentially a simplification and extension of the Eckert(1) method, and is applicable both to two–dimensional and to axisymmetric flows.

Heat Transfer and Laminar Boundary-Layer Distributions in an Internal Subsonic Gas Stream at Temperatures Up to 13,900 Deg R

1969 ◽  
Vol 91 (1) ◽  
pp. 83-90 ◽  
Author(s):  
P. F. Massier ◽  
L. H. Back ◽  
E. J. Roschke
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Laminar Boundary Layer ◽  
Mass Flux ◽  
Free Stream ◽  
Constant Diameter ◽  
Displacement Thickness ◽  
Calorimetric Probe ◽  
Enthalpy Difference ◽  
Probe Measurements

Radial distributions of velocity, enthalpy, and mass flux have been evaluated experimentally in a laminar boundary layer from calorimetric probe measurements obtained in a subsonic flow of arc-heated argon in the entrance region of an axisymmetric constant-diameter duct. Longitudinal distributions of heat flux were also determined. Because of the large free stream to wall temperature ratios the boundary-layer mass flux exceeded that of the free stream sufficiently to produce negative values of the displacement thickness. The longitudinal distributions of the heat transfer and the radial distributions of the enthalpy difference and the velocity were found to agree reasonably well with laminar boundary-layer predictions which account for large variations in properties.

On Heat Transfer in Laminar Boundary-Layer Flows of Liquids Having a Very Small Prandtl Number

1958 ◽  
Vol 25 (3) ◽  
pp. 173-180 ◽  
Author(s):  
G. W. MORGAN ◽  
A. C. PIPKIN ◽  
W. H. WARNER
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Prandtl Number ◽  
Laminar Boundary Layer ◽  
Boundary Layer Flows

The Compressible Laminar Boundary Layer on a Yawed Infinite Wing

1954 ◽  
Vol 5 (2) ◽  
pp. 85-100 ◽  
Author(s):  
L. F. Crabtree
Keyword(s):  
Boundary Layer ◽  
Prandtl Number ◽  
Incompressible Fluid ◽  
Laminar Boundary Layer ◽  
Compressible Fluid ◽  
Equations Of Motion ◽  
Absolute Temperature ◽  
Direct Solution ◽  
Coefficient Of Viscosity ◽  
Compressibility Effects

SummaryA study of the laminar boundary layer on a yawed infinite wing in a compressible fluid is made. A method is presented for the investigation of compressibility effects by direct solution of the linearised equations of motion, first considerably simplified by the extension of a transformation due to Illingworth and Stewartson, which assumes a heat-insulated surface and a fluid of unit Prandtl number and a coefficient of viscosity which is proportional to the absolute temperature. As an example of this procedure the boundary layer near a stagnation point is calculated. The simplifications necessary for an extension of the momentum method, which is available for a yawed infinite wing in an incompressible fluid, are discussed, and this method is recommended for a first evaluation of the effect of compressibility.

Flow Structure and Heat Transfer Characterization of a Blunt-Fin-Induced Shock-Wave/Laminar Boundary-Layer Interaction

2021 ◽  
Author(s):  
Jorge Castro Maldonado ◽  
James A. Threadgill ◽  
Stuart A. Craig ◽  
Jesse C. Little ◽  
Stefan H. Wernz
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Shock Wave ◽  
Flow Structure ◽  
Laminar Boundary Layer ◽  
Layer Interaction ◽  
Boundary Layer Interaction
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