On Heat Transfer in Laminar Boundary Layers at High Prandtl Number

1956 ◽  
Vol 23 (10) ◽  
pp. 937-948 ◽  
Author(s):  
GEORGE W. MORGAN ◽  
W. H. WARNER
Keyword(s):  
Heat Transfer ◽  
Prandtl Number ◽  
Boundary Layers ◽  
Laminar Boundary Layers ◽  
High Prandtl Number

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.

Scale Analysis of Thermocapillary Weld Pool Shape With High Prandtl Number

2011 ◽  
Author(s):  
P. S. Wei ◽  
C. L. Lin ◽  
H. J. Liu
Keyword(s):  
Prandtl Number ◽  
Boundary Layers ◽  
Molten Pool ◽  
Surface Flow ◽  
Transport Processes ◽  
Surface Boundary ◽  
Scale Analysis ◽  
Melting Front ◽  
Pool Shape ◽  
High Prandtl Number

The molten pool shape and thermocapillary convection during melting or welding of metals or alloys are self-consistently predicted from parametric scale analysis for the first time. Determination of the molten pool shape is crucial due to its close relationship with the strength and properties of the fusion zone. In this work, surface tension coefficient is considered to be negative values, indicating an outward surface flow, whereas high Prandtl number represents the thermal boundary layer thickness to be less than that of momentum. Since Marangoni number is usually very high, the scaling of transport processes is divided into the hot, intermediate and cold corner regions on the flat free surface, boundary layers on the solid-liquid interface and ahead of the melting front. Coupling among distinct regions and thermal and momentum boundary layers, the results find that the width and depth of the pool can be determined as functions of Marangoni, Prandtl, Peclet, Stefan, and beam power numbers. The predictions agree with numerical computations and available experimental data.

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.

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