Laminar Free Convection From a Downward-Projecting Fin

1968 ◽  
Vol 90 (1) ◽  
pp. 63-70 ◽  
Author(s):  
G. S. H. Lock ◽  
J. C. Gunn
Keyword(s):  
Boundary Layer ◽  
Free Convection ◽  
Prandtl Number ◽  
Experimental Program ◽  
Boundary Layer Problem ◽  
Theoretical Predictions ◽  
Theoretical Results ◽  
Good Agreement ◽  
Quiescent Fluid

A theoretical analysis of conduction through and free convection from a tapered, downward-projecting fin immersed in an isothermal quiescent fluid is presented. The problem is solved by assuming quasi-one-dimensional heat conduction in the fin and matching the solution to that of the convection system, which is treated as a boundary layer problem. For an infinite Prandtl number, solutions are derived which take the form of a power law temperature distribution along the fin. The effect of this power (n) on heat transfer, drag, and the corresponding boundary layer profiles is discussed. It is shown that n is independent of the fin profile and dependent on a single nondimensional group χ. The theoretical results for infinite Prandtl number are compared with corresponding results derived from previous work using a Prandtl number of unity. The effect of Prandtl number on the determination of n and consequently the fin effectiveness is found to be extremely small. The results of an experimental program are also presented. These consist of temperature profiles and the n — χ relation for different fin geometries and surrounding fluids. Comparison with the theoretical predictions reveals good agreement.

Determination of the turbulent Prandtl number in an asymptotic boundary layer with suction

1981 ◽  
Vol 16 (1) ◽  
pp. 57-61
Author(s):  
M. A. Gol'dshtik ◽  
S. S. Kutateladze ◽  
A. M. Lifshits
Keyword(s):  
Boundary Layer ◽  
Prandtl Number ◽  
Turbulent Prandtl Number ◽  
Asymptotic Boundary

Experimental and theoretical fatigue-crack propagation lives of variously notched plates

1974 ◽  
Vol 9 (2) ◽  
pp. 61-66 ◽  
Author(s):  
R A Smith ◽  
K Jerram ◽  
K J Miller
Keyword(s):  
Fatigue Life ◽  
Crack Propagation ◽  
Finite Element Analyses ◽  
Intensity Factors ◽  
Complex Profile ◽  
Propagation Law ◽  
Theoretical Predictions ◽  
Life Predictions ◽  
Theoretical Results

The fatigue lives of variously notched plates have been determined theoretically and experimentally. Theoretical predictions of fatigue lives involved the determination of stress-intensity factors from finite-element analyses. By invoking a crack propagation law, fatigue-life predictions were made for four specimens. Fatigue experiments were conducted on four notched plates subjected to end load plus bending. Comparison with theoretical results shows that the experimental lives were greater by factors of 1.30 to 1.54. These results are most satisfactory since (1) a safe prediction of fatigue life has been made for a complex profile subjected to non-simple loading conditions, and (2) a theoretical elastic analysis has sufficed for a situation involving plastic strains.

scholarly journals Nanomechanics of few-layer materials: do individual layers slide upon folding?

2020 ◽  
Vol 11 ◽  
pp. 1801-1808
Author(s):  
Ronaldo J C Batista ◽  
Rafael F Dias ◽  
Ana P M Barboza ◽  
Alan B de Oliveira ◽  
Taise M Manhabosco ◽  
...  
Keyword(s):  
2D Materials ◽  
Adhesion Energy ◽  
Flexural Properties ◽  
2D Systems ◽  
Number Of Layers ◽  
Graphene Flakes ◽  
Theoretical Predictions ◽  
Tip Enhanced Raman Spectroscopy ◽  
Good Agreement

Folds naturally appear on nanometrically thin materials, also called “2D materials”, after exfoliation, eventually creating folded edges across the resulting flakes. We investigate the adhesion and flexural properties of single-layered and multilayered 2D materials upon folding in the present work. This is accomplished by measuring and modeling mechanical properties of folded edges, which allows for the experimental determination of the bending stiffness (κ) of multilayered 2D materials as a function of the number of layers (n). In the case of talc, we obtain κ ∝ n 3 for n ≥ 5, indicating no interlayer sliding upon folding, at least in this thickness range. In contrast, tip-enhanced Raman spectroscopy measurements on edges in folded graphene flakes, 14 layers thick, show no significant strain. This indicates that layers in graphene flakes, up to 5 nm thick, can still slip to relieve stress, showing the richness of the effect in 2D systems. The obtained interlayer adhesion energy for graphene (0.25 N/m) and talc (0.62 N/m) is in good agreement with recent experimental results and theoretical predictions. The obtained value for the adhesion energy of graphene on a silicon substrate is also in agreement with previous results.

Calculation of a Turbulent Boundary Layer Downstream of a Step Change in Surface Temperature

1979 ◽  
Vol 101 (1) ◽  
pp. 144-150 ◽  
Author(s):  
L. W. B. Browne ◽  
R. A. Antonia
Keyword(s):  
Boundary Layer ◽  
Heat Flux ◽  
Prandtl Number ◽  
Surface Temperature ◽  
Reynolds Shear Stress ◽  
Turbulent Viscosity ◽  
Step Change ◽  
Mean Temperature ◽  
Thermal Layer ◽  
Good Agreement

Mean temperature and heat flux distributions in a thermal layer that develops within a momentum boundary layer subjected to a step change in surface temperature are calculated using two different methods. The method of Bradshaw and Unsworth, which uses the method of Bradshaw, Ferriss and Atwell to determine the mean velocity and Reynolds shear stress distributions and then assumes a constant turbulent Prandtl number for the heat flux calculation, yields heat flux distributions that are significantly different than the available experimental results at small distances from the step. Good agreement between calculations and experimental values is achieved when the distance x from the step is about 20 δ0, where δ0 is the boundary layer thickness at the step. To obtain good agreement with measurements of heat flux and mean temperature near the step, estimated distributions of turbulent viscosity and effective Prandtl number have been derived using an iterative updating procedure and the calculation method of Patankar and Spalding. These distributions are compared with those available in the literature. Calculated heat flux distributions show that the internal thermal layer is only likely to reach self-preserving conditions when x exceeds 40 δ0.

Explicit formulation for the axial collapse of a pipe during drilling

2010 ◽  
Vol 224 (8) ◽  
pp. 1547-1549
Author(s):  
A Almasi
Keyword(s):  
Closed Form ◽  
Plastic Hinge ◽  
Variable Length ◽  
Experimental Results ◽  
Displacement Curve ◽  
Explicit Formulation ◽  
Theoretical Predictions ◽  
Hinge Zone ◽  
Good Agreement

New closed-form expressions are introduced for ax-symmetric progressive axial collapse of pipes that use a plastic folding mechanism based on variable length of an active plastic hinge zone. A procedure for determination of a load—displacement curve of axial pipe collapse is presented. Theoretical predictions give a good agreement with the experimental results owing to the influence of presented new refinements.

scholarly journals On the boundary-layer structure of high-Prandtl-number horizontal convection

2010 ◽  
Vol 652 ◽  
pp. 299-331
Author(s):  
P. G. DANIELS
Keyword(s):  
Boundary Layer ◽  
Temperature Distribution ◽  
Prandtl Number ◽  
Layer Structure ◽  
Lower Surface ◽  
Horizontal Layer ◽  
Linear Temperature ◽  
Boundary Layer Problem ◽  
Boundary Layer Structure ◽  
Horizontal Boundary

This paper describes the boundary-layer structure of the steady flow of an infinite Prandtl number fluid in a two-dimensional rectangular cavity driven by differential heating of the upper surface. The lower surface and sidewalls of the cavity are thermally insulated and the upper surface is assumed to be either shear-free or rigid. In the limit of large Rayleigh number (R → ∞), the solution involves a horizontal boundary layer at the upper surface of depth of order R−1/5 where the main variation in the temperature field occurs. For a monotonic temperature distribution at the upper surface, fluid is driven to the colder end of the cavity where it descends within a narrow convection-dominated vertical layer before returning to the horizontal layer. A numerical solution of the horizontal boundary-layer problem is found for the case of a linear temperature distribution at the upper surface. At greater depths, of order R−2/15 for a shear-free surface and order R−9/65 for a rigid upper surface, a descending plume near the cold sidewall, together with a vertically stratified interior flow, allow the temperature to attain an approximately constant value throughout the remainder of the cavity. For a shear-free upper surface, this constant temperature is predicted to be of order R−1/15 higher than the minimum temperature of the upper surface, whereas for a rigid upper surface it is predicted to be of order R−2/65 higher.

Thermal Behavior and Friction in Journal Bearings

1970 ◽  
Vol 92 (3) ◽  
pp. 373-380 ◽  
Author(s):  
Al. Nica
Keyword(s):  
Experimental Data ◽  
Thermal Behavior ◽  
Heat Dissipation ◽  
Journal Bearings ◽  
Friction Torque ◽  
Operating Characteristics ◽  
Lubricant Flow ◽  
Theoretical Predictions ◽  
Theoretical Results ◽  
Good Agreement

This paper deals with friction and the field of temperature in the lubricant film of journal bearings. Theoretical results regarding the thermal behavior are checked with experimental data and good agreement is found. Emphasis is put on the variation of temperature and lubricant flow with the operating characteristics of the bearing and it is seen that theoretical predictions for minima of friction torque are backed by temperature measurements. Further on, the friction torque and the mechanism of heat dissipation in bearings are dealt with, in order to verify the assumptions used in the calculation schemes. The means of efficiently cooling the bearing are also discussed, as well as the part played by the divergent zone in this process.

Similarity and stability of the laminar boundary layer in a streamwise corner

1981 ◽  
Vol 377 (1770) ◽  
pp. 269-288 ◽  
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Conclusive Evidence ◽  
Experimental Results ◽  
Solid Surfaces ◽  
Boundary Layer Problem ◽  
Streamwise Pressure Gradient ◽  
The Stability ◽  
Limiting Case ◽  
Theoretical Results

The study of laminar viscous flow along the line of intersection of two solid surfaces at right angles is examined in its present state, and out­standing differences between various experimental and theoretical results are analysed. New experimental results are presented in which the stability of the corner boundary layer is examined in terms of the degree of streamwise similarity of its velocity profiles. Conclusive evidence is found that the layer does not exist in stable laminar form when the streamwise pressure gradient is zero and the Reynolds number much above about 10 4 . The new results also help to explain the differences between various experimental results, and between theory and experi­ment, which have characterized the corner boundary layer problem for several years. By extrapolation, an approximate prediction is obtained of what the velocity profile of the corner boundary layer would be in the limiting case of zero pressure gradient, if the layer were stable in that state. The predicted profile is compared with the results of current theories.

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