Mathematical models of momentum transfer in the boundary layer

2013 ◽  
Vol 86 (3) ◽  
pp. 604-613 ◽  
Author(s):  
A. G. Laptev ◽  
T. M. Farakhov
Keyword(s):  
Boundary Layer ◽  
Mathematical Models ◽  
Momentum Transfer

Polymer Solutions and Their Mathematical Models

2020 ◽  
pp. 84-93
Author(s):  
V.V. Pukhnachev ◽  
A.G. Petrova ◽  
O.A. Frolovskaya
Keyword(s):  
Boundary Layer ◽  
Mathematical Models ◽  
Polymer Solution ◽  
Time Derivative ◽  
Stationary Flow ◽  
Second Grade ◽  
Aqueous Polymer ◽  
Aqueous Polymer Solution ◽  
Grade Fluid ◽  
Layered Flow

Mathematical models for the motion of weak solutions of polymers have been studied over the past 50 years. The initial model (Voitkunskii, Amfilokhiev, and Pavlovskii, 1970) contains two key parameters - relaxation viscosity and shear stress relaxation time. In the limiting case, when the last parameter is small, the Pavlovskii model (1971) arises. Its equations are close to second-grade fluid equations (Rivlin and Eriksen, 1955). The paper contains an overview of the works on all three models and new results related to the Pavlovskii model. The solution to the problem of the un-steady layered flow of an aqueous polymer solution in a layer with a free boundary, the boundary condition on which includes the time derivative of the desired function is constructed. We derive the equations that describe the motion of a polymer solution in a laminar boundary layer near a rectilinear plate. The parameter included in equations characterizes the ratio of the thickness of the Prandtl boundary layer to the thickness of the relaxation boundary layer. We study the influence of this parameter on the motion picture by the example of a stationary flow near a critical point.

The nonlinear phase of wave growth leading to chaos and breakdown to turbulence in a boundary layer as an example of an open system

1990 ◽  
Vol 430 (1878) ◽  
pp. 3-24 ◽  
Keyword(s):  
Boundary Layer ◽  
Time Series ◽  
Differential Equations ◽  
Mathematical Models ◽  
Flow Regime ◽  
Open System ◽  
Broadband Noise ◽  
Periodic Component ◽  
Velocity Fluctuations ◽  
Nonlinear Phase

The spatial development of boundary-layer instabilities has been investigated experimentally in a flow régime where nonlinearities are important. Detailed measurements of the evolution of a regular periodic wavetrain into an irregular or chaotic one are reported. It was found that the broadband noise content of the motion grew very rapidly downstream when the amplitude of the periodic component was sufficiently large. The almost explosive growth of the broadband element provided velocity fluctuations with chaotic time series similar to those generated by mathematical models based on low-order differential equations.

A Simple Model for Turbulent Boundary Layer Momentum Transfer on a Flat Plate

2010 ◽  
Vol 33 (6) ◽  
pp. 867-877 ◽  
Author(s):  
M. H. Khademi ◽  
A. Zeinolabedini Hezave ◽  
D. Mowla ◽  
M. Taheri
Keyword(s):  
Boundary Layer ◽  
Simple Model ◽  
Turbulent Boundary Layer ◽  
Flat Plate ◽  
Momentum Transfer

Fundamentals of the Theory of Rotating Fluids

1963 ◽  
Vol 30 (4) ◽  
pp. 481-485 ◽  
Author(s):  
L. N. Howard
Keyword(s):  
Fluid Dynamics ◽  
Boundary Layer ◽  
Mathematical Models ◽  
Rotating Flows ◽  
Laboratory Studies ◽  
Geophysical Fluid Dynamics ◽  
Rotating Fluids ◽  
Ekman Boundary Layer ◽  
Physical Phenomena

This paper gives an expository survey of some of the principal mathematical models which have been used in the theory of rotating fluids, together with a discussion of several explicit examples. Some of these examples are related to geophysical fluid dynamics; others more directly to laboratory studies. In all cases the examples have been selected to illustrate some of the most important physical phenomena which are characteristic of rotating flows and distinguish them from other fluid motions. Physical concepts, such as the Taylor-Proudman effects, the Ekman boundary layer, and Rayleigh’s analogy, which have proved useful in obtaining a general understanding of rotating fluids, are presented and discussed.

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