Mathematical Models in Boundary Layer Theory

Mathematical Models in Boundary Layer Theory

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Description

Since Prandtl first suggested it in 1904, boundary layer theory has become a fundamental aspect of fluid dynamics. Although a vast literature exists for theoretical and experimental aspects of the theory, for the most part, mathematical studies can be found only in separate, scattered articles. Mathematical Models in Boundary Layer Theory offers the first systematic exposition of the mathematical methods and main results of the theory. Beginning with the basics, the authors detail the techniques and results that reveal the nature of the equations that govern the flow within boundary layers and ultimately describe the laws underlying the motion of fluids with small viscosity. They investigate the questions of existence and uniqueness of solutions, the stability of solutions with respect to perturbations, and the qualitative behavior of solutions and their asymptotics. Of particular importance for applications, they present methods for an approximate solution of the Prandtl system and a subsequent evaluation of the rate of convergence of the approximations to the exact solution. Written by the world's foremost experts on the subject, Mathematical Models in Boundary Layer Theory provides the opportunity to explore its mathematical studies and their importance to the nonlinear theory of viscous and electrically conducting flows, the theory of heat and mass transfer, and the dynamics of reactive and muliphase media. With the theory's importance to a wide variety of applications, applied mathematicians-especially those in fluid dynamics-along with engineers of aeronautical and ship design will undoubtedly welcome this authoritative, state-of-the-art treatise.show more

Product details

  • Hardback | 528 pages
  • 164.3 x 243.8 x 32.5mm | 716.68g
  • Taylor & Francis Inc
  • Chapman & Hall/CRC
  • Boca Raton, FL, United States
  • English
  • 2003.
  • 1584880155
  • 9781584880158

Table of contents

The Navier-Stokes Equations and Prandtl Derivation of the Prandtl System Solution of the Boundary Layer System as the First Approximation to Asymptotic Solution of the Navier-Stokes Equations near the Boundary Separation of the Boundary Layer Setting of the Main Problems for the Equations of Boundary Layer Boundary Layer Equations for Non-Newtonian Fluids Boundary Layers in Magnetohydrodynamics Stationary Boundary Layer: von Mises Variables Continuation of Two-Dimensional Boundary Layer Asymptotic Behavior of the Velocity Component along the Boundary Layer Conditions for Boundary Layer Separation Self-Similar Solutions of the Boundary Layer Equations Solving the Continuation Problem by the Line Method On Three-Dimensional Boundary Layer Equations Comments Stationary Boundary Layer: Crocco Variables Axially Symmetric Stationary Boundary Layer Symmetric Boundary Layer The Problem of Continuation of the Boundary Layer Weak Solutions of the Boundary Layer System Nonstationary Boundary Layer Axially Symmetric Boundary Layer The Continuation Problem for a Nonstationary Axially Symmetric Boundary Layer Continuation of the Boundary Layer: Successive Approximations On t-Global Solutions of the Prandtl System for Axially Symmetric Flows Stability of Solutions of the Prandtl System Time-Periodic Solutions of the Nonstationary Boundary Layer System Solving the Nonstationary Prandtl System by the Line Method in the Time Variable Formation of the Boundary Layer Solutions and Asymptotic Expansions for the Problem of Boundary Layer formation: The Case of Gradual Acceleration Formation of the Boundary Layer about a Body that Suddenly Starts to Move Comments Finite-Difference Method Solving the Boundary Layer Continuation Problem by the Finite Difference Method Solving the Prandtl System for Axially Symmetric Flows by the Finite Difference Method Comments Diffraction Problems for the Prandtl System Boundary Layer with Unknown Border between Two media Mixing of Two Fluids with Distinct Properties at the Interface between Two Flows Comments Boundary Layer in Non-Newtonian Flows Symmetric Boundary Layer in Pseudo-Plastic Fluids Weak Solutions of the Boundary Layer Continuation Problem for Pseudo-Plastic Fluids Nonstationary Boundary Layer for Pseudo-Plastic Fluids Continuation of the Boundary Layer in Dilatable Media Symmetric Boundary Layer in Dilatable Media Comments Boundary Layer in Magnetic Hydrodynamics Continuation of the MHD Boundary Layer in Ordinary Fluids Solving the Equations of the MHD Boundary Layer in Pseudo-Plastic Fluids Self-Similar Solutions of the MHD Boundary Layer System for a Dilatable Fluid Solving the Equations of Boundary Layer for Dilatable Conducting Fluids in a Transversal Magnetic Field Comments Homogenization of Boundary Layer Equations Homogenization of the Prandtl System with Rapidly Oscillating Injection and Suction Homogenization of the Equations of the MHD Boundary Layer in a Rapidly Oscillating Magnetic Field Comments Some Open Problems References Indexshow more