Thermodynamics and Higher-Order Fluid Theories

Abstract

Four boundary value problems in unsteady simple shear flow are considered. Solutions for the second-order fluid approximation are listed, including a solution which seems to be new. For the third-order fluid approximation solutions are obtained for the linearized versions of the various problems. The Second Law of Thermodynamics, reduced to the requirement that the rate of deformation work be non-negative, is applied to these solutions. The signs of the pertinent second-order material constant is not determined whereas the signs of the pertinent third-order constants are determined. On the other hand, the Second Law places restrictions on the allowable solutions; for some problems no solution is valid. The implications of these results are discussed.

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Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1965
Accession Number
ADA395518

Entities

People

  • D. C. Leigh

Organizations

  • Princeton University

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Boundaries
  • Boundary Value Problems
  • Coefficients
  • Constitutive Equations
  • Couette Flow
  • Differential Equations
  • Energy
  • Equations
  • Flow
  • Linear Momentum
  • Materials
  • Partial Differential Equations
  • Poiseuille Flow
  • Pressure Gradients
  • Shear Flow
  • Steady State
  • Thermodynamics

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Fluid Dynamics.