Rigorous Bounds and Relations Among Spatial and Temporal Approximations in the Theory of Combustion

Abstract

Rigorous bounds on temperature and concentration are obtained for a model reacting system incorporating spatial variation, reactant consumption, and Arrhenius kinetics. Similar bounds are obtained for the Semenov (spatially uniform) approximation. Temperatures predicted by the Frank-Kamenetskii (stationary) approximation are shown to be upper bounds on the temperature of the complete time-dependent system. The latter supports numerical and approximate analytic arguments that the critical value of the Frank-Kamenetskii heat generation parameter in the stationary approximation is a lower bound on analogously defined critical parameter values in the complete system. The fundamental mathematical tool is a comparison result for systems of parabolic partial differential equations.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1980
Accession Number
ADA092855

Entities

People

  • Jagdish Chandra
  • Paul W. Davis

Organizations

  • Worcester Polytechnic Institute

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Abstracts
  • Boundaries
  • Classification
  • Combustion
  • Demographic Cohorts
  • Differential Equations
  • Diffusion
  • Dissipation
  • Equations
  • Heat Capacity
  • Heat Of Activation
  • Kinetics
  • Partial Differential Equations
  • Security
  • Specific Heat
  • Stationary
  • Thermal Diffusion

Readers

  • Calculus or Mathematical Analysis
  • Combustion science or combustion engineering.