A FIRST-ORDER TIME CONSTANT ESTIMATION FOR NONLINEAR DIFFUSION PROBLEMS

Laurent Simon, Juan Ospina

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

A Laplace transform-based procedure was proposed to calculate the effective time constant for a class of nonlinear diffusion problems. The governing mathematical representation was first estimated with a linear model by omitting the nonlinear term. The solution to this problem was later introduced into the original equation, which was solved with Laplace transforms, resulting in a first-order approximation of the real system's behavior. A time constant was calculated using frequency-domain expressions. Two case studies were considered to illustrate the methodology. As the rate of heat supplied to a rod is raised, the speed at which the temperature reached an equilibrium value decreased. Increasing the maximum velocity in reaction-diffusion transport by a factor of three lowered the time constant by only 1.7%. The applications of this method range from biosensor dynamics to process control.

Original languageEnglish (US)
Pages (from-to)719-736
Number of pages18
JournalChemical Engineering Communications
Volume201
Issue number6
DOIs
StatePublished - Jun 2014

All Science Journal Classification (ASJC) codes

  • Chemistry(all)
  • Chemical Engineering(all)

Keywords

  • Diffusion
  • Effective time constant
  • Heat transfer
  • Kinetics
  • Mathematical modeling
  • Nonlinear dynamics

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