Semi-analytical source method for reaction⇓diffusion problems

Kevin D Cole, B. Cetin, Y. Demirel

Research output: Contribution to journalArticle

Abstract

Estimation of thermal properties, diffusion properties, or chemical–reaction rates from transient data requires that a model is available that is physically meaningful and suitably precise. The model must also produce numerical values rapidly enough to accommodate iterative regression, inverse methods, or other estimation procedures during which the model is evaluated again and again. Applications that motivate the present work include process control of microreactors, measurement of diffusion properties in microfuel cells, and measurement of reaction kinetics in biological systems. This study introduces a solution method for nonisothermal reaction–diffusion (RD) problems that provides numerical results at high precision and low computation time, especially for calculations of a repetitive nature. Here, the coupled heat and mass balance equations are solved by treating the coupling terms as source terms, so that the solution for concentration and temperature may be cast as integral equations using Green’s functions (GF). This new method requires far fewer discretization elements in space and time than fully numeric methods at comparable accuracy. The method is validated by comparison with a benchmark heat transfer solution and a commercial code. Results are presented for a first-order chemical reaction that represents synthesis of vinyl chloride.

Original languageEnglish (US)
Article number061301
JournalJournal of Heat Transfer
Volume140
Issue number6
DOIs
StatePublished - Jun 1 2018

Fingerprint

Vinyl Chloride
heat balance
mass balance
Biological systems
Green's function
Reaction kinetics
Integral equations
Process control
integral equations
casts
regression analysis
Chemical reactions
chemical reactions
reaction kinetics
Green's functions
Thermodynamic properties
thermodynamic properties
heat transfer
chlorides
Heat transfer

Keywords

  • Cross-dependence
  • Exact green’s function
  • Heat transfer
  • Mass transfer
  • Nonlinear partial differential equation
  • Piecewise-constant source

ASJC Scopus subject areas

  • Materials Science(all)
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering

Cite this

Semi-analytical source method for reaction⇓diffusion problems. / Cole, Kevin D; Cetin, B.; Demirel, Y.

In: Journal of Heat Transfer, Vol. 140, No. 6, 061301, 01.06.2018.

Research output: Contribution to journalArticle

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