Semi-analytical source method for reaction-diffusion problems

[+] Author and Article Information
Kevin D. Cole

Mechanical and Materials Engineering, W342 Nebraska Hall, University of Nebraska–Lincoln, Lincoln, NE 65588-0656 USA

Dr. Barbaros Cetin

Mechanical Engineering, Bilkent University, 06800 Bilkent, Ankara, Turkey

Yasar Demirel

Chemical and Biomolecular Engineering, University of Nebraska–Lincoln, Lincoln, NE 68588-0643 USA

1Corresponding author.

ASME doi:10.1115/1.4038987 History: Received August 25, 2017; Revised December 15, 2017


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 non-isothermal reaction-diffusion 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. 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.

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