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A Singular Perturbation Problem for Steady State Conversion of Methane Oxidation in Reverse Flow Reactor
Aang Nuryaman1,3, Agus Yodi Gunawan1, Kuntjoro Adji Sidarto1 & Yogi Wibisono Budhi2
1Industrial and Financial Mathematics Research Group,
Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung
Jalan Ganesa 10 Bandung, Jawa Barat 40132, Indonesia
2Design and Development Processing Research Group, Faculty of Industrial Technology, Institut Teknologi Bandung, Jalan Ganesa 10 Bandung,
Jawa Barat 40132, Indonesia
3Department of Mathematics, Faculty of Mathematics and Natural Science
Lampung University, Jl. Soemantri Brojonegoro 1, Gedong Meneng,
Bandarlampung 35145, Indonesia
Email: aangnuryaman@gmail.com
Abstract. The governing equations describing the methane oxidation process in reverse flow reactor are given by a set of convective-diffusion equations with a nonlinear reaction term, where temperature and methane conversion are dependent variables. In this study, the process is assumed to be one-dimensional pseudo homogeneous model and takes place with a certain reaction rate in which the whole process of reactor is still workable. Thus, the reaction rate can proceed at a fixed temperature. Under this condition, we restrict ourselves to solve the equations for the conversion only. From the available data, it turns out that the ratio of the diffusion term to the reaction term is small. Hence, this ratio is considered as small parameter in our model and this leads to a singular perturbation problem. In the vicinity of small parameter in front of higher order term, the numerical difficulties will be found. Here, we present an analytical solution by means of matched asymptotic expansions. Result shows that, up to and including the first order of approximation, the solution is in agreement with the exact and numerical solutions of the boundary value problem.
Keywords: asymptotic analysis; boundary layer; methane oxidation process; pseudo homogeneous; reverse flow reactor; steady state conversion.
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