The governing equations describing methane oxidation in a 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 a one-dimensional pseudohomogeneous model and takes place with a certain reaction rate in which thewhole process ofthereactor is still workable. Thus, the reaction rate can proceed at a fixed temperature. Under these conditions, we can restrict ourselves to solving 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 a small parameter in our model and this leads to a singular perturbation problem. Numerical difficulties will be found in the vicinity of a small parameter in front of a higher order term. Here, we present an analytical solutionby means of matched asymptotic expansions. The 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.

The integrability of traveling wave solution mappings can be obtained as reductions of the discrete generalized ΔΔ modified Korteweg-de Vries (ΔΔ-mKdV) equation. The properties of the integrable discrete dynamical system can be examined through the level set of integral function. In this paper, we show that the integral of a threedimensional traveling wave solution mapping derived from generalized ΔΔ-mKdV equation can be made in the normal form.

Optimisasi merupakan sebuah proses untuk mendapatkan nilai minimum atau maksimum dari sebuah fungsi peluang. Salah satu masalah yang melibatkan proses optimisasi yaitu Travelling Salesman Problem (TSP). Studi kasus TSP yang dibahas dalam penelitian ini adalah berkenaan dengan permasalahan pendistribusian barang yang dilakukan oleh PT. Pos Indonesia di Kota Bandar Lampung. Beberapa permasalahan yang dimaksud antara lain keterlambatan pengiriman barang, kurang puasnya pelayanan kantor pos, rute pendistribusian barang yang rumit dan lain-lain. Penyelesaian masalah yang dihadapi oleh PT. Pos Indonesia dengan menggunakan konsep TSP yang dimaksud dapat diselesaikan dengan Metode Algoritma Genetika (algoritma pencarian yang didasarkan atas mekanisme seleksi alami dan evolusi biologis). Pengunaan metode Algoritma Genetika dalam menyelesaikan masalah yang dibahas memberikan hasil bahwa untuk mencapai posisi optimal proses pengujian yang menggunakan order crossover dan inversion mutation perlu dilakukan pengulangan proses sebanyak 8 kali. (80%).

Methane (CH4) is one of the most dangerous greenhouse gases in the atmosphere. A reverse flow reactor is utilized to convert CH4 to carbon dioxide (CO2) as a means of reducing the effect of global warming. The dynamics of its dependent variables can be stated by a set of convective-diffusion equations. In this article, we examined analytical solutions of temperature dynamics and methane conversion for a 1-D pseudo homogeneous model without refrigeration by using the homotopy analysis method. The results show that temperature and conversion of methane will go to constant when time goes to infinity. ABSTRAK: Metana (CH4) merupakan salah satu gas rumah hijau paling berbahaya di atmosfera. Reaktor aliran balik telah dipakai bagi menukar CH4 kepada CO2 bagi mengurangkan kesan pemanasan global. Dinamik pemboleh ubah bersandar ini dapat diterangkan melalui satu set persamaan konvektif-difusi. Artikel ini akan mengkaji penyelesaian analisis dinamik suhu dan penukaran metana bagi model 1-D pseudo-homogen tanpa penyejukan dengan menggunakan kaedah analisis homotopi. Hasil kajian menunjukkan bahawa suhu dan penukaran metana akan berterusan dengan masa tak terhingga.

In this paper, we study a solution of a set of convective-diffusion equations arising from methane combustion in reverse flow reactor. Here, temperature and concentration of methane are dependent variables. By scaling process, a nonlinear reaction rate term can be approximated as a linear term, resulting in linear convective-diffusion equations. We consider the steady state regime for small ratio of the diffusion and convective terms. This leads to a singular perturbation problem. Using variable transformation, the problem can be converted into a regular perturbation-like problem. Asymptotic solution shows that, up to and including the second order of approximation, the solution is in agreement with numerical solutions of the boundary value problem.