{"title":"用同伦摄动法解析求解氧化反应的一维拟齐次模型","authors":"A. Nuryaman","doi":"10.32734/JORMTT.V1I1.751","DOIUrl":null,"url":null,"abstract":"In this paper, we propose an analytical solution of convective-diffusion equation that derived from an oxidation reaction in a chemical reactor. Here, concentration of feed gas as dependent variable. In this study, the reaction are assumed to be a one-dimensional pseudo homogeneous model and it is evaluated at a certain reaction rate. By rescaling process, the nonlinear term of the reaction rate can be approximated by a linear term, resulting a linear convective-diffusion equation with an initial condition and a set of boundary conditions. Here, we present an analytic solution of the initial condition and the boundary conditions using the homotopy perturbation method. The results show that at the end of the reactor, the solution is in agreement with numerical solution of the initial and boundary conditions.","PeriodicalId":372795,"journal":{"name":"Journal of Research in Mathematics Trends and Technology","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2019-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"An Analytical Solution Of 1-D Pseudo Homoneneous Model For Oxidation Reaction Using Homotopy Perturbation Method\",\"authors\":\"A. Nuryaman\",\"doi\":\"10.32734/JORMTT.V1I1.751\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we propose an analytical solution of convective-diffusion equation that derived from an oxidation reaction in a chemical reactor. Here, concentration of feed gas as dependent variable. In this study, the reaction are assumed to be a one-dimensional pseudo homogeneous model and it is evaluated at a certain reaction rate. By rescaling process, the nonlinear term of the reaction rate can be approximated by a linear term, resulting a linear convective-diffusion equation with an initial condition and a set of boundary conditions. Here, we present an analytic solution of the initial condition and the boundary conditions using the homotopy perturbation method. The results show that at the end of the reactor, the solution is in agreement with numerical solution of the initial and boundary conditions.\",\"PeriodicalId\":372795,\"journal\":{\"name\":\"Journal of Research in Mathematics Trends and Technology\",\"volume\":\"1 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-02-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Research in Mathematics Trends and Technology\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.32734/JORMTT.V1I1.751\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Research in Mathematics Trends and Technology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.32734/JORMTT.V1I1.751","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
An Analytical Solution Of 1-D Pseudo Homoneneous Model For Oxidation Reaction Using Homotopy Perturbation Method
In this paper, we propose an analytical solution of convective-diffusion equation that derived from an oxidation reaction in a chemical reactor. Here, concentration of feed gas as dependent variable. In this study, the reaction are assumed to be a one-dimensional pseudo homogeneous model and it is evaluated at a certain reaction rate. By rescaling process, the nonlinear term of the reaction rate can be approximated by a linear term, resulting a linear convective-diffusion equation with an initial condition and a set of boundary conditions. Here, we present an analytic solution of the initial condition and the boundary conditions using the homotopy perturbation method. The results show that at the end of the reactor, the solution is in agreement with numerical solution of the initial and boundary conditions.