None V. Vijayalakshmi, None V. Ananthaswamy, None J. Anantha Jothi
{"title":"球形催化剂和生物催化剂非等温稳态R-D方程的半解析研究","authors":"None V. Vijayalakshmi, None V. Ananthaswamy, None J. Anantha Jothi","doi":"10.37934/cfdl.15.12.6076","DOIUrl":null,"url":null,"abstract":"The Lane-Emden Boundary Value Problem as it appears in chemical applications, science, and biochemical applications are employed. Two specific models are solved by applying the Ananthaswamy-Sivasankari method (ASM). The model in first problem is a reaction–diffusion equation of a spherical catalyst and the model in second problem is the reaction–diffusion process of a spherical biocatalyst. Obtain a reliable semi-analytical expression of the effectiveness factors and the concentrations. A graph is constructed for the obtained semi-analytical solutions.The effects of several parameters like dimensionless activation energy, Thiele modulus and dimensionless heat of reaction are shown in graphical representation. Our semi-analytical solution is compared with numerical simulation by using MATLAB and finds good fit in all parameters. The new analytical method ASM is helpful to solve many non-linear problems mainly Reaction-Diffusion equation.","PeriodicalId":9736,"journal":{"name":"CFD Letters","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Semi- Analytical Study on Non-Isothermal Steady R-D Equation in a Spherical Catalyst and Biocatalyst\",\"authors\":\"None V. Vijayalakshmi, None V. Ananthaswamy, None J. Anantha Jothi\",\"doi\":\"10.37934/cfdl.15.12.6076\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The Lane-Emden Boundary Value Problem as it appears in chemical applications, science, and biochemical applications are employed. Two specific models are solved by applying the Ananthaswamy-Sivasankari method (ASM). The model in first problem is a reaction–diffusion equation of a spherical catalyst and the model in second problem is the reaction–diffusion process of a spherical biocatalyst. Obtain a reliable semi-analytical expression of the effectiveness factors and the concentrations. A graph is constructed for the obtained semi-analytical solutions.The effects of several parameters like dimensionless activation energy, Thiele modulus and dimensionless heat of reaction are shown in graphical representation. Our semi-analytical solution is compared with numerical simulation by using MATLAB and finds good fit in all parameters. The new analytical method ASM is helpful to solve many non-linear problems mainly Reaction-Diffusion equation.\",\"PeriodicalId\":9736,\"journal\":{\"name\":\"CFD Letters\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-10-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"CFD Letters\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.37934/cfdl.15.12.6076\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"CFD Letters","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.37934/cfdl.15.12.6076","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"Mathematics","Score":null,"Total":0}
Semi- Analytical Study on Non-Isothermal Steady R-D Equation in a Spherical Catalyst and Biocatalyst
The Lane-Emden Boundary Value Problem as it appears in chemical applications, science, and biochemical applications are employed. Two specific models are solved by applying the Ananthaswamy-Sivasankari method (ASM). The model in first problem is a reaction–diffusion equation of a spherical catalyst and the model in second problem is the reaction–diffusion process of a spherical biocatalyst. Obtain a reliable semi-analytical expression of the effectiveness factors and the concentrations. A graph is constructed for the obtained semi-analytical solutions.The effects of several parameters like dimensionless activation energy, Thiele modulus and dimensionless heat of reaction are shown in graphical representation. Our semi-analytical solution is compared with numerical simulation by using MATLAB and finds good fit in all parameters. The new analytical method ASM is helpful to solve many non-linear problems mainly Reaction-Diffusion equation.