Sajid Khan, Zeshan Zulifqar, Muhammad Ashraf, Asma Qadeer
{"title":"经过垂直锥体的自由对流的近似闭式解法","authors":"Sajid Khan, Zeshan Zulifqar, Muhammad Ashraf, Asma Qadeer","doi":"10.1002/htj.23079","DOIUrl":null,"url":null,"abstract":"<p>This paper presents a technique to find the closed-form solution of the boundary-value problem representing free convection flow past a vertical cone. Partial differential equations that govern the flow are converted into nonlinear ordinary differential equations with the aid of similarity transformations. First, a numerical solution is obtained with the help of the bvp4c package of MATLAB, and then utilizing the numerical solution, the closed-form solution is obtained. The accuracy of the closed-form solution is analyzed by the residual technique. Graphs of the residuals of the governing equations indicate that our approximate closed-form solution closely matches the exact solution.</p>","PeriodicalId":44939,"journal":{"name":"Heat Transfer","volume":null,"pages":null},"PeriodicalIF":2.8000,"publicationDate":"2024-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Approximate closed-form solution of free convection flow past a vertical cone\",\"authors\":\"Sajid Khan, Zeshan Zulifqar, Muhammad Ashraf, Asma Qadeer\",\"doi\":\"10.1002/htj.23079\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>This paper presents a technique to find the closed-form solution of the boundary-value problem representing free convection flow past a vertical cone. Partial differential equations that govern the flow are converted into nonlinear ordinary differential equations with the aid of similarity transformations. First, a numerical solution is obtained with the help of the bvp4c package of MATLAB, and then utilizing the numerical solution, the closed-form solution is obtained. The accuracy of the closed-form solution is analyzed by the residual technique. Graphs of the residuals of the governing equations indicate that our approximate closed-form solution closely matches the exact solution.</p>\",\"PeriodicalId\":44939,\"journal\":{\"name\":\"Heat Transfer\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.8000,\"publicationDate\":\"2024-05-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Heat Transfer\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1002/htj.23079\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"THERMODYNAMICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Heat Transfer","FirstCategoryId":"1085","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/htj.23079","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"THERMODYNAMICS","Score":null,"Total":0}
Approximate closed-form solution of free convection flow past a vertical cone
This paper presents a technique to find the closed-form solution of the boundary-value problem representing free convection flow past a vertical cone. Partial differential equations that govern the flow are converted into nonlinear ordinary differential equations with the aid of similarity transformations. First, a numerical solution is obtained with the help of the bvp4c package of MATLAB, and then utilizing the numerical solution, the closed-form solution is obtained. The accuracy of the closed-form solution is analyzed by the residual technique. Graphs of the residuals of the governing equations indicate that our approximate closed-form solution closely matches the exact solution.