Naeem Ullah, D. N. K. Marwat, Montaha Mohamed Ibrahim Mohamed, Sana Ben Moussa
{"title":"具有指数型非线性运动学的薄膜在多孔移动和非平面薄片上的稳定流动","authors":"Naeem Ullah, D. N. K. Marwat, Montaha Mohamed Ibrahim Mohamed, Sana Ben Moussa","doi":"10.1002/zamm.202300057","DOIUrl":null,"url":null,"abstract":"A generalized model of flow of viscous thin film has been presented and the film is maintained over a porous, moving and non‐flat sheet. We categorically emphasized on the nonuniform and nonlinear kinematics of the sheet and deformation of thin film and variation of all quantities specified at the boundaries are taken of exponential type. The combined effects of deformation of both thin film and sheet along with the nonlinear kinematics of sheet have been analyzed on the characteristics of flow. The governing partial differential equations are transformed into ordinary differential equations (ODEs) by using similarity transformations and the final problem of ODEs is solved with the help of bvp4c technique, whereas, the result for the velocity and skin friction are graphed for different values of the injection (suction), stretching (shrinking) and deformation (contraction/expansion) of both thin film and sheet parameters. Note that the increasing, decreasing, uniform, linear, nonlinear and boundary layer behaviors of the velocity profiles and skin friction are noted for multiple choices of the parameters. Moreover, flows in upstream and downstream directions have been observed for different values and diverse nature of the parameters.","PeriodicalId":23924,"journal":{"name":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","volume":null,"pages":null},"PeriodicalIF":2.3000,"publicationDate":"2023-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Steady flow of thin film over porous moving and non‐flat sheet with nonlinear kinematics of exponential type\",\"authors\":\"Naeem Ullah, D. N. K. Marwat, Montaha Mohamed Ibrahim Mohamed, Sana Ben Moussa\",\"doi\":\"10.1002/zamm.202300057\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A generalized model of flow of viscous thin film has been presented and the film is maintained over a porous, moving and non‐flat sheet. We categorically emphasized on the nonuniform and nonlinear kinematics of the sheet and deformation of thin film and variation of all quantities specified at the boundaries are taken of exponential type. The combined effects of deformation of both thin film and sheet along with the nonlinear kinematics of sheet have been analyzed on the characteristics of flow. The governing partial differential equations are transformed into ordinary differential equations (ODEs) by using similarity transformations and the final problem of ODEs is solved with the help of bvp4c technique, whereas, the result for the velocity and skin friction are graphed for different values of the injection (suction), stretching (shrinking) and deformation (contraction/expansion) of both thin film and sheet parameters. Note that the increasing, decreasing, uniform, linear, nonlinear and boundary layer behaviors of the velocity profiles and skin friction are noted for multiple choices of the parameters. Moreover, flows in upstream and downstream directions have been observed for different values and diverse nature of the parameters.\",\"PeriodicalId\":23924,\"journal\":{\"name\":\"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.3000,\"publicationDate\":\"2023-08-31\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://doi.org/10.1002/zamm.202300057\",\"RegionNum\":4,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1002/zamm.202300057","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Steady flow of thin film over porous moving and non‐flat sheet with nonlinear kinematics of exponential type
A generalized model of flow of viscous thin film has been presented and the film is maintained over a porous, moving and non‐flat sheet. We categorically emphasized on the nonuniform and nonlinear kinematics of the sheet and deformation of thin film and variation of all quantities specified at the boundaries are taken of exponential type. The combined effects of deformation of both thin film and sheet along with the nonlinear kinematics of sheet have been analyzed on the characteristics of flow. The governing partial differential equations are transformed into ordinary differential equations (ODEs) by using similarity transformations and the final problem of ODEs is solved with the help of bvp4c technique, whereas, the result for the velocity and skin friction are graphed for different values of the injection (suction), stretching (shrinking) and deformation (contraction/expansion) of both thin film and sheet parameters. Note that the increasing, decreasing, uniform, linear, nonlinear and boundary layer behaviors of the velocity profiles and skin friction are noted for multiple choices of the parameters. Moreover, flows in upstream and downstream directions have been observed for different values and diverse nature of the parameters.
期刊介绍:
ZAMM is one of the oldest journals in the field of applied mathematics and mechanics and is read by scientists all over the world. The aim and scope of ZAMM is the publication of new results and review articles and information on applied mathematics (mainly numerical mathematics and various applications of analysis, in particular numerical aspects of differential and integral equations), on the entire field of theoretical and applied mechanics (solid mechanics, fluid mechanics, thermodynamics). ZAMM is also open to essential contributions on mathematics in industrial applications.