Artificial boundary method for the fractional second-grade fluid flow on a semi-infinite plate with the effects of magnetic field and a power-law viscosity
{"title":"Artificial boundary method for the fractional second-grade fluid flow on a semi-infinite plate with the effects of magnetic field and a power-law viscosity","authors":"","doi":"10.1016/j.aml.2024.109263","DOIUrl":null,"url":null,"abstract":"<div><p>As a typical representative of viscoelastic fluids, second-grade fluids have many applications, such as paints, food products, and cosmetics. In this paper, the equation for describing the fractional second-grade fluid with the power-law viscosity on a semi-infinite plate under the influence of a magnetic field is studied. The numerical solution is obtained using the finite difference method. To handle the semi-unbounded region, the (inverse) <span><math><mi>z</mi></math></span>-transform is applied to establish the absorbing boundary condition (ABC) for the solution at the cut-off point. In addition, the numerical example analyzes the superiority of the ABC over the directly truncated boundary condition and the effects of different parameters on the velocity distribution. The conclusion is that the slip parameter, power-law exponent parameter, and power-law index parameter promote the fluid flow, while the magnetic field and fractional parameter hinder the fluid flow.</p></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":2.9000,"publicationDate":"2024-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematics Letters","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0893965924002830","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
As a typical representative of viscoelastic fluids, second-grade fluids have many applications, such as paints, food products, and cosmetics. In this paper, the equation for describing the fractional second-grade fluid with the power-law viscosity on a semi-infinite plate under the influence of a magnetic field is studied. The numerical solution is obtained using the finite difference method. To handle the semi-unbounded region, the (inverse) -transform is applied to establish the absorbing boundary condition (ABC) for the solution at the cut-off point. In addition, the numerical example analyzes the superiority of the ABC over the directly truncated boundary condition and the effects of different parameters on the velocity distribution. The conclusion is that the slip parameter, power-law exponent parameter, and power-law index parameter promote the fluid flow, while the magnetic field and fractional parameter hinder the fluid flow.
期刊介绍:
The purpose of Applied Mathematics Letters is to provide a means of rapid publication for important but brief applied mathematical papers. The brief descriptions of any work involving a novel application or utilization of mathematics, or a development in the methodology of applied mathematics is a potential contribution for this journal. This journal''s focus is on applied mathematics topics based on differential equations and linear algebra. Priority will be given to submissions that are likely to appeal to a wide audience.