{"title":"Instability of MHD Fluid Flow through a Horizontal Porous Media in the Presence of Transverse Magnetic Field - A Linear Stability Analysis","authors":"M. Basavaraj","doi":"10.18311/JIMS/2019/17898","DOIUrl":null,"url":null,"abstract":"The study was to conduct a stability analysis of pressure driven ow of an electrically conducting fluid through a horizontal porous channel in the presence of a transverse magnetic field. We employed the Brinkman-extended Darcy model with fluid viscosity is different from effective viscosity. In deriving the equations governing the stability, a simplication is made using the fact that the magnetic Prandtl number Pr m for most of the electrically conducting fluids is assumed to be small. Using the Chebyshev collocation method, the critical Reynolds number Re c , the critical wave number α c and the critical wave speed c c are computed for various values of the parameters present in the problem. The neutral curves are drawn in the (Re, α)- plane for various values of the non-dimensional parameters present in the problem. This study also tells how the combined effect of the magnetic field strength and the porosity of the porous media to delay the onset of instability compare to their presence in isolation. In the absence of some parameters, the results obtained are compared with the existed results to check the accuracy and validity of the present study. An excellent agreement is observed with the existed results.","PeriodicalId":38246,"journal":{"name":"Journal of the Indian Mathematical Society","volume":"86 1","pages":"241-258"},"PeriodicalIF":0.0000,"publicationDate":"2019-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of the Indian Mathematical Society","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.18311/JIMS/2019/17898","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 3
Abstract
The study was to conduct a stability analysis of pressure driven ow of an electrically conducting fluid through a horizontal porous channel in the presence of a transverse magnetic field. We employed the Brinkman-extended Darcy model with fluid viscosity is different from effective viscosity. In deriving the equations governing the stability, a simplication is made using the fact that the magnetic Prandtl number Pr m for most of the electrically conducting fluids is assumed to be small. Using the Chebyshev collocation method, the critical Reynolds number Re c , the critical wave number α c and the critical wave speed c c are computed for various values of the parameters present in the problem. The neutral curves are drawn in the (Re, α)- plane for various values of the non-dimensional parameters present in the problem. This study also tells how the combined effect of the magnetic field strength and the porosity of the porous media to delay the onset of instability compare to their presence in isolation. In the absence of some parameters, the results obtained are compared with the existed results to check the accuracy and validity of the present study. An excellent agreement is observed with the existed results.
期刊介绍:
The Society began publishing Progress Reports right from 1907 and then the Journal from 1908 (The 1908 and 1909 issues of the Journal are entitled "The Journal of the Indian Mathematical Club"). From 1910 onwards,it is published as its current title ''the Journal of Indian Mathematical Society. The four issues of the Journal constitute a single volume and it is published in two parts: issues 1 and 2 (January to June) as one part and issues 3 and 4 (July to December) as the second part. The four issues of the Mathematics Student (another periodical of the Society) are published as a single yearly volume. Only the original research papers of high quality are published in the Journal of Indian Mathematical Society.