Hydromagnetic thin film flow: Linear stability

Handle URI:
http://hdl.handle.net/10754/552877
Title:
Hydromagnetic thin film flow: Linear stability
Authors:
Amaouche, Mustapha; Ait Abderrahmane, Hamid; Bourdache, Lamia
Abstract:
This paper deals with the long wave instability of an electroconductor fluid film, flowing down an inclined plane at small to moderate Reynolds numbers, under the action of electromagnetic fields. A coherent second order long wave model and two simplified versions of it, referred to as first and second reduced models (FRM and SRM), are proposed to describe the nonlinear behavior of the flow. The modeling procedure consists of a combination of the lubrication theory and the weighted residual approach using an appropriate projection basis. A suitable choice of weighting functions allows a significant reduction of the dimension of the problem. The full model is naturally unique, i.e., independent of the particular form of the trial functions. The linear stability of the problem is investigated, and the influence of electromagnetic field on the flow stability is analyzed. Two cases are considered: the applied magnetic field is either normal or parallel to the fluid flow direction, while the electric field is transversal. The numerical solution of the Orr-Sommerfeld (OS) eigenvalue problem and those of the depth averaging model are used to assess the accuracy of the reduced models. It is found that the current models have the advantage of the Benney-like model, which is known to asymptote the exact solution near criticality. Moreover, far from the instability threshold, the current reduced models continue to follow the OS solution up to moderate Reynolds numbers, while the averaging model diverges rapidly. The model SRM gives better results than FRM beyond sufficiently high Reynolds numbers.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Citation:
Hydromagnetic thin film flow: Linear stability 2013, 88 (2) Physical Review E
Publisher:
American Physical Society (APS)
Journal:
Physical Review E
Issue Date:
30-Aug-2013
DOI:
10.1103/PhysRevE.88.023028
Type:
Article
ISSN:
1539-3755; 1550-2376
Additional Links:
http://link.aps.org/doi/10.1103/PhysRevE.88.023028
Appears in Collections:
Articles; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorAmaouche, Mustaphaen
dc.contributor.authorAit Abderrahmane, Hamiden
dc.contributor.authorBourdache, Lamiaen
dc.date.accessioned2015-05-14T12:55:34Zen
dc.date.available2015-05-14T12:55:34Zen
dc.date.issued2013-08-30en
dc.identifier.citationHydromagnetic thin film flow: Linear stability 2013, 88 (2) Physical Review Een
dc.identifier.issn1539-3755en
dc.identifier.issn1550-2376en
dc.identifier.doi10.1103/PhysRevE.88.023028en
dc.identifier.urihttp://hdl.handle.net/10754/552877en
dc.description.abstractThis paper deals with the long wave instability of an electroconductor fluid film, flowing down an inclined plane at small to moderate Reynolds numbers, under the action of electromagnetic fields. A coherent second order long wave model and two simplified versions of it, referred to as first and second reduced models (FRM and SRM), are proposed to describe the nonlinear behavior of the flow. The modeling procedure consists of a combination of the lubrication theory and the weighted residual approach using an appropriate projection basis. A suitable choice of weighting functions allows a significant reduction of the dimension of the problem. The full model is naturally unique, i.e., independent of the particular form of the trial functions. The linear stability of the problem is investigated, and the influence of electromagnetic field on the flow stability is analyzed. Two cases are considered: the applied magnetic field is either normal or parallel to the fluid flow direction, while the electric field is transversal. The numerical solution of the Orr-Sommerfeld (OS) eigenvalue problem and those of the depth averaging model are used to assess the accuracy of the reduced models. It is found that the current models have the advantage of the Benney-like model, which is known to asymptote the exact solution near criticality. Moreover, far from the instability threshold, the current reduced models continue to follow the OS solution up to moderate Reynolds numbers, while the averaging model diverges rapidly. The model SRM gives better results than FRM beyond sufficiently high Reynolds numbers.en
dc.publisherAmerican Physical Society (APS)en
dc.relation.urlhttp://link.aps.org/doi/10.1103/PhysRevE.88.023028en
dc.rightsArchived with thanks to Physical Review Een
dc.titleHydromagnetic thin film flow: Linear stabilityen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalPhysical Review Een
dc.eprint.versionPublisher's Version/PDFen
dc.contributor.institutionDepartment of Physics, Route de Targa-Ouzemour, Béjaia 06000, Algeriaen
kaust.authorAit Abderrahmane, Hamiden
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