Transient drainage of the thin film of linearly viscous MHD fluid on a slippery flat belt

This paper considered the transient drainage of a linearly viscous magnetohydrodynamic (MHD) fluid down a vertical flat slippery belt. An inhomogeneous partial differential equation with an inhomogeneous boundary condition was developed. Exact solutions for the velocity distribution, flow rate, surface profile, and variable thickness were then computed. The effect of MHD and the slip parameter on the velocity, flow rate, and surface profile were then considered. The effect of the magnetic field on the derived flow properties was discussed and represented graphically. It was determined that the absence of the magnetic field and the assumption of no-slip boundary conditions reduced the problem to the well-known Jeffreys problem. Key words: thin film flow, linearly viscous fluid model, MHD, exact solutions, transient drainage, slippery belt. Nous etudions ici le drainage transitoire d'un fluide MHD a viscosite lineaire, descendant sur une courroie verticale, plate et glissante. Afin de le decrire, nous developpons une equation differentielle aux derivees partielles inhomogene avec une condition limite inhomogene. Nous calculons des solutions exactes pour la distribution de vitesse, le taux d'ecoulement, le profil de surface et l'epaisseur variable. Nous considerons alors l'effet du caractere MHD et du parametre de glissement sur la vitesse, le taux d'ecoulement et le profil de surface. Nous discutons l'effet d'un champ magnetique sur les proprietes d'ecoulement et representons cet effet graphiquement. Nous determinons ensuite, qu'en l'absence de champ magnetique et sans condition limite de glissement, le probleme se reduit au probleme bien connu de Jeffreys. [Traduit par la Redaction] Mots-cles: ecoulement d'un film mince, modele de fluide a viscosite lineaire, MHD, solutions exactes, drainage transitoire, courroie glissante. PACS Nos.: 01, 47, 02.30.
1. Introduction The flow of fluid in the form of thin layers is called thin-film flow. A thin film consists of an expanse of liquid bounded by a solid body [...]