International Conference on Applications of Mathematics to Nonlinear Sciences. Electron. J. Diff. Eqns., Conference 24 (2017), pp. 85-101.

Free surface dynamics of thin MHD second-grade fluid over a heated nonlinear stretching sheet

Kiran Kumar Patra, Satyananda Panda, Mathieu Sellier

Abstract:
This article presents a long-wave theory for the free surface dynamics of magnetohydrodynamics (MHD) second-grade fluid over a non-uniform heated flat elastic sheet. An evolution equation for the film thickness is derived from the instationary Navier-Stokes equations using regular asymptotic expansion with respect to the small aspect ratio of the flow domain. The derived thin film equation is solved numerically using finite volume method on a uniform grid system with implicit flux discretization. The finding reveals the dependency of the thinning behavior of the fluid film on the stretching speed and the non-Newtonian second-grade parameter.

Published November 15, 2017.
Math Subject Classifications: 76A05, 76A10, 76A20, 76M12, 80A20.
Key Words: Thin liquid film; heat transfer; second-grade fluid; free surface flow; magnetic field; long-wave theory.

Show me the PDF file (297 K), TEX file for this article.

Kiran Kumar Patra
Department of Mathematics
National Institute of Technology Calicut
NIT(P.O)-673601, Kerala, India
email: kirankumarpatra1984@gmail.com
Satyananda Panda
Department of Mathematics
National Institute of Technology Calicut
NIT(P.O)-673601, Kerala, India
email: satyanand@nitc.ac.in
Mathieu Sellier
Department of Mechanical Engineering
University of Canterbury, Private Bag 4800
Christchurch 8140, New Zealand
email: mathieu.sellier@canterbury.ac.nz

Return to the table of contents for this conference.
Return to the EJDE web page