Zeitschrift für angewandte Mathematik und Physik ZAMP

, Volume 57, Issue 1, pp 133–159

Nonlinear Kelvin-Helmholtz instability of two miscible ferrofluids in porous media

Authors

  • Galal M. Moatimid
    • Department of Mathematics Faculty of EducationAin Shams University
Original Paper

DOI: 10.1007/s00033-005-2067-1

Cite this article as:
Moatimid, G.M. Z. angew. Math. Phys. (2005) 57: 133. doi:10.1007/s00033-005-2067-1

Abstract.

The nonlinear theory of the Kelvin-Helmholtz instability is employed to analyze the instability phenomenon of two ferrofluids through porous media. The effect of both magnetic field and mass and heat transfer is taken into account. The method of multiple scale expansion is employed in order to obtain a dispersion relation for the first-order problem and a Ginzburg–Landau equation, for the higher-order problem, describing the behavior of the system in a nonlinear approach. The stability criterion is expressed in terms of various competing parameters representing the mass and heat transfer, gravity, surface tension, fluid density, magnetic permeability, streaming, fluid thickness and Darcy coefficient. The stability of the system is discussed in both theoretically and computationally, and stability diagrams are drawn.

Keywords.

Nonlinear instabilitymultiple scale methodsferrofluidsporous media

Copyright information

© Birkhäuser Verlag, Basel 2006