International Scholarly Research Network ISRN Mechanical Engineering Volume 2011, Article ID 597172, 8 pages doi:10.5402/2011/597172 Research Article Gravitational Instability of Rotating Viscoelastic Partially Ionized Plasma in the Presence of an Oblique Magnetic Field and Hall Current M. F. El-Sayed 1 and R. A. Mohamed 2 1 Department of Mathematics, Faculty of Education, Ain Shams University, Heliopolis, Roxy, Cairo 11757, Egypt 2 Department of Physics, Faculty of Education, Ain Shams University, Heliopolis, Roxy, Cairo 11757, Egypt Correspondence should be addressed to M. F. El-Sayed, mfahmye@yahoo.com Received 29 January 2011; Accepted 17 March 2011 Academic Editor: P. M. Mariano Copyright © 2011 M. F. El-Sayed and R. A. Mohamed. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The gravitational instability of a rotating Walters B ′ viscoelastic partially ionized plasma permeated by an oblique magnetic field has been investigated in the presence of the effects of Hall currents, electrical resistivity, and ion viscosity. The dispersion relation and numerical calculations have been performed to obtain the dependence of the growth rate of the gravitational unstable mode on the various physical effects. It is found that viscosity and collision frequency of plasma have stabilizing effects, while viscoelasticity and angular frequency of rotation have destabilizing effect; the electrical resistivity has a destabilizing effect only for small wavenumbers; the density of neutral particles and the magnetic field component in z-direction have stabilizing effects for wavenumbers ranges k< 5 and k< 10, respectively; the Hall current has a slightly destabilizing effect. Finally, the inclination angle to z-direction has a destabilizing effect to all physical parameters. 1. Introduction The gravitational instability problem of an infinite homoge- nous medium was first considered by Jeans [1]. According to Jeans’ criterion, an infinite homogenous self-gravitating atmosphere is unstable for all wavenumbers k less than Jeans’ wavenumber k j =  Gρ/S, where ρ is the density, S is the velocity of sound in the gas, and G is the gravitational constant. This problem has been studied by several authors under varying assumptions of hydrody- namics and hydromagnetics, and a comprehensive account of these investigations has been given by Chandrasekhar [2] in his monograph on problems of hydrodynamic and hydromagnetic stabilities. He showed that Jeans’ criterion remains unaffected by the separate or simultaneous presence of uniform rotation and uniform magnetic field. The combined effects of uniform rotation, Hall currents, finite conductivity, and finite Larmor radius on gravitational instability have been studied by Bhatia [3]. Yu and Sanborn [4] studied the internal gravitational instability in a stratified anisotropic plasma. Bhatia [5] and also Barbian and Ras- mussen [6] studied the gravitational instability of a rotating anisotropic plasmas. Ariel [7] studied the gravitational instability of a rotating anisotropic plasma with Hall current effect. In cosmic physics, there are several situations such as chromosphere, solar photosphere, and in cool interstellar cloud where the plasma are frequently not fully ionized but may instead be partially ionized so that the interaction between the ionized fluid and the neutral gas becomes important. The importance of such collisions between ionized fluid and neutral gas on the ionization rate in these regions have been pointed by Mamun and Shukla [8]. They studied a new magnetic Jeans instability in a non-uniform partially ionized plasma. Pandey et al. [9] studied Jeans instability of an inhomogeneous streaming dusty plasma.