Article

Abstract

The unsteady flow and heat transfer of an electrically conducting, viscous, incompressible fluid bounded by two parallel nonconducting porous plates are studied taking the Hall effect into consideration. An external uniform magnetic field is applied normal to the plates, and the fluid motion is subjected to a constant pressure gradient and a uniform suction and injection. An analytical solution for the governing equations of motion is obtained and a numerical solution for the energy equation including the Joule and the viscous dissipation terms is developed. The effect of the Hall term on both the velocity and temperature distributions is examined. Résumé: Tenant compte de l'effet Hall, nous étudions le flux instable et le transfert de chaleur d'un fluide conducteur, visqueux et compressible, confiné par deux plaques parallèles poreuses et non-conductrices. Le champ magnétique extérieur est maintenu perpendiculaire aux deux plaques. Le mouvement du fluide est assuré par un gradient de pression et alimenté par injection et succion uniformes. Nous avons développé une solution analytique pour l'équation gouvernant le mouvement, ainsi qu'une solution numérique pour l'équation d'energie qui inclut les dissipations de Joule et de viscosité. Nous examinons l'effet du terme de Hall sur les distributions de vitesse et de température. [Traduit par la rédaction] Can. J. Phys. Downloaded from www.nrcresearchpress.com by University of Saskatchewan on 09/24/12 For personal use only.

Transient Hartmann Flow with Heat Transfer Considering the Ion Slip

“…It should be mentioned that the results obtained herein reduce to those reported by Soundalgekar et al [8,9] in the steady state and when $ ¼ 0. Also the steady state reported by Attia [11] with no ion slip is reproduced by setting b i ¼ 0 in the present results. Table I presents the variation of the axial and the transverse skin friction coe⁄cients and the Nusselt number at both walls of the channel with the ion slip parameter b i .…”

“…Unlike the complex velocity V , the temperature distribution depends on C. All calculations have been carried out for C ¼ 5, Pr ¼ 1, and Ec ¼ 0:2. In order to examine the accuracy and correctness of the solutions, the results for the absence of the ion slip are compared and shown to be in complete agreement with those reported by Attia [11].…”

“…Abo-El-Dahab [10] studied the e¡ect of Hall current on the steady Hartmann £ow subjected to a uniform suction and injection at the bounding plates. Later, Attia [11] extended the problem to the unsteady state with heat transfer, taking the Hall e¡ect into consideration while neglecting the ion slip.…”

The effect of suction and injection on unsteady flow of a dusty conducting fluid in rectangular channel

“…The viscous dissipation is taken into consideration. The flow of the fluid is governed by the Navier-Stokes equation which has the form [1,5]. (1) where ñ is the density of the fluid, ì is the viscosity of the fluid, and u = u (y,t) is the velocity component of the fluid in the x-direction.…”

“…Many researchers have considered this problem under different physical effects [1][2][3][4][5]. Most of these studies are based on constant physical properties, although some physical properties vary with temperature and assuming constant properties is a good approximation as long as small differences in temperature are involved [6].…”