Preprint Article Version 1 This version is not peer-reviewed

Convective Instability in a Hele Shaw Cell with the Effect of Through Flow and Magnetic Field

Version 1 : Received: 16 September 2018 / Approved: 17 September 2018 / Online: 17 September 2018 (09:09:04 CEST)

How to cite: Yadav, D. Convective Instability in a Hele Shaw Cell with the Effect of Through Flow and Magnetic Field. Preprints 2018, 2018090290 (doi: 10.20944/preprints201809.0290.v1). Yadav, D. Convective Instability in a Hele Shaw Cell with the Effect of Through Flow and Magnetic Field. Preprints 2018, 2018090290 (doi: 10.20944/preprints201809.0290.v1).

Abstract

In this paper, an analytical investigation of the combined effect of through flow and magnetic field on the convective instability in an electrically conducting fluid layer, bounded in a Hele-Shaw cell is presented within the context of linear stability theory. The Galarkin method is utilized to solve the eigenvalue problem. The outcome of the important parameters on the stability of the system is examined analytically as well as graphically. It is observed that the through flow and magnetic field have both stabilizing effects, while the Hele-Shaw number has destabilizing effect on the stability of system. It is also found that the oscillatory mode of convection possible only when the magnetic Prandtl number takes the values less than unity.

Subject Areas

Linear stability theory; Magneto convection; Through flow; Hele-Shaw cell; Galarkin method.

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