Asymptotic methods in magnetoconvection
type: Item
instance of: scholarly article
title: Asymptotic methods in magnetoconvection
zbMATH Open document ID: 0898.76098
author: N. Rudraiah
published in: Indian Journal of Pure \& Applied Mathematics
publication date: 1997-10-07T00:00:00Z
review text: The author examines the magnetohydrodynamic convection of an electrically and heat conducting non-viscous fluid in a uniform vertical magnetic field. The stability of a thin horizontal layer of a Boussinesq fluid is investigated in Cartesian coordinates with \(z\)-coordinate directed along the magnetic field. The effects of Ampère force and non-uniform temperature gradient on the magnetoconvection are studied analytically using Galerkin expansion. The linear stability analysis is applied, and only the marginal state is considered using a single term of the Galerkin expansion. The author proves that if the magnetic viscosity prevails over the thermal conductivity, the overstability cannot occur and the principle of exchange of stabilities is valid. The method of matched asymptotics is employed to investigate the effect of the Hartmann layers on the magnetoconvection. The critical Rayleigh number, close to that obtained by experiments, is found analytically by a regular perturbation technique. The author demonstrates that the Chandrasekhar's power law is correct only for free-free isothermal boundary conditions. Under other boundary conditions, the critical Rayleigh number obeys the power law with a different constant of proportionality. The critical Rayleigh number depends critically on the heating and does not depend on the nature of boundaries. It is shown that a non-uniform temperature gradient and magnetic field suppress or augment the magnetohydrodynamical convection.
Mathematics Subject Classification ID: 76W05
Mathematics Subject Classification ID: 76R10
Mathematics Subject Classification ID: 80A20
zbMATH DE Number: 1071709
zbMATH Keywords: uniform vertical magnetic field
zbMATH Keywords: Boussinesq fluid
zbMATH Keywords: Ampère force
zbMATH Keywords: non-uniform temperature gradient
zbMATH Keywords: Galerkin expansion
zbMATH Keywords: linear stability analysis
zbMATH Keywords: magnetic viscosity
zbMATH Keywords: thermal conductivity
zbMATH Keywords: principle of exchange of stabilities
zbMATH Keywords: method of matched asymptotics
zbMATH Keywords: Hartmann layers
zbMATH Keywords: critical Rayleigh number
zbMATH Keywords: Chandrasekhar's power law
reviewed by: Oleg A. Sinkevich
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1071709