• S P Bhattacharyya

      Articles written in Proceedings – Mathematical Sciences

    • Instability of a planar liquid layer in an alternating longitudinal magnetic field with non-zero mean

      S P Bhattacharyya M Abbas

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      The conducting liquid interface is found to undulate in an alternating magnetic field. It was shown earlier that ifM =B02/μηω, B0, ω, μ andη being the amplitude (complex) of the alternating longitudinal magnetic field imposed at the interface, the angular frequency of the field, the magnetic permeability and the viscosity respectively, and ifMc was the critical value ofM then the planar layer was stable or unstable according asM < Mc orM > Mc. In this paper we have determined the stability criterion when in addition to the alternating longitudinal field there acts a uniform field in the same direction. After comparing our results with those obtained earlier, in the absence of the uniform field, we find that the additional uniform field has a significant destabilizing effect.

    • Convective instability of a rotating layer of ferromagnetic fluid

      S P Bhattacharyya M Abbas

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      The instability of a hot horizontal layer of ferromagnetic fluid rotating about a vertical axis has been investigated when the Prandtl numberP < 1. Earlier it was shown that forP > 1 the overstability cannot occur. In this paper the convective and overstable marginal states have been investigated separately forP < 1 and it is found that though convective marginal state is possible for alla, the non-dimensional wave number, and N the Taylor number, the overstability is possible only ifN > (1 +P)π4/(1 −P) and in case the condition is satisfied, overstability is possible for all those values ofa which satisfya2 < [N(1 −P)π2/(1 +P)]1/3 − π2. IfRc(con) andRc(o.s) are the critical values of the convective and the overstable marginal states respectively, then it is also found thatRc(con) <Rc(o.s) providedN is not sufficiently large.

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