Convective instability of a rotating layer of ferromagnetic fluid |
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Authors: | S P Bhattacharyya M Abbas |
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Institution: | (1) Department of Mathematics, Indian Institute of Technology, 400 076 Powai, Bombay, India;(2) Department of Computer Science and Engineering, Indian Institute of Technology, 400 076 Powai, Bombay, India |
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Abstract: | 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)π
4/(1 −P) and in case the condition is satisfied, overstability is possible for all those values ofa which satisfya
2 < N(1 −P)π
2/(1 +P)]
1/3 − π2. IfR
c
(con)
andR
c
(o.s)
are the critical values of the convective and the overstable marginal states respectively, then it is also found thatR
c
(con)
<R
c
(o.s)
providedN is not sufficiently large. |
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Keywords: | Stability convective marginal state overstability ferromagnetic fluid |
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