Convective instability of a rotating layer of ferromagnetic fluid

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.     

二元层片共晶凝固过程的特征尺度选择

基于Jackson和Hunt二元规则共晶稳态生长理论,在共晶两相的界面溶质守恒条件中引入密度修正项,改进了共晶两相的界面溶质守恒条件.在此基础上,根据二元层片共晶常规凝固过程中层片组织稳态生长时Gibbs自由能的变化,运用极值形态选择原理确定二元层片共晶凝固过程中层片间距特征尺度选择准则.理论分析表明,对于给定二元共晶合金,在常规凝固条件下的层片间距选择通常为一有限区间.此外,理论分析还表明,二元层片共晶稳态生长时其特征尺度的选择可以呈现超稳定性,而且在给定的凝固条件下超稳定性只和给定合金系的物性参数有关.将该形态选择准则分别运用于物性参数精确已知的Al-Al2Cu,Sn-Pb和CBr4-C2Cl6合金系,表明计算结果与实验结果相符合.