Effects of the Darcy-Prandtl number on the linear stability of stationary convection in rotating mushy layers

The linear stability analysis of convection in the mushy layer of a unidirectionally solidifying binary alloy of close to eutectic composition, subject to Coriolis effects is performed. The simplified model of Amberg and Homsy (J. Fluid Mech., 252, 79-98, 1993), which decouples the mushy layer from the overlying melt and underlying solid, is utilized for a Stefan number of unit order, for a near eutectic limit. The linear stability results indicates that the current formulation captures the effects of small Darcy-Prandtl numbers on the stability of convection and also indicates the correction on the results obtained by Govender and Vadasz (J. Porous Media, 5(2), 113-121, 2002a) for large Darcy-Prandtl numbers. The Rayleigh numbers predicted by the current formulation approaches those predicted by Govender and Vadasz for large Darcy-Prandtl numbers.