Moderate time scale finite amplitude analysis of large stefan number convection in a gravity modulated mushy layer during the solidification of binary alloys

We investigate the convection amplitude in a binary alloy mushy layer subjected to a vibration body force that is collinear with the gravitational acceleration. The analysis shows that the convection amplitude decreases over time for all vibration frequencies tested. The analysis further reveals that as the vibration frequency increases, the convection amplitude subsequently decreases until a critical vibration frequency; at which the amplitude reaches the lowest value. Further increases in the vibration frequency increase the convection amplitude but gradually.