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On Mathematical Modeling, Nonlinear Properties And Stability Of Secondary Flow In A Dendrite Layer, Daniel N. Riahi

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

This paper studies instabilities in the flow of melt within a horizontal dendrite layer with deformed upper boundary and in the presence or absence of rotation during the solidification of a binary alloy. In the presence of rotation, it is assumed that the layer is rotating about a vertical axis at a constant angular velocity. Linear and weakly nonlinear stability analyses provide results about various flow features such as the critical mode of convection, neutral stability curve, preferred flow pattern and the solid fraction distribution within the dendrite layer. The preferred shape of the deformed upper boundary of the layer, …