An equivalent undercooling model to account for flow effect on binary alloy dendrite growth rate

A theoretical analysis is carried out to observe the influence of important flow parameters such as Nusselt number and Sherwood number on the tip speed of an equiaxed dendrite growing in a convecting alloy melt. The effect of thermal and solutal transfer at the interface due to convection is equated to an undercooling of the melt, and an expression is derived for this equivalent undercooling in terms of the flow Nusselt number and Sherwood number. Results for the equivalent undercooling are compared with corresponding numerical values obtained by performing simulations based on the enthalpy method. This method represents a relatively simple procedure to analyze the effects of melt convection on the growth rate of dendrites.