The natural and Marangoni convections formed spontaneously in the melt inside a two-dimensional rectangular open boat were investigated by means of an order-of-magnitude evaluation and a numerical analysis according to the finite difference method. A quantitative evaluation was made of the Grashof number, Marangoni number, Prandtl number and melt depth, all of which affect the interfacial velocity and the velocity distribution of the melt convection. It was concluded that Marangoni convection as well as natural convection is important when the melt is shallow.