“…Based on quasi-steady heat conduction equation and interfacial conditions, including Gibbs-Thomson condition and conservation of energy, theoretical efforts have been performed to study the influences of stability, surface tension, interfacial kinetic effect on the crystal growth [1,2] . Furthermore, Chen, et al [11] examined the system with incoming flow, constructed a mathematical model of spherical crystal considering surface energy, kinetic effect, and verified the different role of convection on upstream and downstream arms. However, the variation of surface tension with temperature and the Marangoni effect induced have been neglected in the publications available.…”