the objective of this research is to produce a control scheme by an inverse method that is capable of acting fast enough to be useful in a real-time manufacturing environment. the scheme should provide a transient boundary condition that produces a prescribed interfacial surface motion with a corresponding desired morphology at the phase interface in solidification problems. in this thesis, an inverse technique is presented for one and two-dimensional heat transfer problems with phase change. it calculates the required boundary temperature to provide a specified interface velocity at the solid-liquid interface. an entropy-based method b used to improve the stability of the proposed algorithm. the effects of free convection in the liquid are &o considered. a control-volume- based finite element method is employed for the numerical solution of the conservation equations for mass, momentum and energy. numerical examples are presented in order to demonstrate the promising capabilities and performance of the proposed formulation. in practical solidification problems, this method can lead to stable and meaningful results.