Transportation of nuclear spent fuel is inevitable over the coming years. However, to ensure the safety of such transport, computational models must be established that are capable of evaluating the thermal characteristics of the containers in which spent fuel is shipped. In an effort to further the development of a satisfactory computational tool, researchers at The University of Texas at Austin have developed a numerical algorithm that utilizes a homogeneous equilibrium model to calculate the effects of two-phase water on the thermal performance of the containers. This model has been evaluated in preparation for its incorporation into TEXSAN, the Texas-Sandia thermal-hydraulic analysis program. In this study, a stream function vorticity formulation routine was employed in order to calculate single- and two-phase mass and energy transport in a simple driven cavity configuration. Furthermore, a simulation of boiling heat transfer and natural convection around an idealized hot wire was performed. The temperature, enthalpy, and velocity distributions were determined and compared favorably to experimental and numerical benchmark results. The stream function vorticity formulation of the homogeneous equilibrium model has thus been demonstrated to be a viable predictive tool, capable of analysis of two-phase multimode heat transfer. This establishes the potential for improved spent-fuel transportation analysis, which is required for ensuring the safety of shipping container designs.