Dr. William T. Sha's longstanding technical achievements and outstanding contributions in the nuclear reactor field are well known both in the United States and abroad. As the director of the Argonne National Laboratory (ANL), I had the privilege of working with Dr. Sha for more than a decade during which he markedly enhanced the reputation of ANL's international reactor programs as the director of the Analytical Thermal Hydraulic Research Program and Multiphase Flow Research Institute. Over many years, his rare combination of analytical rigor and creative insight allowed him to earn international recognition as a leader in the field of thermal hydraulics in both theoretical formulation and reactor design and safety analysis.

His recent work on novel porous media formulation for multiphase flow conservation equations is the subject of this book. “A set of conservation equations of mass, momentum, and energy for two-phase and multiphase flows via time-volume averaging has been rigorously derived for the first time. These equations are in differential-integral form, in contrast to a set of partial differential equations used currently. The integrals arise due to interfacial mass, momentum, and energy transfer.” This is an important discovery that will have far reaching implications for both academic and industrial applications. The recent tragic accident at the Fukushima Nuclear Reactor in Japan, which is a boiling-water reactor involving two-phase or multiphase flows, makes the subject of this book even more timely and important.