An accurate description of the fluid flow and heat transfer within a Pressurized Water Reactor (PWR), for the safety analysis and reactor performance is always desirable. In this paper a mathematical model of the fundamental physical phenomena which are associated to a typical PWR is presented. The mathematical model governs the fluid dynamics in the reactor. Using commercial software CFX, a computational fluid dynamics (CFD) code, a three-dimensional flow distribution in the downcomer and the lower plenum of the reactor was also calculated and a valuable analysis of the reactor performance is given. Due to computational limits, simplifications of the core, downcomer and the lower plenum of the reactor are introduced. Nevertheless, it has been shown that computational fluid dynamics and in particular appropriate usage of CFX software improves our understanding of fluid flow distribution, velocity distribution and heat transfer in different parts of the reactor pressure vessel, in particular, in the downcomer and the lower plenum.