ABSTRACT
Most real-life ¨uid ¨ow phenomena are mathematically represented by the well-known Navier-Stokes (N-S) equations that are based on the continuum hypothesis. The N-S equations are a set of a nonlinear partial-differential equations arrived at by conservation of transport properties such as mass, momentum, and energy for an inŽnitesimal control volume. The N-S equations are based on the following universal laws of conservation: Conservation of Mass, Conservation of Momentum, and Conservation of Energy. The equation that results from applying the Conservation of Mass law to a ¨uid is called the continuity equation. The Conservation of Momentum law is nothing more than Newton’s Second Law. When this law is applied to a ¨uid ¨ow, it yields a vector equation known as the momentum equation. The Conservation of Energy law is identical to the First Law of Thermodynamics, and the resulting ¨uid dynamic equation is named the energy equation. Below is a description of each one of those governing equations. They are taken directly from Tannehill et al. (1997). In addition, a presentation is made for porous media models.
