3. Mathematical Description of Physical Phenomena

The chapter provides an overview of the conservation principles governing fluid flow, heat and mass transfer, and other related transport phenomena of interest in this book. The physical laws controlling the conservation principles are translated into mathematical relations, written in the form of partial differential equations, representing the needed vehicle for their simulations. First the continuity, momentum, and energy equations (collectively known as the Navier-Stokes equations) expressing the principles of conservation of mass, momentum, and total energy, respectively, are derived. This is followed by the development of a typical conservation equation for a general scalar, vector, or tensor quantity. The mathematical properties of the various terms in these equations are also examined. Moreover, the common practice of writing the conservation equations in a non-dimensional form using dimensionless quantities is explained and some of the dimensionless groups resulting from the application of this procedure, which are very useful for performing parametric studies of engineering problems, are discussed.