TABLE OF CONTENTS Each time we try to solve a new problem related to momentum and heat and mass transfer in a fluid, it is convenient to start with a set of equations based on basic laws of conservation for physical systems. These equations include
The continuity equation (conservation of mass)
The equation of motion (conservation of momentum)
The energy equation (conservation of energy, or the first law of thermodynamics)
The conservation equation for species (conservation of species)
These equations are sometimes called the equations of change, inasmuch as they describe the change of velocity, temperature, and concentration with respect to time and position in the system.
The first three equations are sufficient for problems involving a pure fluid (a pure substance is a single substance characterized by an unvarying chemical structure). The fourth equation is added for a mixture of chemical species, i.e., when mass diffusion with or without chemical reactions is present.
The control volume: When deriving the conservation equations, it is necessary to select a control volume. The derivation can be performed for a volume element of any shape in a given coordinate system, although the most convenient shape is usually assumed for simplicity (e.g., a rectangular shape in a rectangular coordinate system). For illustration purposes, different coordinate systems are shown in Fig. 10.1. In selecting a control volume, we have the option of using a volume fixed in space, in which case the fluid flows through...
