Introduction

In the study of transport phenomena in moving fluids, the fundamental laws of motion (conservation of mass and Newton's second law) and energy (first law of thermodynamics) are applied to an elemental fluid. Two approaches are possible:

1. a particle approach or

2. a continuum approach.

In the particle approach, the fluid is assumed to consist of particles (molecules, atoms, etc.) and the laws are applied to study particle motion. Fluid motion is then described by the statistically averaged motion of a group of particles. For most applications arising in engineering and the environment, however, this approach is too cumbersome because the significant dimensions of the flow are considerably bigger than the mean-free-path length between molecules. In the continuum approach, therefore, statistical averaging is assumed to have been already performed and the fundamental laws are applied to portions of fluid (or control volumes) that contain a large number of particles. The information lost in averaging must however be recovered. This is done by invoking some further auxiliary laws and by empirical specifications of transport properties such as viscosity µ, thermal conductivity k, and mass diffusivity D. The transport properties are typically determined from experiments. Notionally, the continuum approach is very attractive because one can now speak of temperature, pressure, or velocity at a point and relate them to what is measured by most practical instruments.