1 Introduction

The transport of mass, momentum and energy through a fluid are the consequences of molecular motion and molecular interaction. At the macroscopic level, associated with the transport of each dynamic variable is a transport coefficient or property, denoted by X, such that the flux, J, of each variable is proportional to the gradient of a thermodynamic state variable such as concentration or temperature. This notion leads to the simple phenomenological laws such as those of Fick, Newton and Fourier for mass, momentum or energy transport, respectively,

Here, Y is the appropriate state variable conjugate to the flux J and X, and depends on the thermodynamic state of the system. These linear, phenomenological laws are fundamental to all processes involving the transfer of mass, momentum or energy but, in many practical circumstances encountered in industry, the fundamental transport mechanisms arise in parallel with other means of transport such as advection or natural convection. In those circumstances, the overall transport process is far from simple and linear. However, the description of such complex processes is often rendered tractable by the use of transfer equations, which are expressed in the form of linear laws such as

Here, the transport coefficient, C, is not simply a function of the thermodynamic state of the system but may depend on the geometric configuration of the system and the properties of surfaces for example. We are concerned here with the transport properties, X