A The Continuum Approximation

The motivation forthis approach, apart from an anticipated simplification ofthe problem, is that, in many applications of applied science or engineering, we are concerned with fluid motions or heat transfer in the vicinity of bodies, such as airfoils, or in confined geometries, such as a tube or pipeline, where the physical dimensions are very much larger than any molecular or intermolecular length scale of the fluid. The desired description of fluid motion is then at this larger, macroscopic level where, for example, an average of the forces of interaction between the fluid and the bounding surface may be needed, but not the instantaneous forces of interaction between this surface and individual molecules of the fluid. 

Once the continuum hypothesis has been adopted, the usual macroscopic laws of classical continuum physics are invoked to provide a mathematical description of fluid motion and/or heat transfer in nonisothermal systems - namely, conservation of mass, conservation of linear and angular momentum (the basic principles of Newtonian mechanics), and conservation of energy (the first law of thermodynamics). Although the second law of thermodynamics does not contribute directly to the derivation of the governing equations, we shall see that it does provide constraints on the allowable forms for the so-called constitutive models that relate the velocity gradients in the fluid to the short-range forces that act across surfaces within the fluid. 

---