传递1.1.ppt

§ NEWTON’S LAW OF VISCOSITY  (MOLECULAR TRANSPORT OF MOMENTUM)
In Fig. -1 we show a pair of large parallel plates, each one with area A, separated by a distanceγ. In the space between them is a fluid—either a gas or a liquid. This system is initially at rest, but at time t = 0 the lower plate is set in motion in the positive x direction at a constant velocity V.

Fig. -1
The buildup to the steady, laminar velocity profile for a fluid contained between two plates. The flow is called "laminar" because the adjacent layers of fluid ("laminae") slide past one another in an orderly fashion.
§ NEWTON’S LAW OF VISCOSITY

As time proceeds, the fluid gains momentum, and ultimately the linear steady-state velocity profile shown in the figure is established. We require that the flow be laminar (“laminar” flow is the orderly type of flow that one usually observes when syrup is poured, in contrast to “turbulent” flow, which is the irregular, chaotic flow one sees in a high-speed mixer ).
§ NEWTON’S LAW OF VISCOSITY

When the final state of steady motion has been attained, a constant force F is required to maintain the motion of the lower plate. Common sense suggests that this force may be expressed as follows:
(-1)
That is, the force should be proportional to the area and to the velocity, and inversely proportional to the distance between the plates. The constant of proportionality μis a property of the fluid, defined to be the viscosity.
§ NEWTON’S LAW OF VISCOSITY

We now switch to the notation that will be used throughout the book. First we replace F/A by the symbol τyx, which is the force in the x direction on a unit area perpendicular to the y direction. It is understood that this is the force exerted by the fluid of lesser y on the fluid of greater y. Furthermore, we repl