Momentum transfer in laminar flow

Using the negative sign convention for stress components, Newton s law of viscosity can be written as 

In equation 1.68, pvx is the fluid s momentum per unit volume. The quantity pjp, denoted by v, is known as the kinematic viscosity. In SI units v has the units m2/s. 

Heat conduction is described by Fourier s law and diffusion by Fick s first law  

Equation 1.70 shows that the molar diffusional flux of component A in the y-direction is proportional to the concentration gradient of that component. The constant of proportionality is the molecular diffusivity 2. Similarly, equation 1.69 shows that the heat flux is proportional to the gradient of the quantity pCpT, which represents the. concentration of thermal energy. The constant of proportionality klpCp, which is often denoted by a, is the thermal diffusivity and this, like 2, has the units m2/s. 

By analogy, equation 1.68 shows that a shear stress component can be interpreted as a flux of momentum because it is proportional to the gradient of the concentration of momentum. In particular, ryx is the flux in the y-direction of the fluid s x-component of momentum. Furthermore, the kinematic viscosity v can be interpreted as the diffusivity of momentum of the fluid. 

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