4.0 - Transient Momentum Transfer and Relaxation

Abstract

Newton's law of viscosity relates the shear stress to the shear rate with the constant of proportionality––the viscosity of the fluid––which offers resistance to flow. The damped wave momentum transfer and relaxation equation can arise from the accumulation term in the theory of kinetic theory of gases and derivation of physical properties of monatomic gases from molecular properties. From a molecular view, the viscosity can be derived and the momentum transport mechanism can be illustrated. Euler equation includes the damped wave transport and relaxation effects and neglects the viscous effects. The mass times acceleration on the fluid is equal to the sum of the pressure forces, gravity forces, and viscous forces in the Navier–Stokes equation. To this two more terms are added. One is because of the damped wave transport and relaxation and provides an “acceleration force” that becomes important when the accumulation of momentum term becomes higher than an exponential rise in time. The other term is because of the variation of pressure with time. These two terms are on account of the relaxation phenomena in the fluid. This later analysis provides well bounded results and removes the anomalies due to an infinite speed of momentum propagation.