Generalized hydrodynamics and microflows

A mathematical model was developed within the framework of generalized hydrodynamics for the description of flows in microsystems where the Knudsen number is largest and the aspect ratio is not so small. The model was based on a set of empirical generalized hydrodynamic equations, fashioned from the steady-state generalized hydrodynamic equations derived from the boltzmann equation in a manner consistent with the laws of thermodynamics. Unlike the Newtonian law of viscosity and the Fourier law of heat conduction, the equations used for the model were highly nonlinear but thermodynamically consistent. To obtain an analytic formula for the flow rate, which exhibits a knudsen minimum, the differential equation for pressure distribution was also solved.