Approximations for Steady Unidirectional Slip Flows in Elliptic Microchannels

Abstract

Consider steady flows in a channel whose cross section Ω is an ellipse, flows with the Navier slip boundary condition. Denote the volume flow rate by Q. We apply to elliptic cross section a recent simple approximation, a rigorous lower bound R on Q, requiring, along with the channel's area and perimeter, the calculation of just the torsional rigidity and two other domain functionals. This avoids the need for solving the partial differential equation repeatedly for differing values of the slip parameter.