Theoretical investigation of steady isothermal slip flow in a curved microchannel with a rectangular cross-section and constant radii of wall curvature

The paper presents results of an investigation of the slip flow in a curved microchannel with a rectangular cross-section. Solutions of the problem were obtained analytically using the Fourier method and the method of the eigenfunction decomposition demonstrating thus the applicability of two different analytical approaches to the solution of the fluid flow problems in microchannels. In addition, a numerical approach based on the Lattice Boltzmann method (LBM) was employed. The velocity profiles in the microchannel were obtained with the help of the infinite series solutions validated against the numerical simulations. The solution yields the relations, which enable estimating the hydraulic resistance coefficient and the initial length of the developing flow in the microchannel as the functions of the Knudsen number and the flow curvature parameter.