Perturbation solutions of Poiseuille flows of weakly compressible Newtonian liquids

Both the planar and axisymmetric isothermal Poiseuille flows of weakly compressible Newtonian liquids with constant shear and bulk viscosities are solved up to the second-order. A linear equation of state is assumed and a perturbation analysis of the primary flow variables is performed using compressibility as the perturbation parameter. The effects of compressibility, the bulk viscosity, the aspect ratio, and the Reynolds number on the velocity and pressure fields are studied and comparisons are made with available analytical results.