Modelling Compressible Blood Flow with Slip in a Constricted Rectangular Flow Domain

The abnormal narrowing of blood vessels is known to affect the characterization of blood flow through these constricted regions. Both theoretical and clinical research has suggested that these changes in flow are associated with cardiovascular related diseases. Analytic, numerical, and particle based methods have been employed to solve the Navier-Stokes momentum integral equations associated with compressible, Newtonian fluid flow. In this thesis, the Karman-Pohlhausen method is used to transform a system of partial differential equations into a single second-order, non-linear differential equation in terms of the density. Numerical solutions are presented and important flow features, including the role of slip and compressibility, are discussed. The choice to use a symmetric rectangular channel, rather than a cylindrical one, is largely motivated by the opportunity to compare the numerical solutions with experimental data collected from a rectangular microchannel. The numerical results also indicate similar trends in the flow characteristics for the rectangular channel as compared to previous results using cylindrical models.