Numerical investigation of power-law non-Newtonian fluid flow in concentric annular geometry using finite difference method with convergence analysis

Through a detailed numerical study, the steady, laminar, incompressible power-law non-Newtonian fluid flow in concentric annular geometry is discussed. A FDM with Picard iterative scheme is used to solve the non-linear momentum equation in cylindrical coordinate under “No Slip” conditions to study the motion of the system. The computational domain is divided into 100 radial nodes, and has a tolerance of 10-6. The flow behaviour index is analysed for 0.6,1.0 and 1.4 corresponding to shear-thinning fluid, Newtonian fluid & shear-thickening fluid respectively. A trend of increasing flow resistance is seen for shear-thickening fluids with the results showing a reduction in the maximum speed from 0.260 m/s to 0.138 m/s as flow behaviour index increases from 0.6 to 1.4. Just as in the previous example, the volumetric flow rate has a nonlinear decrease for an increasing n. The numerical solution of the Newtonian case (n=1) is able to confirm the accuracy of the numerical method proposed, indicating acceptable agreement with the analytical solution of the same. In addition, smooth and stable velocity and shear stress distributions indicate that the numerical scheme is robust. The influence of the rheological characteristics on the characteristics of flow is significant and hence the study clarifies the important role of the rheological parameters during analyzing the non-Newtonian annular flow for engineering applications.