Similarity solutions of boundary layer flows in a channel filled by non-newtonian fluids

Similarity solutions of non-Newtonian fluids are getting much attention to researchers because of their practical importance in the field of science and engineering. Currently, most of researchers focus their work on non-Newtonian fluids over a sheet. However, only a few of them pay their attention towards the geometry of channel due to the complexity of governing equations. Therefore, this study attempts to investigate the numerical solutions of new problems of laminar incompressible Nanofluids, Casson fluids and Micropolar fluids under various fluid flow conditions. Each considered fluid involves porous channel walls, stretching or shrinking walls, and expanding or contracting walls with the influence of various physical parameters. Mathematical formulations such as the law of conservation, momentum or angular momentum, heat and mass transfer are performed on the new problems. After the mathematical
formulation is developed, the governing fluid flow equations of partial differential equations are then transformed into boundary value problems (BVPs) of nonlinear ordinary differential equations (ODEs) by using the suitable similarity transformations. After converting high order BVPs into the equivalent first order system of BVPs, shootlib function in Maple 18 software is employed to obtain the similarity solutions of nonlinear ODEs. The numerical results in this study are compared with the existing solutions in literature for the purpose of validation. The results are found to be in good agreement with the existing solutions. Multiple solutions of some of the problems particularly in porous channel with expanding or contracting walls also exist for the case of strong suction. This study has successfully find the numerical solutions of the
new problems for various fluid flow conditions. The results obtained from this study can serve as a theoretical reference in related fields.