Perturbation solutions for a micropolar fluid flow in a semi-infinite expanding or contracting pipe with large injection or suction through porous wall

Abstract

We investigate an unsteady incompressible laminar micropolar flow in a semi-infinite porous pipe with large injection or suction through a deforming pipe wall. Using suitable similarity transformations, the governing partial differential are transformed into a coupled nonlinear singular boundary value problem. For large injection, the asymptotic solutions are constructed using the Lighthill method, which eliminates singularity of solution in the high order derivative. For large suction, a series expansion matching method is used. Analytical solutions are validated against the numerical solutions obtained by Bvp4c.

Keywords

• expansion ratio
• micropolar fluid
• lighthill method
• singular perturbation method
• bvp4c
• 5.10.hj
• 47.15.cb
• 47.50.-d