Micropolarity Effects on the Bickley-Plane-Laminar-Jet

TL;DR

This paper develops a new similarity solution for steady laminar micropolar fluid jets, transforming PDEs into ODEs, solved numerically, revealing how micropolarity influences flow characteristics and stresses.

Contribution

It introduces a novel similarity transformation applicable to both Newtonian and micropolar fluids, enabling numerical analysis of micropolar jet flows.

Findings

Micropolarity increases microrotation and stresses near the jet.

The similarity transformation simplifies PDEs to ODEs for analysis.

Micropolar effects significantly influence flow and stress distributions.

Abstract

In this study, it was formulated the boundary-value-problem (BVP), comprising partial differential equations (PDEs), of steady flow for plane, laminar jet of a micropolar fluid. A new similarity transformation/solution was derived which is valid not only for the Newtonian fluids but also for the micropolar fluids. Obviously, this transformation will be transformed the PDEs into the ordinary differential equations (ODEs). These ODEs were solved numerically by the finite difference method. The obtained results were compared with existing results [1, 12] for the Newtonian fluids. The comparison was favourable. As the aciculate particles in a micropolar fluid can rotate without translation, the micropolarity effects must have influence on fluid-speed, microrotation, stresses, couple stresses and discharge. This influence was highlighted in the present study. If viscosity coupling parameter K1 (being the measure of micropolarity) increases then microrotation, fluid-flux, stresses and couple stresses intensify in the vicinity of the jet along y-direction. The fluid-flux, , for a fixed value of K1 and for the micropolar as well as Newtonian fluids. In addition, the stress and the couple stress tensors are non-symmetric.