**1. Introduction**

The developments are carried out in the field of fluid dynamics which was initiated by Euler [1] by proving his famous equations of fluid flow for ideal (inviscid) fluids. Fluid dynamics is a subset of the science that looks at the materials in motion. Hydrodynamics deals with the fluids which are in motion. Fluid dynamics comes under science of fluid mechanics along with the other subcategories as fluid statics, which corresponds to fluids at rest, while fluid dynamics includes fluids in motion. Fluid is defined as a matter in a gas or liquid state. Fluid dynamics is governed by the regulations of preservation of mass, energy and linear momentum. These laws state that the total amount in a closed model remains unchangeable and the energy and mass cannot be formed or demolished. They can deform but will not disappear. Another governing law is the continuum hypothesis which defines that they are uninterrupted and their characteristics fluctuate all over. The history of fluid dynamics can be found in Rouse and Ince [2] and Tokaty [3].

#### **1.1 Micropolar fluid**

The subject of micro-polar fluids attained higher degree by many researchers because when the fluid is with the suspended particles we cannot analyze the properties of fluid flow by regular Newtonian fluid characteristics. Generally this fluid is defined as non-Newtonian comprising of small firm cylindrical matters, polymer liquids, liquefied suspensions, animal blood and such related components. The existence of dust or smoke especially, gas are characterized as micro-polar

fluids in fluid dynamics. Eringen [4, 5] had taken the initiation in describing the subject of micropolar fluids. In his theory he considered the local impacts emerging from the micro-structure and the inherent movement of the fluid elements. Peddieson and McNitt [6], Ariman et al. [7] addressed many investigations and applications of micropolar fluid mechanics, which are also described in the works of Lukaszewicz [8] and Eringen [9]. A.J. Chamkha et al. [10] analyzed the wholly established free convection of micropolar fluid in a upright passage.
