Boundary Layer Flow of Micropolar Fluid by an Exponentially Stretching Surface

Abstract

In the contemporary period, new substances are incorporated in the industrial processes which cannot be characterized as Newtonian fluids such as colloids, surfactant solution, liquid crystals, etc. Consequentially, several non-Newtonian fluids have been put forward. Among these occur certain rheologically complex fluids, that is fluids consisting of particles with microstructure, which have conspicuous utilization in chemical, pharmaceutical, engineering and food industries. The discrete particles of the aforementioned fluids may vary in shape, may have the ability to shrink or expand and above all they might rotate on their own not depending upon the movement and rotation of the fluid. So, the flow properties of these fluids cannot be adequately described by Navier-Stokes equations alone, due to their diversified structure. Hence it was the need of the hour to formulate a theory considering deformation, geometry, local structure and intrinsic motion of the individual particles. Therefore, Eringen [1-2] propounded the hypothesis of micropolar fluids, which gives an accurate model for such fluids by including the micro-rotational momentum equation besides the classical momentum equation. This new equation is based on the principle of conservation of angular momentum by introducing a new vector field (the micro-rotation) also involving spin vector and micro-inertia tensor besides the velocity vector giving the total angular velocity of rotating particles. Micropolar fluids physically characterize fluids that comprise rigid, arbitrarily aligned spherical particles dispersed within a viscid medium exhibiting intrinsic rotational micro-motions. Due to its diverse applications in various industries such as pharmaceutical, food, chemical and 2 technological processes, the micropolar fluid phenomenon is more significant and realistic. Applications of micropolar fluids include colloidal solutions, complex fluids containing additives like crystals, fluids with fibrous structures, muddy fluids, particle suspensions, exotic lubricants as well as there exist some biological fluids which model micropolar fluid such as animal blood. Several analytical and experimental attempts have been conducted to examine the flow behavior of micropolar nanofluid under various circumstances, geometries and attributes. After the initial manifestation of the concept of micropolar fluid, a detailed overview of the phenomenon was given by Lukaszewicz [3] and Eringen [4] in their books. Chaim [5] discussed solution for micropolar fluid flow past a stretching surface. Then the heat transfer analysis of micropolar fluid by a stretching sheet was performed numerically by Hassanien et al. [6]. The influence of uniform suction/blowing through the stretching surface on the boundary layer flow of micropolar fluid was probed by Kelson et al.