Time dependent flow problem induced by a rotating cone

Abstract

The motion of a rigid body which takes place in such a way that all of its particles move in circles about an axis with a common angular velocity is called rotational flow.The concept ofrotational flows over a rotating coneis extensively used in numerous industrial and manufacturing applications such as in design of turbines and turbo machines, in meteorology, in estimating the flight path of rotating wheels, in rotating heat exchanger, in stabilized missiles and in the modeling of many geophysical vortices. No doubt, the thermal buoyancy force arising due to cooling or heating of a rotating surface may changeexpressively the flow and thermal fields and thus the heat transfer behavior in the manufacturing process. In several practical applications, the order of magnitudes of buoyancy and viscous forces are similar for moderate flow velocities and large surface temperature differences and convective heat transfer process is thus called as mixed convection. The buoyancy forces due to temperature and concentration differences are noteworthy in mixed convection thermal and concentration diffusions. In fact the buoyancy forces causing a pressure gradient in the boundary layer that modify the velocity, temperature and concentration distributions and so the rate of heat and mass transfer between the surface and fluid. Indeed, mixed convection flows over cone shaped bodies have a marvelous role in various engineering applications and many heat transfer problems such as cooling of electronic systems, solar collectors, nuclear reactors,chemical processing equipment, and lubricating grooves. Other areas of applications are in crystal growing, materials processing such as float glass production, galvanizing, metal coating, drying and casting technologies and food processing.The extensive literature on mixed convective rotating flows along heat and mass transfer shows that the studies confined only for steady boundary layer flows. However, in many practical situations, the flow can be unsteady due to the time dependent free stream velocity or the curvature of the body or the surface mass transfer or even possibly due all these effects. Only a limited attention has been focused to this kind of study. Therefore, the present work is an effort to inspect this less focus area of research. Mostly, the fluids in industrial processes are non-Newtonian. Food mixing and chyme movement in the intestine, polymer solutions, paint, shampoos, cosmetic products body fluids, pasta, ice cream, ice, mud etc are relevant examples.As the features of non-Newtonian fluids are not revealed by a single fluid model, therefore several fluid models are defined and deliberatedby