Exact solutions for some types of newtonian and non-newtonian fluids
It is well known that many manufacturing processes in industry nowadays involve Newtonian and non-Newtonian fluids. In nature, water and air are examples of Newtonian fluid. Whereas apple sauce, drilling muds, ketchup sauce, shampoo, blood and many others belongs to the class of non-Newtonian fluids...
| Summary: | It is well known that many manufacturing processes in industry nowadays involve Newtonian and non-Newtonian fluids. In nature, water and air are examples of Newtonian fluid. Whereas apple sauce, drilling muds, ketchup sauce, shampoo, blood and many others belongs to the class of non-Newtonian fluids. Due to the variety of such fluids it is very difficult to suggest a single constitutive equation which can describe the rheological behavior of all these fluids. Therefore, several models of Newtonian and non-Newtonian fluids have been proposed. In this thesis, the unsteady flows of Casson and micropolar fluids are considered over an oscillating vertical plate whereas magnetohydrodynamic flow of a nanofluid over an accelerated vertical plate and linear stretching sheet are studied. All these problems are modelled using the fundamental equations of fluid dynamics. The proposed model of each problem depends on a system of governing equations along with imposed initial and boundary conditions. Appropriate non-dimensional variables are introduced to reduce the governing equations along with imposed conditions into dimensionless forms. Exact solutions of each problem are obtained by using the Laplace transform method. Moreover, the classical solutions corresponding to the Stokes first problem and Newtonian fluid are also obtained as a special case. The exact solutions of velocity, temperature and concentration are plotted graphically and discussed for different parameters. Results show that velocity decreases significantly with an increasing of Casson parameter but it increases when Grashof number and Newtonian heating parameter are increased. Further, in the case of micropolar fluid, angular velocity increases near the plate and decreases away from the plate due to an increase in viscosity parameter. It is found that temperature increases due to suspension of different nanoparticles as well as carbon nanotubes water based nanofluids. The exact solutions obtained in the present study are very important not only because they are solutions of some fundamental flows, but also due to the fact that they serve as accuracy standards for approximate methods, whether numerical, asymptotic or experimental. |
|---|