Exact solutions of unsteady free convection flow of Casson, nano, and micropolar fluids over an oscillating vertical plate

Abstract

Fluid-mechanics is an ancient science that is incredibly alive today. Therefore, the modern technologies require a deeper understanding of the behaviour of real fluids. Based on the relationship between shear stress and the rate of strain, fluids can be categorized as Newtonian fluids and non-Newtonian fluids. Various non- Newtonian fluid models have been used to investigate the behaviour of fluid motion, because of their universal nature. Solution corresponding to Newtonian and non- Newtonian fluids problem have received considerable attention due to their numerous applications in industries. This thesis is devoted to study the unsteady free convection flow of Newtonian fluid (nanofluids) and non-Newtonian fluids (Casson and micropolar fluids) over an oscillating vertical plate. Specifically, free convection flows of Casson fluids and micropolar fluids were studied with and without magnetohydrodynamic and porosity effects. Whereas studied in nanofluids also considered ramped wall temperature. Laplace transform was used to solve the partial differential equations governing the motion. The expressions of the obtained solutions for velocity, temperature and concentration were presented in simple forms. Skin friction, Nusselt number and Sherwood number were also calculated. The analytical results were plotted and discussed for magnetic, porosity, radiation, nanoparticle volume friction, Casson and microrotation parameters as well as Prandtl, Grashof and modified Grashof numbers. For Casson fluid, it was observed that velocity decreases with increasing values of Casson parameter as Casson fluid exhibits yield stress. In case of nanofluids, it was found that fluid velocity was greater for isothermal temperature as compared to ramped wall temperature of the plate. However, for micropolar fluid, microrotations increases near the plate and decreases far away from the plate due to an increase in viscosity parameter. The results showed that for long time interval, the oscillations have similar amplitudes and phase shift that persists for all times. For verification, the obtained solutions were recovered as special cases. The existing solutions in the literature were also reduced to their limiting cases of the present results. The exact solutions obtained in this thesis serve as a benchmark to verify approximate methods, whether asymptotic, experimental or numerical.