Mixed convection flow of viscous and second grade fluids due to non–coaxial rotation

Abstract

Unsteady flow of viscous and second grade fluids in non-coaxial rotation past a vertical oscillating disk have been studied by a number of researchers due to wide applications in boundary layer control, food processing, mixer machines and cooling turbine blades. Therefore, in this research, heat and mass transfer of viscous and second grade fluids were studied. The effect of magnetohydrodynamics (MHD) flow through a porous medium was considered. The main purpose of this study was to obtain the exact solutions for four problems of non-coaxial rotating flow. Two problems were studied for viscous fluid, whereas another two problems were studied for second grade fluid. All problems were considered in mixed convection flow and without magnetic and porosity effects. Appropriate non-dimensional variables were used to simplify the governing equations into non-dimensional equations along with initial and boundary conditions. Through this non-dimensional process, the non-dimensional parameters such as Grashof number, modified Grashof number, Prandtl number, Schmidt number, velocity of oscillation, magnetic, porosity and second grade fluid were obtained. The exact solutions for velocity, temperature and concentration expressions were obtained by using Laplace transform technique. From these corresponding expressions, the skin friction, Nusselt number and Sherwood number were calculated. The solutions were plotted graphically to discuss the influence of non-dimensional parameters in velocity, temperature and concentration profiles. Results show that, velocity profile with magnetic effect is lower compared to velocity without magnetic effect, whereas the velocity with heat and mass transfer phenomena is higher than just a heat transfer. It is also observed that velocity of second grade fluid solutions is always lower compared to the velocity of viscous fluid. All the obtained results are compared with published results and found to be in good agreement, validating the obtained solutions. The exact solutions obtained in this thesis provide an interesting and complete benchmark to verify numerical schemes for solving different complex flow situations.