Numerical solutions for casson and williamson nanofluids over a stretching sheet - Kho, Yap Bing (2018)
The unique characteristic of non-Newtonian fluids is that they do not obey the Newtonian law of viscosity. With the rheological behaviour properties, the classical Navier Stokes equations are no longer appropriate to define all the non-Newtonian fluids. Non-Newtonian fluids can be defined in several categories like visco-elastic, time-dependent viscosity and non-Newtonian viscosity. Such fluids are oils, ketchup, food paste, paints and colloidal solutions. Non-Newtonian fluids have gained much attraction due to their better performance in industrial and technological applications compared to Newtonian fluids. In this study, there are two types of non-Newtonian fluids, namely, the Casson and Williamson nanofluids, were selected to be investigated. Meanwhile, several types of boundary conditions studied were constant wall temperature, Newtonian heating and slip conditions. Other conditions considered were thermal radiation effect, magnetic field and porosity of the medium. The proposed model for each problem would depend on the system of governing equations subject to the imposed initial and boundary conditions. Then, suitable non-dimensional variables were introduced to reduce the governing equations into the dimensionless form. Next, the numerical solutions of ordinary differential equations were solved using the Shooting method. These solutions must be asymptotic and must meet the imposed initial and boundary conditions. The comparison for viscous case was conducted to verify that the results of the present study would be reliable and accurate. The numerical solutions of velocity, temperature and concentration profiles were plotted graphically and discussed with different parameters. The skin friction coefficient, local Nusselt number and Sherwood number also have been studied and examined. Results showed that the velocity profile had decreased significantly with increase in Casson and Williamson parameters. The wall temperature increased when Casson and Williamson parameters increased. Besides, it is noticed that these parameter must not exceed the critical values respectively; otherwise, the fluid lost its characteristics. The non-Newtonian fluids in the present study were found to have better conductivity in heat transfer compared with base fluids. Also, the Newtonian heating parameter leads increase the wall tempearature in the fluid fow over a stretching sheet. The physical solutions for Newtonian heating parameter were also analysed. The numerical solutions obtained in the present study would be important in the validations of fundamental flow because of the accuracy standards for approximate method, analytical and experimental method.