Numerical solutions for convective boundary layer flow over a solid sphere of newtonion and non-newtonion fluids - Hamzeh Taha, Salman Alkasasbeh (2015)
In this thesis, the mathematical modelling for the six main problems on convection boundary layer flows over a solid sphere has been considered. The first two problems on the effect of radiation on magnetohydrodynamic for steady free convection boundary layer flows in a viscous and micropolar fluid have been investigated. Further, the other four problems were mixed convection boundary layer flows in a viscous, micropolar, nanofluid and a porous medium filled with a nanofluid, respectively. All these problems focused on the solid sphere with convective boundary conditions in which the heat is supplied through a bounding surface of finite thickness and finite heat capacity. In order to solve these problems, the dimensional equations that governed the fluid flow and heat transfer were transformed into dimensionless equations by using appropriate dimensionless variables. Stream functions were introduced, yielding a function representing velocities. Similarity variables were used to deduce the dimensionless governing equations into a system of nonlinear partial differential equations. This system was solved numerically by using the numerical scheme, namely as Keller-box method. Numerical solutions were obtained for the local heat transfer coefficient, the local wall temperature, the local Nusselt number and the local skin friction coefficient, as well as the velocity, temperature and angular velocity profiles. The features of the fluid flow and heat transfer characteristics for different values of the Prandtl number Pr, magnetic parameter, radiation parameter, micropolar parameter, nanoparticle volume fraction, mixed convection parameter conjugate parameter and coordinate running along the surface of the sphere x, were analyzed and discussed. In conclusion, when the radiation parameter increased, the values of the temperature, velocity and skin friction coefficient decreased while the heat transfer coefficient increased. Next, as magnetic parameter increased the temperature increased but the velocity, skin friction coefficient and heat transfer coefficient decreased. Furthermore, the conjugate parameter increased the values of the local heat transfer coefficient and thus, the local skin friction coefficient increased. Additionally, the mixed convection parameter increased the values of the local heat transfer coefficient and hence the local skin friction coefficient also increased. On the other hand, the copper nanoparticles have the highest local heat transfer coefficient compared to aluminum oxide and titanium dioxide nanoparticles. Moreover, the copper nanoparticles also have the highest the local skin friction coefficient, followed by titanium dioxide and aluminum oxide nanoparticles.