Mathematical modelling of convective flow over a horizontal circular cylinder with convective boundary conditions in viscous, micropolar and nanofluid - Norhafizah, Md Sarif (2018)
Fluid flow and heat transfer play a significant factor in industrial processes, manufacturing and engineering applications. Therefore, a model is needed to enhance the process of fluid flow and heat transfer, as the final products are heavily reliant upon the kinematics of the flow and the simultaneous heating or cooling. However, the mathematical description of fluid flow and heat transfer specifically in geometry of horizontal circular cylinder are quite difficult to solve due to the nonlinearity existence and coupled equations. Indeed, obtaining an analytical solution requires additional effort and time meanwhile to setup an experiment is costly. In such a case, numerical methods provide means to solve the problem. Therefore, the governing equation of fluid flow and heat transfer together with the boundary conditions are solved numerically. Normally when modelling convection flow, many researchers applied constant wall temperature or constant heat flux in the boundary conditions. Nevertheless, these types of boundary conditions appear insufficient to adequately describe the heating process for some cases. Another type of boundary condition; where convection heats the bottom surface of the cylinder are applied in this study. This type of heating process is called convective boundary condition. Motivated by this newly type of boundary condition, the numerical scheme derived in this research is anticipated to provide a theoretical reference to other analytical solution or for future experimental work. Five different problems of fluid flow and heat transfer have been considered by incorporating convective boundary conditions as thermal heating. Accordingly, these mathematical models are then derived for steady laminar forced, free, and mixed convection boundary layer flows over a horizontal circular cylinder immersed in three types of fluid namely viscous, micropolar fluid and nanofluid. The governing parabolic partial differential equations describing the flow are transformed using non-similar transformation, which is then solved numerically using the unconditionally stable implicit finite difference scheme known as the Keller-box method. The numerical codes in the form of computer programmes are developed using MATLAB software. The numerical results obtained consists of velocity, temperature, nanoparticle volume fraction profiles, skin friction and heat transfer for various parameters of physical conditions such as convective, mixed convection, Lewis number, porosity parameters, as well as Prandtl number. It was observed that in all considered problems, the profiles of velocity and temperature profiles increase for increased values of convective boundary conditions. In the case of nanofluids, the values of nanoparticle volume fraction profile increases with with the increment on the values of convective boundary condition. Correspondingly, as the value of convective parameter increases, the skin friction coefficient increase as well except for nanofluid where the convective parameter decreased in both cases; Tiwari and Das, and Buongiorno. However for heat transfer coefficient and Nusselt number, it was observed that the effects of convective parameter has increased significantly. In conclusion, by applying the convective boundary condition over a horizontal circular cylinder, it is found that the trend of the solutions obtained for the convective boundary condition case is similar to the constant wall temperature case, especially when convective parameter γ →∞.