Free and mixed convective boundary layer flow of a viscoelastic fluid past a horizontal circular cylinser

Abstract

The study o f viscoelastic fluid has become increasingly important in the last few years. This is mainly due to its many applications in petroleum drilling, manufacturing o f food and paper, and many other similar activities. In this thesis, the steady free and mixed convective boundary layer flow of a viscoelastic fluid past a horizontal circular cylinder has been studied separately subject to their own constant surface temperature boundary conditions. For the problem of m ixed convection, the study also considered the problem that subjected to constant heat flux boundary conditions. The constitutive equations of viscoelastic fluids usually generate a higher-order derivative term in the momentum equation than equations of Newtonian fluid. Thus, there are insufficient boundary conditions to solve the problems of viscoelastic fluid completely. Therefore, the augmentation o f an extra boundary condition is needed at infinity (far from the wall). In each case, the governing boundary layer equations are first transformed into a non-dimensional form, and then into a set of non similar boundary layer equations which are solved numerically using an efficient im plicit finite-difference method known as K eller-box scheme. Numerical result presented include velocity profiles, temperature profiles, heat transfer characteristics, namely the local heat transfer, local skin friction coefficient and local wall temperature distribution for a w ide range of material paramater K (viscoelastic parameter), prandtl number Pr, and m ixed convection parameter X. In each problem, it is found that velocity distributions decrease when the value of viscoelastic parameter, K increases, whereas the opposite behaviour is observed for the temperature distribution. It is worth mentioning that the results obtained in viscoelastics fluids when the parameter K = 0 (Newtonian fluids) are in excellent agreement with those obtained in viscous fluids (Newtonian fluids).