Transient free convection of a second-grade fluid flowing in a vertical cylinder

摘要

The intention of the present article is to examine the transient effect on the free convection of the second-grade fluid flowing in a vertical cylinder. We have found the analytical solution of the derived governing partial differential equations in nondimensional form corresponding to the velocity as well as the tem-perature fields by applying the Laplace transforma-tion method in terms of the Bessel function of the first kind. To obtain the impacts of the appropriate parameters related to the given equations, such as the second-grade fluid parameter and the Prandtl num-ber, the numerical values of the velocity are discussed and displayed in graphs. Furthermore, the mass flow rate and the skin friction at the inner surface of the cylinder are given in a tabular form. The influence of the second-grade fluid parameter is to decelerate the velocity as well as the mass flow rate and to enhance the steady-state time.