Numerical Analysis of Couple Stress Fluid Past an Infinite Vertical Cylinder

Abstract

Numerical analysis is performed to study the transient free convective boundary layer flow of a couple stress fluid past an infinite vertical cylinder, in the absence of body forces and body couples. A set of nondimensional governing equations, namely, the continuity, momentum and energy equations are derived, which are unsteady, non-linear and coupled. The couple stress fluid flow model introduces the length dependent effect based on the material constant and dynamic viscosity. Also, it introduces the biharmonic operator in the Navier-Stokes equations, which is not present in the case of Newtonian fluids. As there are no analytical or direct numerical method available to solve these unsteady, non-linear and coupled equations, they are solved using the CFD techniques. An unconditionally stable Crank-Nicolson type of implicit finite difference scheme is employed to obtain the discretized forms of the governing equations. The discretized equations are solved using the Thomas and pentadiagonal algorithm. The results concerning the velocity and temperature profiles across the boundary layer are illustrated graphically and discussed for different values of Prandtl number. Transient effects of velocity and temperature are analyzed and compared with those of the Newtonian fluids. The heat transfer characteristics are analyzed and compared with those of Newtonian fluids with the help of average skin-friction and Nusselt number and are shown graphically. It is observed that the deviation of transient velocity and temperature profiles from the hot wall of a couple stress fluid is more in comparison with that of Newtonian fluids.