Application of HAM to the von Kármán Swirling Flow with Heat Transfer Over a Rough Rotating Disk

In this study, analytical solution to the classical von Kármán swirling viscous flow with heat transfer is obtained. Using similarity transformations the governing partial differential equations are reduced to a set of coupled, nonlinear ordinary differential equations and the conventional no-slip boundary conditions are replaced by partial slip boundary conditions due to the roughness of the disk. An effective analytical method for fully coupled and highly nonlinear differential equations, called Homotopy Analysis Method (HAM) is adopted and the solutions are obtained in the form of an convergent Taylor series. The effect of azimuthally anisotropic roughness, radially anisotropic roughness and isotropic roughness on the velocity and temperature profiles are studied in detail. Result shows that HAM is very efficient and easy to implement.