Lie group analysis of flow and heat transfer over a stretching rotating disk

Abstract

The present paper discusses steady three dimensional flow and heat transfer of viscous fluid on a rotating disk stretching in radial direction. Using Lie group theory symmetries of the governing equations are calculated. Imposing restrictions from the boundary conditions it is shown that the similarity in the problem can be achieved for two types of radially stretching velocities namely; linear and power-law. Linear stretching has already been discussed in the literature; however power-law stretching is discussed here for the first time. Using new similarity transformations, the governing partial differential are transformed into a system of ordinary differential equations which are later treated both analytically and numerically. Exact analytical solutions are found for the case of pure stretching and the large stretching parameter case, for power-law stretching index n=3. Numerical solutions are obtained for combined effects of stretching and rotation for all values of n using Keller box method. Comparison of numerical solution with the corresponding analytical solution (for n=3) shows an excellent agreement. The quantities of physical interest, such as azimuthal and radial skin friction and also Nusselt number are presented and discussed physically.