Flow of power-law fluid over a stretching surface: A Lie group analysis

This paper investigates the boundary layer flow of power-law fluid over a permeable stretching surface. The use of Lie group analysis reveals all possible similarity transformations of the problem. The application of infinitesimal generator on the generalized surface stretching conditions leads to two possible surface conditions which leads to the possibility of two types of stretching velocities namely; the power-law and exponential stretching. The power-law stretching has already been discussed in the literature, however exponential stretching is investigated here for the first time. Interestingly, an exact analytical solution of the non-linear similarity equation for exponential stretching is developed for shear thinning fluid with power-law index n=1/2. This solution is further extended to a larger class of shear thinning fluids (n≈1/2) using perturbation method. In addition, the numerical solution for shear thinning fluid is also presented. The two solutions match excellently for shear thinning fluids. Analytical solution for shear thickening fluid is not tractable and the numerical solution is presented for completeness.

► Flow of power-law fluid over exponentially stretching surface is examined 1st time.
► Exact solution is presented for the power-law index n=1/2.
► Results are obtained using numerical as well as analytical method.
► The two solutions for shear thinning fluids match excellently.
► All existing similarity transformations become special case of this paper.