Lie Symmetry Group for Unsteady Free Convection Boundary-Layer Flow over a Vertical Surface

The Lie symmetry group transformation method was used to investigate the partial differential equations that model the motion of a natural convective unsteady flow past to a non-isothermal vertical flat surface. The one-parameter Lie group transformation was applied twice consecutively to convert the motion governing equations into a system of ordinary differential equations. The obtained system of ordinary differential equations was solved numerically using the Lobatto IIIA formula (implicit Runge-Kutta method). The effect of the Prandtl number on the temperature and velocity profiles is illustrated graphically.