Unsteady free convection from elliptic cylinders at large Grashof numbers

This paper solves the problem of unsteady free convection from an inclined elliptic cylinder both numerically and analytically. An analytical solution valid for small times and large Grashof numbers is derived and compared with numerical solutions to the governing Navier-Stokes and energy equations. The equations are expressed in terms of a streamfunction and vorticity and are solved subject to no-slip and constant heat flux on the surface together with quiescent far-field and initial conditions. Comparisons between the analytical and numerical solutions are made as well as with experiments. Satisfactory agreement is found in all cases.