Abstract
The complete Lie algebra of classical infinitesimal symmetries of the nonlinear diffusion-convection equation in two and three dimensions is presented. Except for some cases involving constant diffusivity, a complete reduction to an ordinary differential equation is not possible. However, closed-form solutions are obtained for special forms of both the 2D and 3D nonlinear diffusion-convection equations, using a symmetry reduction and an additional physical constraint. This extends the small list of closed-form transient solutions already known.