Series solutions of unsteady free convection flow in the stagnation-point region of a three-dimensional body

The unsteady three-dimensional free convection flow in the stagnation-point region on a general curved isothermal surface placed in an ambient fluid is studied. By introducing new similarity transformations, the momentum and energy balance equations are reduced to a set of three fully coupled nonlinear partial differential equations. These equations are solved analytically for some various values of the ratio of the two principal radii of curvature. The accurate series solutions are obtained which are uniformly valid for all dimensionless time in the whole spatial region 0⩽η<∞.