This paper addresses the second Leveque problem with uniform wall heat flux adhering to the original two-dimensional energy conservation equation with variable coefficients in cylindrical coordinates. The semi-analytic procedure to be proposed combines the transversal method of lines (TMOL) with the Frobenius version of the power series method. The hybrid solution that emerges from this combination holds unique features that distinguish it from the traditional solution methods. In principle, due to the presence of a two-point backward formulation, the approximate analytic solution is considered first-order accurate. However, using as guidance the computed local convection coefficient at various transversal lines, it is demonstrated that the approximate analytic TMOL/Frobenius solution is better than first-order accurate. © 2005 Elsevier Ltd. All rights reserved.