In this paper, some exact solutions for 2-D convective heat transfer between two parallel penetrable walls were derived and analyzed based on field synergy theory. They are valuable to further develop the field synergy principle and understand how to improve or to weaken field synergy in practice. In addition, these solutions can be used as benchmarks to verify numerical solutions and to develop numerical schemes, grid generation methods and so forth. All solutions given in this paper can be proven easily by substituting them into the governing equations. (C) 2008 Elsevier Ltd. All rights reserved.