The "field synergy principle", a theory to approach best convection result proposed by Guo, Tao et al., has been developing since the end of last century. Besides the principle itself, there have been a lot of studies about the field synergy including computational approaches and experimental means to demonstrate and apply this principle. However, an opposite research direction: "non-synergy" - how can we obtain worst convection result - is also worth researching for the theory and practice. Until now detailed studies have hardly been published in the open literatures. In this paper, a basic theoretical non-synergy research is presented, some algebraically explicit analytical exact solutions for the governing partial differential equation set of two-dimensional laminar incompressible full field non-synergy are derived using the extraordinary methods promoted by the authors, for example, the method of separating variables with the addition and other hybrid method. The obtained solutions include the conditions with the heat source, the mass flow source or no any sources. The physical feature of various solutions are discussed and explained by the means of figures. Besides theoretical meaning, the solutions can be benchmark solutions to develop the computational heat transfer. (C) 2009 Elsevier Ltd. All rights reserved.