Starting from the solution presented by Bertoli [1] of a convective and radiant heat transfer model in the pneumatic particle transport, to lumped parameters in the fluid phase and distributed in the solid phase, this article shows that several different analytical solutions for heat transfer problems can be recovered using exclusively the limit operations. The attained limiting solutions are compared with expressions in the literature. For the purpose of a generalization the method's details are presented. The length scales involved in the phenomenon are considered. (C) 2012 Elsevier B.V. All rights reserved.