The classical Jeffery-Hamel flow due to a point source or sink in convergent/divergent channels is extended in this paper for the first time in the literature to the case where the stationary channel walls are permitted to stretch or shrink. Such a physical mechanism is characterised by means of a parameter in the wall boundary conditions of the governing nonlinear differential equation. Results show that the classical flow and heat features are considerably altered by the application of sufficient stretching/shrinking of the walls. Stretching of the convergent or divergent channel is found to amplify the velocity profiles with an opposite effect in the case of shrinking resulting in back flow regions. As far as the temperature field is concerned, stretching leads to production of more heat in the flow, however, thermal layer is lowered and cooling is achieved by the presence of channel shrinking, which might have significant technological consequences. (C) 2014 Elsevier Ltd. All rights reserved.