This study extends the earlier work on fully developed convection with viscous dissipation in the fluid phase and in the presence of a porous medium, by including the thermally developing effects. The governing two-equation model is solved by finding the particular and homogeneous solutions. The characteristics of temperature profiles along the axial direction when solid conduction is dominant, are distinctive in the two-equation model, unlike the local thermal equilibrium model. The local heat transfer coefficients depend strongly on the relative thermal resistance to fluid and solid conduction and to a lesser extent on Brinkman number and porous medium shape factor. (C) 2011 Elsevier Ltd. All rights reserved.