The steady laminar flow and heat transfer characteristics of a continuously moving vertical sheet of extruded material are studied close to and far downstream from the extrusion slot. Uniform or non-uniform suction/injection is allowed at the surface. The velocity and temperature variations, obtained by a finite-volume method, are used to map out the entire forced, mixed and natural convection regimes. The effects of the Prandtl number (Pr), the buoyancy force parameter (B) and the suction/injection parameter (D) on the friction and heat transfer coefficients are investigated. Comparisons of results with local-similarity method and finite-difference solutions of the boundary layer equations and with exact analytic solutions for asymptotic suction flows show an excellent agreement. The region close to the extrusion slot is characterized as a diffusion dominated region in which Nu(x)Re(x)(-1/2) drops sharply with increasing Richardson number (Ri(x)). This is followed by a forced-convection dominated region in which Nu(x)Re(x)(-1/2) levels off with increasing Ri(x) until the buoyancy effect sets in. A mixed convection region where increasing buoyancy effect enhances the heat transfer rate follows. Finally, this region is followed downstream by a natural-convection dominated region in which Nu(x)Re(x)(-1/2) approaches asymptotically the pure natural convection results. For the case of uniform suction and far downstream from the slot, the boundary layer thickness becomes constant and the heat transfer rate approaches a constant asymptotic suction value independent of the heat convection mode. Critical values of Ri(x) to distinguish the various convection regimes are determined for different Pr, B and D. (C) 2003 Elsevier Ltd. All rights reserved.