An analysis has been made of the fluid flow and heat transfer in a vertically oriented cylindrical enclosure in whose lower and upper walls there are small apertures through which fluid passes into and out of the enclosure. The throughflow stream induces a recirculating flow in the enclosure. Furthermore, natural convection motions are induced in the enclosure owing to the temperature difference between the entering stream and the enclosure walls. The strengths of the forced and natural convection flows are respectively characterized by the Reynolds and Rayleigh numbers, and the latter may be either positive or negative depending on whether or not the wall temperature Tw exceeds the entering fluid temperature T0. When the throughflow stream is vertically upward, positive-Rayleigh-number natural convection (i.e. Tw > T0) opposes the throughflow-driven recirculation and reduces the heat transfer in the range of small and intermediate Rayleigh numbers. At high Rayleigh numbers, the throughflow stream is overpowered by the natural convection, with resulting high values of heat transfer. For negative Rayleigh numbers (i.e. Tw < T0), the heat transfer is little different from that for zero Rayleigh number.