Laminar mixed convection in the entrance region of an inclined tube with longitudinal external fins (corresponding to the basic element of a flat plate solar collector) has been studied numerically, The system is subjected to a uniform solar flux and convective losses on its top surfaced it is insulated on its bottom surface, The results show that the secondary flow induced by buoyancy has a very significant effect on the axial flow and on the isotherms in both the fluid and the solid, Furthermore, due to circumferential conduction in the tube wall, more heat reaches the fluid from the bottom half of the fluid-solid interface than from its top half. The circumferential ly average Nusselt number shows the usual decrease with axial distance from the tube inlet towards a constant value in the fully developed region. This constant value is considerably higher for the finned tube than the corresponding value for a bare tube. Both these values are significantly higher than one for fully developed forced convection. A parametric study shows the effects of the fin and tube materials, of the solar flux and the fin's width on the thermal performance of the collector.