A numerical study is presented for natural convection in a two-dimensional, partially-divided, rectangular enclosure in which two side walls were maintained at uniform heat flux condition and the top and bottom walls were insulated. The modified Rayleigh number ranging from 104 to 108, the opening ratios of 0, 14, 18 and 12 and the conductivity ratios 0.02, 1 and 50 were investigated for an enclosure aspect ratio (length/height) of 2, partition ratio of 12 and Prandtl number of 7 (for water). Results show that the hot fluid flowed to the other side of the enclosure mainly through the bottom of the partition when there was no opening in the partition, and a weak circulation zone was present in the upper and left quadrant. With an opening in the partition, most of the fluid flowed to the other side through the opening and the circulation zone in the upper and left quadrant was reduced in size or disappeared. The effect of partition conductivity on the heat transfer rate was found rather small and could be neglected. Correlation of the average Nusselt number in terms of the modified Rayleigh number and the opening ratio was obtained and discussed. Results also show that an unopened partial obstruction would reduce the heat transfer rate by 12–44% depending on the modified Rayleigh number.