The effect of eccentricity on heat transfer in upward flow in a vertical, open-ended, annular channel with a diameter ratio of 0.61, an aspect ratio of 18:1, and both internal surfaces heated uniformly has been investigated experimentally. Results have been reported for eccentricities ranging from the concentric case to the near-contact case and three inlet bulk Reynolds numbers, equal approximately to 1500, 2800, and 5700. This work complements our recently reported experimental results on natural convection in the same facility. The present results are deemed to be largely in the mixed convection regime with some overlap with the forced convection regime and likely to include cases with laminar, transitional, and turbulent flows in at least a part of the test section. Small eccentricity had an essentially negligible effect on the overall heat transfer rate, but high eccentricity reduced the average heat transfer rate by up to 60%. High eccentricity also resulted in wall temperatures in the narrow gap region that were much higher than those in the open channel. The concentric-case Nusselt number was higher than the Dittus–Boelter prediction, whereas the highly eccentric-case Nusselt number was significantly lower than that.