Convection in the annulus between two horizontal coaxial cylinders resulting from gravity modulation in a microgravity environment is investigated for the first time. The three-dimensional transient equations of fluid motion and heat transfer are solved to study the unsteady flow structures in a large-gap annulus. The gravity fluctuations are shown to induce recirculating flows that reverse direction of rotation in response to the gravitational reversals. Except for a short period of time following flow reversal, at low modulation frequencies the centers of rotation of these flows are below and above the horizontal angular plane when the acceleration acts in the upward and downward directions, respectively, whereas at high frequencies they are above and below this plane. The effects of gravity modulation on development of secondary flows that arise in narrow- and moderate-gap annuli owing to thermal instability are also investigated. It is found that supercritical transverse rolls repeatedly form, dissipate, and re-form in the upper and lower regions of a narrow-gap annulus as a result of the fluctuating gravity field. At the same frequency, the supercritical rolls in a moderate-gap annulus are much slower to develop between flow reversals. The results show that gravity modulation has a stabilizing effect on the secondary flows compared to the case of a constant gravity force, and this effect diminishes with reduction in either frequency or annulus radius ratio R. The effects of frequency on heat transfer in large-, moderate-, and narrow-gap annuli are also studied. It is found that the time-averaged Nusselt number approaches that of pure conduction at high frequencies and increases toward that for terrestrial natural convection as frequency is reduced. As R is decreased, the increase in time-averaged Nusselt number brought about by reducing frequency becomes a smaller percentage of the value for terrestrial natural convection. The results for large-, moderate-, and narrow-gap annuli subjected to gravity modulation under microgravity are compared to results for steady natural convection under terrestrial conditions to clarify differences in flow behavior. The present work provides the first description of convection in a cylindrical annulus under microgravity, and practical information on the influence of gravity fluctuations on heat transfer in a space environment. (c) 2006 Elsevier Ltd. All rights reserved.