PurposeThe purpose of this paper is to investigate the impact of time-periodic thermal boundary conditions on natural convection flow in a vertical micro-annulus.Design/methodology/approachAnalytical solution in terms of Bessel’s function and modified Bessel’s function of order 0 and 1 is obtained for velocity, temperature, Nusselt number, skin friction and mass flow rate.FindingsIt is established that the role of Knudsen number and fluid–wall interaction parameter is to decrease fluid temperature, velocity, Nusselt number and skin friction.Research limitations/implicationsNo laboratory practical or experiment was conducted.Practical implicationsCooling device in electronic panels, card and micro-chips is frequently cooled by natural convection.Originality/valueIn view of the amount of works done on natural convection in microchannel, it becomes interesting to investigate the effect that time-periodic heating has on natural convection flow in a vertical micro-annulus. The purpose of this paper is to examine the impact of time-periodic thermal boundary conditions on natural convection flow in a vertical micro-annulus.