The periodic unsteady natural convection flow and heat transfer in a square enclosure containing a concentric circular cylinder is numerically studied. The temperature of the inner circular cylinder fluctuates periodically with time at higher averaged value while the temperature of the enclosure keeps lower constant, and the natural convection is driven by the temperature difference. The two-dimensional natural convection is simulated with high accuracy temporal spectral method and local radial basis functions method. The Rayleigh number is studied in the range 10(3) <= Ra <= 10(6), the temperature pulsating period ranges from 0.01 to 100 and the temperature pulsating amplitudes are a = 0.5, 1.0 and 1.5. Numerical results reveal that the fluid flow and heat transfer is strongly dependent on the pulsating temperature of inner cylinder. Comparing with the steady state natural convection, the heat transfer is enhanced generally for the time-periodic unsteady natural convection, and the local maximum heat transfer rate is observed for Ra = 10(5) and 10(6). Moreover, the phenomenon of backward heat transfer is discussed quantitatively. Also, the influence of pulsating temperature on the unsteady fluid flow and heat transfer are discussed and analyzed. (C) 2014 Elsevier Ltd. All rights reserved.