Heat and momentum transport is investigated theoretically and numerically considering a rectangular enclosure filled with clear fluid or with fully saturated porous medium, under time-periodic horizontal heating. Numerical simulations, of various configurations, indicate that the natural convection activity within the enclosure peaks at several discrete frequencies, with the climax attained at a heating frequency referred to as resonance frequency. A general theory for predicting this resonance frequency is developed from the natural frequency of the Bow circulating inside the enclosure. The resonance frequency can be calculated by solving a system of non linear equations, function of the averaged Rayleigh number, the Prandtl number, the enclosure aspect ratio, the heating amplitude, and the Darcy number for the porous medium case. Theoretical predictions agree well with numerical results. It is shown that the convection intensity within the enclosure increases linearly with heating amplitude for a wide range of parameters. Moreover, the flow response to pulsating heat is continuously enhanced as the system becomes more permeable. Time evolution graphs, phase-plane portraits, and streamlines highlight several distinct phases of the periodic heating process.