Heat and mass transfer is investigated numerically with steady-state laminar natural convection through a vertical enclosure cylinder filled with saturated liquid porous media. The vertical wall is under a constant magnetic field and different time periodic heating boundary condition, and the top and bottom surfaces are cold. Continuity, momentum and energy equations (governing equations used in this model) are transformed to dimensionless equations. The finite difference approach with the Line Successive Over-Relaxation (LSOR) method is used to obtain all the computational results. This study covers the heat transfer, the temperature distribution and the flow stream in the domain under the variation of different parameters presented by low range of Rayleigh number (10=Ra=103), aspect ratio of the cylinder (0.5, 1, 2 & 5), temperature amplitude (0.0, 0.2, 0.4, 0.6, 0.8) and the time period (0.005, 0.01, 0.03, 0.05, 0.1). The code used is validated by modifying it to analyze the Nusselt number in the existing experimental literature of Izadpanah et. al. This work shows that Nusselt number decreases (with different gradient) with increasing the aspect ratio when the aspect ratio and it increases as the Rayleigh number increases. The centerline temperature has a proportional relationship with the heating amplitude and the heating period (as the system receive more heat) and is inversely proportional with Rayleigh number. In this work, a correlation expressing a relation between the Nu as a function of the mentioned parameters is developed.