Natural Convection Heat and Mass Transfer in the Vertical Cylindrical Porous Channel Under the Effects of Time-Periodic Boundary Condition

Abstract Heat and mass transfer are investigated numerically with steady-state laminar natural convection through a vertical cylindrical enclosure filled with a liquid-saturated porous medium. The vertical wall is under a constant magnetic field and various durations of periodic heating boundary condition; the top and bottom surfaces are kept at a constant cold temperature. Continuity, momentum, and energy equations are transformed to dimensionless equations. The finite difference approach with the line successive over-relaxation (LSOR) method is used to obtain the computational results. This study covers the heat transfer, the temperature distribution, and the velocity field in the domain under the variation of different parameters. The code used is validated by modifying it to analyze the Nusselt number in the existing experimental literature of Izadpanah et al. (1998, “Experimental and Theoretical Studies of Convective Heat Transfer in a Cylindrical Porous Medium,” Int. J. Heat Fluid Flow, 19(6), pp. 629–635). This work shows that Nusselt number decreases (with varying gradient) as the aspect ratio increases, and that 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 receives more heat) and is inversely proportional with Rayleigh number. Increasing the Rayleigh number causes increased convective velocity, which affects the position of the hot region, and causes a decrease in the temperature field. Increasing the aspect ratio results in a warm stream at the center of the cylinder, and when the time period of the heating increases, the circulation becomes faster and the intensity of the temperature contour layers decreases. In this work, a correlation for Nu as a function of the mentioned parameters is developed.