Periodic Natural Convection Inside a Fluid Saturated Porous Medium Made of Disconnected Solid Obstacles: A Continuum Approach

Abstract

Results of a numerical study considering the periodic natural convection inside a fluid saturated porous medium are presented. The porous medium is obtained by placing four, large and uniformly distributed solid obstacles of regular (square) shape inside the enclosure, a structure that hinders the option of seeking a porous-continuum modeling approach. The periodic heating is achieved by imposing a time-periodic and spatially uniform high temperature condition at one of the walls of the enclosure, while the other wall is maintained at a constant, uniform and low temperature; the horizontal surfaces are set as adiabatic. Heat transfer results are obtained then by following a continuum modeling approach, and reported on a parametric form with the Prandtl number fixed equal to 7, and the Rayleigh number inside the enclosure varying from 103 to 107. The boundary layer interference phenomenon, observed for the case of constant horizontal heating, is also observed in the case of periodic heating. The visualization of the natural convection process via isotherms and streamlines, together with the periodic (time-varying) Nusselt number, allows the identification of a singular dynamic behavior, including the storage of thermal energy inside the enclosure.