Transient three-dimensional natural convection in confined porous media

Abstract Experimental investigations of natural convection in a confined porous medium have shown that motion may be two-dimensional or three-dimensional. The mode of the convection is dependent on the physical configuration and the Rayleigh number. This paper deals with the theoretical results obtained from the finite difference solution of the equations describing transient natural convection in porous media. The equations had been made more amenable to a numerical solution by introducing a vector potential, which may be regarded as the three-dimensional counterpart of the stream function. Numerical results indicate that under certain conditions three-dimensional motion would result in significantly higher heat transfer rates across the porous medium than two-dimensional motion at the same Rayleigh number. The convection pattern of the three-dimensional motion is illustrated by isometric projections of isothermal surfaces and streaklines which trace the path of a fluid particle. The linearized equations are solved to provide an estimate of the number of possible convective modes as a function of the Rayleigh number.