A numerical and experimental study is performed to analyze the steady-state natural convection fluid flow and heat transfer in a vertical rectangular enclosure that is partially filled with a vertical layer of a fluid-saturated porous medium. The flow in the porous layer is modeled utilizing the Brinkman–Forchheimer–extended Darcy equations. The numerical model is verified by conducting a number of experiments, with spherical glass beads as the porous medium and water and glycerin as the fluids, in rectangular test cells. The agreement between the flow visualization results and temperature measurements and the numerical model is, in general, good. It is found that the amount of fluid penetrating from the fluid region into the porous layer depends strongly on the Darcy (Da) and Rayleigh (Ra) numbers. For a relatively low product of Ra × Da, the flow takes place primarily in the fluid layer, and heat transfer in the porous layer is by conduction only. On other hand, fluid penetrating into a relatively highly permeable porous layer has a significant impact on the natural convection flow patterns in the entire enclosure.

A numerical and experimental study is reported of natural convection in a vertical rectangular fluid enclosure that is partially filled with a fluid-saturated porous medium. Velocities, stresses, temperatures, and heat fluxes are assumed to be continuous across the fluid/porous-medium interface, and the conservation equations for the fluid and the porous regions are combined into a single set of equations for numerical solution. Thermocouples as well as a Mach-Zehnder interferometer are used to measure temperature distributions and infer fluid flow patterns within the fluid and the porous medium. For various test cells, porous-layer configurations and fluid-solid combinations, the model predictions show excellent agreement with the experimental measurements. It is found that the intensity of natural convection is always much stronger in the fluid regions, while the amount of fluid penetrating into the porous medium increases with increasing Darcy and Rayleigh numbers. The degree of penetration of fluid into the porous medium depends strongly on the porous-layer geometry and is less for a horizontal porous layer occupying the lower half of the test cell. If penetration takes place, the flow patterns in the fluid regions are significantly altered and the streamlines show cusps at the fluid/porous-medium interfaces. For a high effective-thermal-conductivity porous medium, natural convection in the medium is suppressed, while the isotherms bend sharply at the fluid/porous-medium interface.

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A numerical study of n o n -J I i a n natuml convection in a vertieal enclosure f l e d with a porous medium is performed. The flow is modeled using the Brinkman-Forchheimerextended Darcy equations. The governing equations are solved with the SIMPLER a l p rirhm and good agreement with previously reported numerical and experimental results is found. An order of magnitude analysis and the numerical results demonshute the impor tance of m n -J I i a n effects. For high M y numbers (Da > lo-'), both extensions are of the same order of magnitude and must be used simultaneously. I n oddirion, Forchheimer's extension must be included for Pr s 1.0 and all J I y numbers. FEnaly, Nusselt number comlclrions an presented for three dijjcrent mnges of the DMy number covering wide mnges of the governing pornmeters.

An analysis of multidimensional melting is performed which takes account of natural convection induced by temperature differences in the liquid melt. Consideration is given to the melt region created by a heated vertical tube embedded in a solid which is at its fusion temperature. Solutions were obtained by an implicit finite-difference scheme tailored to take account of the movement of the liquid-solid interface as melting progresses. The results differed decisively from those corresponding to a conventional pure-conduction model of the melting problem. The calculated heat transfer rate at the tube wall decreased at early times and attained a minimum, then increased and achieved a maximum, and subsequently decreased. This is in contrast to the pure conduction solution whereby the heat transfer rate decreases monotonically with time. The thickness of the melt region was found to vary along the length of the tube, with the greatest thickness near the top. This contrasts with the uniform thickness predicted by the conduction solution. These findings indicate that natural convection effects, although unaccounted for in most phase change analyses, are of importance and have to be considered.