Purpose - The purpose of this paper is to focus on the numerical analysis of transient free convection heat transfer in partially porous cylindrical domains. The authors analyze the dependence of velocity and temperature fields on the geometry, by analyzing transient flow behavior for different values of cavity aspect ratio and radii ratio; both inner and outer radius are assumed variable in order to not change the difference ro -ri . Moreover, several Darcy numbers have been considered. Design/methodology/approach - A dual time-stepping procedure based on the transient artificial compressibility version of the characteristic-based split algorithm has been adopted in order to solve the transient equations of the generalized model for heat and fluid flow through porous media. The present model has been validated against experimental data available in the scientific literature for two different problems, steady-state free convection in a porous annulus and transient natural convection in a porous cylinder, showing an excellent agreement. Findings - For vertically divided half porous cavities, with Rayleigh numbers equal to 3.4 ? 106 for the 4:1 cavity and 3.4 ? 105 for the 8:1 cavity, the numerical results show that transient oscillations tend to disappear in presence of cylindrical geometry, differently from what happens for rectangular one. The magnitude of this phenomenon increases with radii ratio; the porous layer also affects the stability of velocity and temperature fields, as oscillations tend to decrease in presence of a porous matrix with lower value of the Darcy number. Research limitations/implications - A proper analysis of partially porous annular cavities is fundamental for the correct estimation of Nusselt numbers, as the formulas provided for rectangular domains are not able to describe these problems. Practical implications - The proposed model represents a useful tool for the study of transient natural convection problems in porous and partially porous cylindrical and annular cavities, typical of many engineering applications. Moreover, a fully explicit scheme reduces the computational costs and ensures flexibility. Originality/value - This is the first time that a fully explicit finite element scheme is employed for the solution of transient natural convection in partially porous tall annular cavities

The numerical modeling of natural convection in partially porous annuli is a topic of rising interest, due to its practical applications for the provisional analyses of several engineering applications such as geothermal down-hole heat exchangers, chemical reactors, etc. Though a large number of papers focused on the modeling of this phenomenon under steady-state conditions, only few works consider its transient thermal evolution and no works are available referred to partially porous annular cavities. However, most of the real technical applications operate in dynamic mode, for this reason, this paper focuses on the transient numerical analysis of heat transfer in partially porous annular enclosures, where natural convection occurs. A fully explicit version of the CBS algorithm is employed here to solve the generalized porous medium model which describes both the sub-domains of the cavity using only one equations set; a dual time stepping technique is employed for transient analyses. Several cases have been analyzed, by changing the cavity aspect ratio and thermo-physical parameters of the fluid. Several results have been presented by changing both porous medium's properties and geometrical characteristics of the domain. The obtained results highlight that both the properties and the position of porous layer, inserted into the computational domain, strongly influence the thermal behavior of the cavity.

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This paper provides a sensitivity analysis on the influence of one porous layer insert on the transient behavior of natural convection in a tall annular enclosure in presence of large source terms. The porous medium which partially fills the cavity is characterized by a low value of the Darcy number, typical of insulating materials and metallic foams, often employed in heat exchangers and other engineering applications. A stabilized, fully explicit version of the Compressibility Based Scheme is here employed and validated against experimental data available in the scientific literature for steady and unsteady convection in vertical cylindrical enclosures. Several analyses are presented here by changing both the geometrical features of the cavity and the properties of the porous domain. The results of these analyses demonstrate that not only the thermo-physical properties of the porous medium but also the position and the thickness of the porous layer strongly affect the transient behavior of the convective phenomena occurring in the cavity.

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