Natural convection in nonhomogeneous heat-generating media: Comparison of continuum and porous-continuum models

The present work investigates the appropriateness of using a porous-continuum (PC) based model for simulating the flow and heat transfer within a fluid-filled enclosure containing a matrix of 16 evenly distributed, heat-generating solid blocks. This configuration aims at mimicking the pool storage of radioactive nuclear fuel elements. Results from the continuum (C) model, obtained by solving the transport equations within each (fluid and solid) constituent, are compared to results from the PC model, obtained by using volume-averaged, general transport equations. Streamline and isotherm distributions identify nuances particular to each model. An average Nusselt number along each surface of the enclosure indicates a large discrepancy between the two models, particularly along the top and bottom surfaces. Although much easier to implement and numerically more efficient, the PC model should be avoided when the Rayleigh number is low (Ra <= 10(5)) and the porosity is high (phi <= 0.5), and when the Rayleigh number is high (Ra >= 10(6)) and the porosity is low (phi < 0.5). Moreover, the PC model is inappropriate when the Rayleigh number and the porosity are high (e.g., for Ra = 10(6) and phi >= 0.9, and for Ra = 10(7) and phi >= 0.8) for failing to capture the unsteady regime observed when the more elaborated C model is used.