Theoretical Analysis of Natural Convection in an Enclosure Filled with Disconnected Conducting Square Solid Blocks

Abstract

Two different approaches have been implemented to interpret the existing data in Merrikh and Lage (2005a, in: Pop, Ingham, Transport Phenomena in Porous Media, Elsevier, Oxford) pertinent to the pore-scale simulation of natural convection in a laterally heated square enclosure filled with a fluid bathing discrete, disconnected and conducting solid blocks. Mathematical analysis of the problem based on the least squares method leads us to a Nu-Ra correlation with the solid-to-fluid thermal conductivity ratio and the porous medium permeability as the controlling parameters. In this study, while the porosity is fixed, the permeability is varied by changing either the block size or the number of blocks. Hence, three independent variables N, Ra, and κ being the number of blocks, Rayleigh number, and the conductivity ratio between the solid and the fluid, respectively, affect the overall heat transfer process. Based on a simplified thermal resistance approach, an alternative correlation is proposed to predict the Nusselt number as a function of the aforementioned parameters. Detailed analysis of the results and the expected errors are presented.

Eulerian–Lagrangian modeling of solid particle behavior in a square cavity with several pairs of heaters and coolers inside

“…Using the least squares method to curve-fit numerical simulation results, similar to Hooman and Merrikh [35], an estimate for Nu tot as a function of Rayleigh number (10 4 ≤ Ra ≤ 10 7 ) and number of the coolers (1 ≤ N ≤ 3) is given by:…”

Eulerian–Lagrangian analysis of solid particle distribution in an internally heated and cooled air-filled cavity

“…Using the least squares method to curve-fit numerical simulation results, similar to Hooman and Merrikh [34], an estimate for Nu tot as a function of Rayleigh number (10 4 6 Ra 6 10 7 ) and number of the HACs (1 6 N 6 3) can be found:…”

Interaction Effects Between Surface Radiation and Double-Diffusive Turbulent Natural Convection in an Enclosed Cavity Filled With Solid Obstacles

“…Typical examples in this category are the works by Das and Reddy [2006], Desrayaud and Lauriat [2001], Laaroussi and Lauriat [2008] and Yoon et al [2010], all of which are limited to steady state two dimensional laminar natural convection flow of Rayleigh number ranging from 10⁵ to 10⁸. Das and Reddy [2006] and Yoon et al [2010] have reported the fluid flow and heat transfer in a differentially heated rectangular cavity containing just one disconnected solid product, and de Lemos [2005a and2005b] and Hooman and Merrikh [2010] investigated the cavity filled with several. The findings from these research works show that when a limited number of solid products are involved, the fluid flow is predominantly confined between the vertical walls and the first column of the objects.…”