Natural Convection in Triangular Attics Filled with Porous Medium Heated from Below

Abstract

A finite volume analysis is performed to investigate the effects of uniform heating of the bottom wall on natural convection in an isosceles triangular attic space filled with saturated porous medium. The simulations are carried out over a wide range of parameters of Darcy number Da (10⁻⁶ ≤ Da ≤ 10⁻²), Rayleigh number Ra (10¹ ≤ Ra ≤ 10⁸), and attic angle θ (10° ≤ θ ≤ 45°). Numerical results are presented in terms of stream functions, isotherms, velocity profiles, as well as local and average Nusselt numbers. The flow and heat transfer in the attic space are solely determined by the combined parameter DaRa when Da < 10⁻⁴. The effects of Da and Ra have to be considered separately when Da > 10⁻⁴. When DaRa is smaller than a certain value (∼10), the heat transfer in the attic space is conduction-dominated and a simplified model is proposed to calculate the local and average Nusselt numbers. The analytical solutions agree well with the numerical simulations, especially when the attic angle is small. As DaRa increases, convection becomes relatively important. In this situation, conduction is still dominated near the left corner zone while convection becomes relatively important in the rest zone.

Acknowledgments

This work was supported by China National Funds for Distinguished Young Scientists (grant no. 51025623), and the National Natural Science Foundation of China (no. 50806056 and 11142015).