The Prandtl number effect on the optimum heating frequency of an enclosure filled with fluid or with a saturated porous medium

Abstract

This is a fundamental study of the Prandtl number effect on the natural convection flow within an enclosure subjected to intermittent heating from the side. Previous studies, considering an enclosure filled with fluid or with a fluid saturated porous medium having a Prandtl number equal to seven, have demonstrated the existence of convection resonance when the heat pulsating frequency approaches the natural flow frequency of the system. The natural frequency of the flow can be well estimated using a general theory valid for fluid systems and for fully saturated porous medium systems. The results presented here test the validity of the theory for estimating the resonance frequency of systems with different Prandtl number. Numerical simulations confirm the existence of a preferred (resonance) heat pulsating frequency that compares well with the theoretical estimates. They also indicate that natural convection resonance is smoothed (damped), for the same Rayleigh number and the same Darcy number (in the case of a porous medium), when the Prandtl number increases or decreases from the value Pr ∼1. Analysis of the theoretical model, in line with the numerical results, indicates that the resonance frequency of a fluid or a porous medium system varies with Pr12.