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RESEARCH PAPERS

# Resonance of Natural Convection Inside a Bidisperse Porous Medium Enclosure

[+] Author Affiliations
Arunn Narasimhan1

Department of Mechanical Engineering, Heat Transfer and Thermal Power Laboratory, Indian Institute of Technology, Madras, Chennai 600036, India, arunn@iitm.ac.in

B. V. K. Reddy

Department of Mechanical Engineering, Heat Transfer and Thermal Power Laboratory, Indian Institute of Technology, Madras, Chennai 600036, India, bvkreddy680@gmail.com

1

Corresponding author.

J. Heat Transfer 133(4), 042601 (Jan 06, 2011) (9 pages) doi:10.1115/1.4001316 History: Received September 22, 2009; Revised January 27, 2010; Published January 06, 2011; Online January 06, 2011

## Abstract

An enclosure filled with blocks made of a microscale porous medium, separated by macrosize pores, can be treated as a bidisperse porous medium (BDPM) enclosure. This study investigates natural convection resonance inside such a BDPM enclosure subjected to time-periodic heat flux at a side wall, with the opposite wall kept isothermal while the top and bottom walls are adiabatic. The BDPM enclosure is made from uniformly spaced, disconnected, square, porous blocks that form the microporous medium saturated with a fluid of $Pr=0.7$. For Rayleigh numbers, $Ra=108$ and $107$, the pulsating wall heat flux is varied over a frequency range of $0.01≤f≤0.1$, and the bidispersion effect is induced by varying both the internal (micropore) Darcy number $(DaI)$ and external (macropore) Darcy number $DaE$. Natural convection resonance is observed in the BDPM enclosure and the resonance heating frequency $fr$ increases with Ra, $DaI$, and $DaE$. However, $fr$ of the BDPM enclosure is always less than that of the corresponding clear fluid enclosure limit (at $DaI→∞$). Predictions of $fr$ using a modified scale analysis incorporating BDPM effects agree well with that arrived by numerical methods.

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## Figures

Figure 1

Schematic of enclosure with 4×4 porous block array (a) geometry, (b) mesh, and (c) pulsating heat flux

Figure 2

The response of instantaneous average Nuc, Num, and θ¯h for a BDPM enclosure at DaI→∞ (the clear fluid limit) and Ra=108 with different heat input frequencies: (a) 0.01, (b) 0.029, and (c) 0.04

Figure 3

The response of instantaneous average Nuc, Num, and θ¯h for a BDPM enclosure at N2=4×4, DaI=10−3, and Ra=108 with different heat input frequencies: (a) 0.01, (b) 0.02, and (c) 0.04

Figure 4

The response of instantaneous average Nuc, Num, and θ¯h for a BDPM enclosure at N2=4×4, DaI→0 (monodisperse limit), and Ra=108 with different heat input frequencies: (a) 0.01, (b) 0.02, and (c) 0.04

Figure 5

Instantaneous volume averaged velocity variation with average hot wall temperature at Ra=108 and f=fr for enclosure with (a) clear fluid, (b) porous blocks (4×4, DaI=10−3), and (c) solid blocks (4×4)

Figure 6

Instantaneous streamlines and isotherms for a BDPM enclosure for DaI→∞ (clear fluid limit) at Ra=108 and resonance frequency fr=0.029

Figure 7

Instantaneous streamlines and isotherms for a BDPM enclosure at N2=4×4, DaI=10−3, ϕE=0.64, and ϕI=0.5 at Ra=108 and resonance frequency fr=0.02

Figure 8

Instantaneous streamlines and isotherms for a BDPM enclosure at N2=4×4, DaI→0 (monodisperse limit), ϕE=0.64 at Ra=108, and resonance frequency fr=0.01

Figure 9

BDPM enclosure Num,max variation with pulsating heat input frequency in the steady oscillatory state for several DaI values at N2=4×4, ϕE=0.64, and Pr=0.7: (a) Ra=108 and (b) Ra=107

Figure 10

Effect of bidispersion (DaI) on the resonance (heating) frequency (fr) for Pr=0.7, N2=4×4, ϕE=0.64, and ϕI=0.5. Comparison of predictions from scale analysis and numerical method.

Figure 11

Effect of bidispersion (by varying ϕE) on the BDPM enclosure Num,max in the steady oscillatory state at N2=4×4, Ra=108, and Pr=0.7

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