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Research Papers: Natural and Mixed Convection

# Natural Convection Inside a Bidisperse Porous Medium Enclosure

[+] Author and Article Information
Arunn Narasimhan1

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

B. V. K. Reddy

Department of Mechanical Engineering, Heat Transfer and Thermal Power Laboratory, Indian Institute of Technology Madras, Chennai 600036, Indiabvkreddy680@gmail.com

1

Corresponding author.

J. Heat Transfer 132(1), 012502 (Nov 04, 2009) (9 pages) doi:10.1115/1.3192134 History: Received May 16, 2009; Revised June 11, 2009; Published November 04, 2009; Online November 04, 2009

## Abstract

Bidisperse porous medium (BDPM) consists of a macroporous medium whose solid phase is replaced with a microporous medium. This study investigates using numerical simulations, steady natural convection inside a square BDPM enclosure made from uniformly spaced, disconnected square porous blocks that form the microporous medium. The side walls are subjected to differential heating, while the top and bottom ones are kept adiabatic. The bidispersion effect is generated by varying the number of blocks $(N2)$, macropore volume fraction $(ϕE)$, and internal Darcy number $(DaI)$ for several enclosure Rayleigh numbers (Ra). Their effect on the BDPM heat transfer (Nu) is investigated. When Ra is fixed, the Nu increases with an increase in both $DaI$ and $DaE$. At low Ra values, Nu is strongly affected by both $DaI$ and $ϕE$. When $N2$ is fixed, at high Ra values, the porous blocks in the core region have negligible effect on the Nu. A correlation is proposed to evaluate the heat transfer from the BDPM enclosure, Nu, as a function of $Raϕ$, $DaE$, $DaI$, and $N2$. It predicts the numerical results of Nu within ±15% and ±9% in two successive ranges of modified Rayleigh number, $RaϕDaE$.

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## Figures

Figure 1

Schematic of enclosure configuration with 4×4 porous block array (a) Geometry (b) Mesh

Figure 2

Streamlines and isotherms for BDPM enclosure with a 4×4 porous block array at Ra=105, DaE=2.53×10−4, Pr=1, γ=1, ϕE=0.64, and ϕI=0.5, for several DaI values: (a) solid blocks, (b) 10−7, (c) 10−5, and (d) 10−3

Figure 3

Effect of internal Darcy number (DaI) on the local velocity and temperature profiles at y∗=0.4 for 4×4 (DaE=2.53×10−4, Pr=1, γ=1, ϕE=0.64, and ϕI=0.5)

Figure 4

Nu variation with Rayleigh number (Ra) for case 4×4 (at DaE=2.53×10−4, Pr=1, γ=1, ϕE=0.64, and ϕI=0.5)

Figure 5

Effect of external porosity (ϕE) on Nu variation with Rayleigh number for case 4×4 (at DaI=10−4, Pr=1, γ=1, and ϕI=0.5)

Figure 6

Streamlines and isotherms for enclosure with different numbers of blocks (at Ra=107, DaI=10−4, Pr=1, γ=1, ϕE=0.64, and ϕI=0.5): (a) 3×3, DaE=4.495×10−4, (b) 6×6, 1.124×10−4, and (c) 8×8, 6.321×10−5

Figure 7

Effect of number of porous blocks (N2) on the local velocity and temperature profiles at y∗=0.42 (at DaI=10−4, Pr=1, γ=1, ϕE=0.64, and ϕI=0.5)

Figure 8

Nu variation with modified Rayleigh number (Ra×DaE) for all the block cases (at Pr=1, γ=1, ϕE=0.64, and ϕI=0.5)

Figure 9

Nu variation with modified Rayleigh number (Ra×DaE) for all the block cases (at Pr=1, γ=1, ϕE=0.64, and ϕI=0.5)

Figure 10

Parity plot of predicted versus actual values for BDPM Nusselt number (Nu)): (a) 10≤RaϕDaE≤200 and (b) 200<RaϕDaE≤104

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