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Research Papers: Porous Media

# Transient Double-Diffusive Convection of Water Around $4°C$ in a Porous Cavity

[+] Author and Article Information
M. Eswaramurthi

UGC DRS Centre for Fluid Dynamics, Bharathiar University, Coimbatore-641 046, India

P. Kandaswamy

UGC DRS Centre for Fluid Dynamics, Bharathiar University, Coimbatore-641 046, Indiapgkswamy@yahoo.co.in

J. Heat Transfer 131(5), 052601 (Mar 17, 2009) (7 pages) doi:10.1115/1.3000608 History: Received November 06, 2007; Revised September 13, 2008; Published March 17, 2009

## Abstract

The buoyancy-driven transient double-diffusive convection in a square cavity filled with water-saturated porous medium is studied numerically. While the right and left side wall temperatures vary linearly from $θa$ to $θo$ and $θo$ to $θb$, respectively, with height, the top and bottom walls of the cavity are thermally insulated. The species concentration levels at the right and left walls are $c1$ and $c2$, respectively, with $c1>c2$. The Brinkman–Forchheimer extended Darcy model is considered to investigate the average heat and mass transfer rates and to study the effects of maximum density, the Grashof number, the Schmidt number, porosity, and the Darcy number on buoyancy-induced flow and heat transfer. The finite volume method with power law scheme for convection and diffusion terms is used to discretize the governing equations for momentum, energy, and concentration, which are solved by Gauss–Seidel and successive over-relaxation methods. The heat and mass transfer in the steady-state are discussed for various physical conditions. For the first time in the literature, the study of transition from stationary to steady-state shows the existence of an overshooting between the two cells and in the average Nusselt number. The results obtained in the steady-state regime are presented in the form of streamlines, isotherms, and isoconcentration lines for various values of Grashof number, Schmidt number, porosity and Darcy number, and midheight velocity profiles. It is found that the effect of maximum density is to slow down the natural convection and reduce the average heat transfer and species diffusion. The strength of convection and heat transfer rate becomes weak due to more flow restriction in the porous medium for small porosity.

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## Figures

Figure 4

(a) Velocity vector, isotherms, and isoconcentrations for Gr1=22,582, ϵ=0.4, Sc=50, and Da=0.001 in the steady-state regime; (b) velocity vector, isotherms, and isoconcentrations for Gr1=50,811, ϵ=0.4, Sc=50, and Da=0.001 in the steady-state regime; (c) velocity vector, isotherms, and isoconcentrations for Gr1=53,634, ϵ=0.4, Sc=50, and Da=0.001 in the steady-state regime; and (d) velocity vector, isotherms, and isoconcentrations for Gr1=64,925, ϵ=0.4, Sc=50, and Da=0.001 in the steady-state regime

Figure 3

Time history of the average Nusselt and Sherwood numbers for various values of Grashof number with ϵ=0.4, Da=0.001, and Sc=50 at Y=(1/2)

Figure 2

(a) Velocity vector, isotherms, and isoconcentrations at τ=100 for Gr1=53,634, ϵ=0.4, Sc=50, and Da=0.001 in the transient state regime; (b) velocity vector, isotherms, and isoconcentrations at τ=1000 for Gr1=53,634, ϵ=0.4, Sc=50, and Da=0.001 in the transient state regime; (c) velocity vector, isotherms, and isoconcentrations at τ=10,000 for Gr1=53,634, ϵ=0.4, Sc=50, and Da=0.001 in the transient state regime; (d) velocity vector, isotherms, and isoconcentrations at τ=25,000 for Gr1=53,634, ϵ=0.4, Sc=50, and Da=0.001 in the transient state regime; (e) velocity vector, isotherms, and isoconcentrations at τ=100,000 for Gr1=53,634, ϵ=0.4, Sc=50, and Da=0.001 in the transient state regime; and, (f) velocity vector, isotherms, and isoconcentrations at τ=126,900 for Gr1=53,634, ϵ=0.4, Sc=50, and Da=0.001 in the transient state regime

Figure 1

Average Nusselt number and Sherwood number for different grid systems with Gr1=59,280, Da=0.001, ϵ=0.4, Sc=50, and Sc=720 in the steady-state regime

Figure 9

The average Nusselt and Sherwood numbers for various higher values of Schmidt number and Grashof number with ϵ=0.4 and Da=0.001 in the steady-state regime

Figure 8

The average Nusselt and Sherwood numbers for various low values of Schmidt number and Grashof number with ϵ=0.4 and Da=0.001 in the steady-state regime

Figure 7

The average Nusselt and Sherwood numbers for various values of Darcy number and Grashof number with ϵ=0.4 and Sc=50 in the steady-state regime

Figure 6

The average Nusselt and Sherwood numbers for various values of porosity and Grashof number with Da=0.001 and Sc=50 in the steady-state regime

Figure 5

Time history of the average Nusselt and Sherwood numbers for various values of Grashof number with ϵ=0.4, Da=0.001, and Sc=50

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