M. MUTHTAMILSELVAN

929

0:0,0,01, 1

TC

UVX Y

YX

0,1,1,0, 01UVC TYX

0,0,0,0&1, 01UVC TXY

The dimensionless variables are defined as:

2,

Da

Darcy number, Pr

, Pr andtl number,

Sc D

, Schmidt number,

23

2

hc

T

T

Ra

L

,

Solutal Rayleigh number, 1c

hc

R

, density inversion

parameter, ,

c

T

Ra

NRa

Buoyancy ratio number.

The average Nusselt number and Sherwood number is

11

00

0

d, d

avg avg

YY

TC

NuX ScX

YY

0

3. Method of Solution

The governing equations along with the boundary condi-

tions are solved numerically employing finite volume

method using staggered grid arrangement. The semi-

implicit method for pressure linked equation (SIMPLE)

is used to couple momentum and continuity equations as

given by Patankar [11]. The third order accurate deferred

QUICK scheme of Hayase et al. [12] is employed to

minimize the numerical diffusion for the convective

terms for both the momentum equations and energy

equation. The solution of the discretized momentum and

pressure correction equations is obtained by TDMA

line-by-line method. For complete details and code vali-

dation, the author is referred to the prior publication [10,

13]. The grid independence test is performed using suc-

cessively sized uniform grids, 21 × 21 to 91 × 91. After

grid independence check considering the accuracy and

the computational time, all the computations are per-

formed with a 41 × 41 grid.

4. Results and Discussion

Computations have been carried out for various values of

the Darcy number (Da = 10–4 - 10–1), the thermal

Rayleigh number (RaT = 102 - 105), the buoyancy ratio

number (N = 0.2 - 0.8), the density inversion parameter

(R = 0.1 - 0.3), the Schmidt number (Sc = 5 - 50) and

fixed value of Pr = 11.573 and porosity (ε = 0.4). The

results are presented as streamlines, isotherms and iso-

concentrations. The rate of heat and mass transfer in the

enclosure is measured in terms of the average Nusselt

and Sherwood numbers.

Figure 2 illustrates the streamlines, isotherms and iso-

concentration of the numerical results for various thermal

Rayleigh number. When RaT = 102 the flow is seen to be

very weak as observed from streamlines. Therefore, the

temperature and isoconcentration distributions are simi-

lar to that with stationary fluid and the heat transfer is

due to purely conduction. When RaT = 103, streamline

show the major cells occupied entire cavity and the mi-

nor cells are visible near bottom corners of the cavity.

During conduction dominant mass transfer, the isocon-

centration contours with c = 0.06 occur symmetrically

near the side walls of the cavity. The other isoconcentra-

tion contours with c ≥ 0.13 are smooth curves which

span the entire cavity and they are generally symmetric

with respect to the vertical symmetric line. As thermal

Rayleigh number increases from 104 to 105 streamline

shows that the bottom corner minor cells are reduced its

strength and size. The corresponding temperature con-

tour illustrates the smooth cure bended towards bottom

of the cavity. It should be noted in Figure 2, with in-

creasing RaT from 102 to 104 the minor cells grow its size

and reduced when RaT = 105. It is observed that the con-

duction heat transfer switches to convection heat transfer

with increasing RaT from 102 to 104. Again the conduc-

tion heat transfer dominates when RaT = 105.

Streamline, isotherm and isoconcentration contours

are displayed in Figure 3, for different values of Schmidt

number. The streamline shows the minor cells are occu-

pied top corners of the cavity and it increases its size and

strength when Sc increases. The circulations are greater

near the center and least at the wall due to no slip

boundary conditions. The greater circulation in each half

of the box follows a progressive wrapping around the

centers of rotation and a more pronounced compression

of the isotherms toward the boundary surfaces of the

cavity occurs. Due to greater circulations near the central

core at the top half of the cavity, there are small gradi-

ents in temperature whereas a large stratification zone of

temperature is observed at the vertical symmetry line due

to stagnation of flow.

Figure 4 shows the average Nusselt and Sherwood

numbers for different density inversion parameter with

different Darcy number. Decreasing of Darcy number

decreased the heat and mass transfer rate. In such situa-

tion the heat transfer is dominated by conduction. Figure

5 illustrate that the average Nusselt and Sherwood num-

ber for thermal Rayleigh number Vs density inversion

parameter. Decreasing of thermal Rayleigh number de-

creased the heat and mass transfer rate. Figure 6 shows

the behavior of the average Nusselt and Sherwood num-

ber for different N Vs Sc. It is found that the average

Nusselt and Sherwood number gets minimum in the den-

Copyright © 2011 SciRes. AM