The study of natural convection involves analysis of surface geometry that is having fluid- saturated porous medium. Various temperature differences are considered between the two isolated walls, while the top wall considered being an adiabatic. CFD tool and mathematical analysis was studied and analyzed to carry out the research. By the help of study, it is analyzed that higher intensity rate of natural convection. The simulation of the various temperatures and initial moisture contents were carried out to determine the effect on the performance of the natural convection. It has been noticed that temperature over the porous medium is uniformly distributed due to conduction, which is little higher in the fluid region. It has been recorded that the high moisture contents at the higher temperature side wall than lower one.

1. IJSRD - International Journal for Scientific Research & Development| Vol. 2, Issue 08, 2014 | ISSN (online): 2321-0613
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An Investigation of effect of Temperature Difference and Initial Moisture
Contents on Natural Convection in Porous Medium
Dipteshkumar R. Patel1
Kapil S. Banker2
Amitkumar V. Patel3
1, 2, 3
Assistant Professor
1,2,3
SVBIT, Vasan, Gandhinagar, Gujarat, India
Abstract— The study of natural convection involves
analysis of surface geometry that is having fluid- saturated
porous medium. Various temperature differences are
considered between the two isolated walls, while the top
wall considered being an adiabatic. CFD tool and
mathematical analysis was studied and analyzed to carry out
the research. By the help of study, it is analyzed that higher
intensity rate of natural convection. The simulation of the
various temperatures and initial moisture contents were
carried out to determine the effect on the performance of the
natural convection. It has been noticed that temperature over
the porous medium is uniformly distributed due to
conduction, which is little higher in the fluid region. It has
been recorded that the high moisture contents at the higher
temperature side wall than lower one.
Keywords: Natural Convection, CFD, Porous Medium
I. INTRODUCTION
Natural convection of heat transfer play an important role
for porous medium. The heat transfer rate significantly
depends on the type of porous medium of material. There
are various area of research, like production, chemical,
environmental, mechanical, petroleum and geological
engineering.
The model with adiabatic top and bottom walls,
while differentially heated side walls. A rectangular
enclosure 5cm in width and 30cm in height. The upper part
of the enclosure is filled with fluid, while the lower part is
filled with porous material. The two dimensional Navier-
Stokes equation governs the fluid medium, while
Brickman’s extension of Darcy’s law is assumed to hold
within the porous region. The 40×40 grid was found to be
sufficiently accurate after carrying out a grid refinement
study. Grid points were closely spaced near the walls and at
the interior between the fluid and porous regions to
accommodate the steep gradients in these regions. Rayleigh
number considered being
5
10 and various Darcy number
used to validate the model.
The properties have been calculated with the help of
Rayleigh Number and the Darcy number, while the Prandtl
number assumed to be 10. The viscous resistance has been
calculated by the help of Darcy number, which is constant
about 788643 at both directions. It varies with different
Darcy number. The density, specific heat, thermal
conductivity and viscosity are calculated to be 1.225 kg/
3
m
, 242 J/kg-K, 0.0242 W/m-K, 0.001 kg/m-s respectively.
The width is calculated by the given Rayleigh number. The
height is assumed to be six times more than the width.
Simulation has been converged in steady state. The
temperature distributions in the bottom region are greatly
influenced by the thermal conduction. On the other hand
convection in the top portion. We have considered 20° (Tc)
temperature at left hand side and 30° (Th) temperature at the
right hand side. It has been seen the convection in the top
region due to the fluid medium.
The Rayleigh and Darcy number considered to be
5
10 and
6
3.5 10
 respectively. The temperature at the
right hand side wall is 30° (Th) and left hand side wall is 20°
(Tc). We need to find physical properties of silicone oil by
the given Prandtl, Rayleigh and Darcy numbers. The viscous
resistance is calculated to be 1777025
-2
m at both
directions by the help of given Darcy number. The density,
specific heat, thermal conductivity of fluid, thermal
conductivity of solid and viscosity are calculated to be 760
kg/
3
m , 1370 J/kg-K, 0.284 W/m-K, 0.512 W/m-K, 0.58
kg/m-s respectively. The physical properties have been
chosen for silicon oil and compare them with the calculated
properties. The operating pressure and operating
temperature are 101325 Pascal and 25° C respectively.
Simulation has been done by the Gambit and Fluent
software packages. 2ddp mode has been considered for the
analysis in the Fluent for the double precision.
II. NUMERICAL FORMULATION
A. Moisture transfer
Moisture transfer is the physical process, which is
ubiquitous in the stored grain. This phenomenon obeys the
conservation laws. It is also called as a source term in the
CFD software packages to simulate the program. It is
normally described as a partial differential equation of the
form,
( )
.( ) .( )a
a a eff w
w
Uw D w S
t

 

    

where  is the quantity of interest in this case is
the humidity of the intergranular air, a is the density of
air,  is the effective diffusion coefficient of  , t is the
time,  is the del operator and S is the source term.
If above equation described in term of symbols
often related with stored grain, we can write as,
( )
.( ) .( )a
a a eff w
w
Uw D w S
t

 

    

As we referred the combined work of Thorpe
(1980, 1982) and Thorpe et al. (1991) that expressed effD is
the effective diffusion coefficient. It is equal to 0.233 vD ,
where vD is the molecular diffusivity of water through air.
The moisture term wS can be expressed as,

2. An Investigation of effect of Temperature Difference and Initial Moisture Contents on Natural Convection in Porous Medium
(IJSRD/Vol. 2/Issue 08/2014/007)
All rights reserved by www.ijsrd.com 29
(1 )w s
W
S
t
 

  

Where, s is the density of grain kernels on dry
basis. The
W
t


can be expressed as,
( )d e
W
k W W
t

  

Where, dk is the drying constant. The work of
O’Callaghanet al. (1971) expressed as,
5094
2000exp( )
273.15
k
T
 

And eW is the moisture content of the outer
surface of the grain kernels, which is expressed as,
1
log( log )e
T c
W r
b a

  
Where, a, b and c are empirical constants and r is
the relative humidity. This is defined as,
sat
p
r
p

In which p is the vapour pressure of the water and
satp is the saturation vapour pressure of free water. Hunter
(1987) expressed the relationship of saturation vapour
pressure of water and temperature:
25
5
6 10 6800
exp( )
( 273.15) 273.25
satp
T T

 
 
0.622
atmwp
p
w


Where, atmp is the atmospheric pressure.
B. Heat transfer
The expression for the heat transfer can be written as a,
Where ac the specific heat of the air is, gc is the grain and
wc is the liquid water. wH is the integral heat of wetting of
the grains, effk is the effective thermal conductivity of the
bulk of grains and hS is the thermal source term. It can be
defined as,
(1 )h s s
W
S h
t
 

  

Where, sh is the heat of sorption of water on the grains.
C. Momentum transfer
The standard momentum transport equation can be defined
by adding source term for the resistance of air flow through
porous media. It can be defined as,
3 3
1 1
( ) 1,2,3
2
a
i ij a ij j
j j
S D U C U u i


 
    
Where, a is the viscosity of the intergranular air
and ju is the component of the velocity in all three
dimensions. The both terms represent resistance, first shows
Darcian resistance and the seconds represents the inertia
resistance. Hunter (1983) expressed the source term in the
form of,
2
i i i
i
dP
S Rv Sv
Dx
   
Where, R and S are constant regardless the
direction of flow. It also assumes that the air flow is
isotropic because of the viscous and inertia resistances. On
the other hand in the work of Hood and Thorpe (1992)
resistance of air flow considered to be tranversevely
orthotropic. They considered resistance of air flow is
constant in any horizontal direction but different in the
vertical direction.
III. RESULT AND DISCUSSION
We have performed simulation with different temperatures
and initial moisture contents to determine the effect of these
factors with the performance of the system, which are
shown below.
Fig. 1: Temperature distributions over fluid and porous layer
with 26ºC to 24 º C temperature differences
Fig. 2: Velocity magnitude over fluid and porous layer with
26ºC to 24 º C temperature differences
Figure 1 shows temperature distributions over fluid
and porous layer with 26ºC to 24 º C temperature
differences. We can see the temperature distribution over the
porous media is linear due to small air flow at the top
region. It is because of the very small temperature
difference. It has been seen that the temperature difference

3. An Investigation of effect of Temperature Difference and Initial Moisture Contents on Natural Convection in Porous Medium
(IJSRD/Vol. 2/Issue 08/2014/007)
All rights reserved by www.ijsrd.com 30
plays an important role in the convection. We can see the
velocity magnitude in the figure 2. It represents high
velocity at the top region on the other hand it is much lower
because of porous medium.
Fig. 3: Temperature distributions over fluid and porous layer
with 28ºC to 22 º C temperature differences
Fig. 4: Velocity magnitude over fluid and porous layer with
28ºC to 22 º C temperature differences
Figure 3, represents temperature distributions over
fluid and porous layer with 28ºC to 22 º C temperature
differences. It has been seen that the convection become
more important with increasing temperature difference. The
temperature distribution over the fluid region is more
nonlinear than the last case. Figure 4 shows the velocity
magnitude, which is very similar with the last case.
Fig. 5: Temperature distributions over fluid and porous
layer with 35ºC to 15 º C temperature differences
Figure 5 shows temperature distributions over fluid
and porous layer with 35ºC to 15 º C temperature
differences. We can see similar relation here what we have
done in the last two cases. Air flow in 35ºC to 15º C
temperatures is much higher that leads temperature
distribution more nonlinear. Figure 6 shows the velocity
magnitude of the system.
Fig. 6: Velocity magnitude over fluid and porous layer with
35ºC to 15 º C temperature differences
Fig. 7: Moisture contains over the fluid and porous layer
with 10% initial moisture contents
Fig. 8: Relative humidity over the fluid and porous layer
with 10% initial moisture contents
Figures 7 and 8 show the moisture contents and the
relative humidity over the fluid and porous regions with
10% of initial moisture contents. We have simulated our
system with the different moisture contents to check the
effect of moisture contents on the performance of system. It
has been recorded that the high moisture contents at the
right hand side wall, while it is very low at the left hand side
wall in the porous medium.
Figures 9 and 10 represent the moisture contents
and relative humidity over the fluid and porous regions with
14% of initial moisture contents. The results are much
similar with the last case. The moisture contents is little
amount of small than the last case. Relative humidity is also
similar with the last case. It is higher at the cold wall than
the hot wall in the porous medium.

4. An Investigation of effect of Temperature Difference and Initial Moisture Contents on Natural Convection in Porous Medium
(IJSRD/Vol. 2/Issue 08/2014/007)
All rights reserved by www.ijsrd.com 31
Fig. 9: Moisture contains over the fluid and porous layer
with 14% initial moisture contents
Fig. 10: Relative humidity over the fluid and porous layer
with 14% initial moisture contents
IV. CONCLUSION
It has been concluded that the flow mostly tend to be move
to the right hand side of the volume over the fluid region. It
is greatly influenced by the high temperature difference. It
reflects temperature distribution more nonlinear. It has been
also noticed that the temperature over the porous medium is
uniformly distributed due to conduction. It is recorded little
higher in the fluid region. It is found that the higher velocity
magnitude at the upper region, while very low velocity
recorded at the bottom region due to porous medium.
Relative humidity is lower over the fluid medium. While in
the porous media it is higher at the cold wall and very lower
at the hot wall.
REFERENCES
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[3] Neal, G and Nader, W, 1974, “Practical significance
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[4] Nguyen, T, 1987, “Natural convection effects in
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