This document summarizes a numerical study of heat transfer characteristics inside a bottom-heated square enclosure. Simulations were conducted for air and Al2O3-water nanofluid inside the enclosure as the conducting medium. Results showed that heat transfer rate, as measured by Nusselt number, increased with increasing hot wall temperature. For air, heat transfer occurred through bulk fluid motion, while for nanofluid it occurred through local interactions. However, nanofluids also exhibited bulk motion at higher temperatures. Isotherm and streamline patterns revealed higher heat transfer and more organized flow for nanofluids compared to air.

1. IJIRST –International Journal for Innovative Research in Science & Technology| Volume 2 | Issue 11 | April 2016
ISSN (online): 2349-6010
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Heat Transfer Characteristics Inside A Bottom
Heated Square Enclosure
Vineeth V. K Ligit George
Assistant Professor UG Student
Department of Mechanical Engineering Department of Mechanical Engineering
Saintgits College of Engineering Saintgits College of Engineering
Linoj V Lalu Stephen Jose Mathew
UG Student UG Student
Department of Mechanical Engineering Department of Mechanical Engineering
Saintgits College of Engineering Saintgits College of Engineering
Vibu Mammen Jacob
UG Student
Department of Mechanical Engineering
Saintgits College of Engineering
Abstract
The present work deals with numerical study of natural convective heat transfer in a 2D square enclosure heated from below.
The top wall is exposed to ambient temperature whereas the side walls are kept adiabatic. The study is conducted for different
conducting mediums inside. The conducting mediums considered for the study are air and Al2O3-water nanofluid. Simulations
are run for a Rayleigh Number variation of 5x107 to 25x107. The heat transfer rate is found to increase with increase in hot wall
temperature. For air, the thermal interactions are achieved through bulk motion of fluid. For Al2O3-water nanofluid, the
mechanism of heat transfer is attained through local fluid interactions. But the nanofluids are also found to exhibit bulk
movement at higher hot wall temperatures. Numerical study was done using FLUENT 14.0.
Keywords: Isotherms, Nano Fluid, Natural Convection, Rayleigh Number, Square Enclosure, Streamlines
_______________________________________________________________________________________________________
I. INTRODUCTION
Natural convection in enclosures has attracted considerable interest of investigators due to its common appearance in several
engineering and environmental problems. Natural convection is the transport process in a fluid, where the motion is derived by
interaction of difference in density and gravitational field. Therefore natural convection does not require any external force,
which makes it an attractive system in thermal control because of its low cost, reliability and simplicity in use.
For the case of a square cavity, a plethora of results are quoted in the literature. Calcagni et al [1] investigated how heat
transfer develops inside a square cavity heated from below for a Rayleigh number variation of 103
-106
. Their study showed that
different convective forms are obtained depending on Rayleigh number. Local Nusselt number evaluation on the heat source
surface showed a symmetrical plume form raising near the heat source borders.
Corcine [2] analyzed the effect of steady laminar natural convection in an air filled 2D rectangular enclosure, heated from
below, and cooled from above. The Rayleigh number variation from 103
and 106
was found to influence the flow patterns, the
temperature distributions and the heat transfer rates.
Pendyala et al [3] studied the heat transfer characteristics during natural convection in enclosures using different fluids. Heat
transfer coefficients for different fluids were estimated for varying Rayleigh number. CFD simulations are performed with
different fluids at a temperature range of 20 K ≤ ΔT ≤ 100 K. Correlations for Nusselt number (Nu) based on predicted findings
have been developed to represent heat transfer characteristics. Sik Hwang et al.[4] theoretically investigated the thermal
characteristics of natural convection in a rectangular cavity heated from below with water-based nanofluids containing alumina
(Al2O3 nanofluids).The effects of the volume fraction, the size of nanoparticles, and the average temperature of nanofluids on
natural convective instability and heat transfer characteristics were presented. The ratio of heat transfer coefficient of nanofluids
to that of base fluid is decreased as the size of nanoparticles increases, or the average temperature of nanofluids is decreased.
Tahrey et al [5] numerically investigated the heat transfer and flow characteristic due to buoyancy forces in a heated enclosure
using nanofluid and their behavior under natural convective heat transfer condition. Simulations were carried out for Rayleigh
numbers ranging from 103
-106
using Al2O3-water nanofluid. They obtained high Nusselt number values for nanofluids compared
to pure water.

2. Heat Transfer Characteristics Inside A Bottom Heated Square Enclosure
(IJIRST/ Volume 2 / Issue 11/ 064)
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In the present work, a bottom heated square enclosure is numerically analyzed. Although in most cases the flow is three
dimensional (3-D), two-dimensional (2-D) results are often satisfactory, especially considering the large reduction in
computational effort.
II. NUMERICAL FORMULATION
A 2-D model of a square enclosure is considered. The bottom wall of the enclosure is kept at a higher temperature while the top
wall is exposed to ambient temperature. Both the vertical walls are kept adiabatic. A schematic representation of the system
under investigation is shown is shown in figure 1.
Fig. 1: Schematic diagram of the square enclosure
The geometric modeling of the defined problem is done using Design Modular. The modeled geometry along with the mesh is
shown in figure 2.
The fluid flow and heat transfer characteristics inside the square enclosure is analysed using ANSYS FLUENT 14.0. The
governing equations of continuity momentum and energy are solved inside the computational domain.
Fig. 2: Geometric model with mesh
Conservation of mass
0.  U (1)
Conservation of momentum
BUPUU 
21
).( 

(2)
Where B is the body force vector defined by,
T
TTg ]0),(,0[ 
 
Conservation of Energy:

3. Heat Transfer Characteristics Inside A Bottom Heated Square Enclosure
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TTU
2
).(   (3)
are solved in the computational domain with the following boundary conditions,
𝑢 = 𝑣 = 0, 𝑇 = 𝑇𝐻 at y=0, 0≤x≤L
𝑇 = 𝑇𝐶, 𝑢 = 𝑣 = 0 at y=L, 0≤x≤L
𝜕𝑇
𝜕𝑥
= 0, 𝑢 = 𝑣 = 0 at x=0,L 0≤y≤L
Pressure based solver with absolute velocity formulation has been used to perform steady state simulation with gravitational
accelerations in the negative y direction. First order upwind scheme is employed for discretization of momentum and energy. For
all the equations, under relaxation have been used. Scaled residuals for continuity, velocity and energy are set to be the
convergence criteria.
A grid independence study is conducted for the model and a grid size of 400 x 400 is fixed, based on bottom heat transfer rate.
Table – 1
Grid Independence Test
Grid Size Bottom Heat Transfer Rate(W)
100*100 26.499
200*200 23.095
300*300 23.153
400*400 22.905
500*500 22.681
III. RESULTS AND DISCUSSION
The heat transfer inside the square enclosure is analysed for two cases. In case 1, the square enclosure is filled with air and in
case 2, the square enclosure is filled with nanofluid. The nanofluid considered for the study are Al2O3 –water nanofluid.
The flow is considered to be laminar and 2-D. The energy received by the fluid at the hot wall is delivered at the cold wall. The
insulated horizontal walls behave as energy corridors for the fluid flow.
The flow is analyzed for a Rayleigh number variation of 5 x107
to 25 x 107
. Table 2 shows the variation of Nu with rise in hot
wall temperature. An increase in Nu indicates an increase in heat transfer rate with rise in hot wall temperature.
Table - 2
Variation of Nu with hot wall temperature.
Temperature of hot wall Nusselt number Rayleigh number
303 34.35 5.53 x107
308 39.88 10.12 x 107
313 41.67 14.25 x 107
318 48.54 17.64 x 107
323 51.06 20.09 x 107
328 53.37 23x107
The figures 3, 4 and 5 shows the isotherm patterns inside the square enclosure with air as the conducting medium.
The isotherms pattern reveals that as Rayleigh number increases, the packing of isotherms near the active walls become
prominent implying a rise in Nusselt number. The stratification in isotherm pattern across the cavity has become a feature for
higher Rayleigh number.
Fig. 3: Isotherm pattern for a hot wall temperature of 30°C for the square enclosure with air inside.

4. Heat Transfer Characteristics Inside A Bottom Heated Square Enclosure
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Fig. 4: Isotherm pattern for a hot wall temperature of 50°C for the square enclosure with air inside.
Fig. 5: Isotherm pattern for a hot wall temperature of 55°C for the square enclosure with air inside.
Fig. 6: Streamlines inside the square enclosure with air inside for a hot wall temperature of 30°C.
Figure 6, 7 and 8 depicts the streamline contours inside the square enclosure with air as conducting medium, for varying
Rayleigh number. They show the presence of recirculation zones which are characteristics of higher Rayleigh number
convection. As Rayleigh number increase the flow becomes stronger, there is a formation of very thin strong shear layer adjacent
to active walls. The secondary vortices are also formed for higher Rayleigh number. It is important to note that the bulk flow is
in clockwise direction whereas recirculation zones are in anticlockwise direction.

5. Heat Transfer Characteristics Inside A Bottom Heated Square Enclosure
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Fig. 7: Streamlines inside the square enclosure with air inside for a hot wall temperature of 50°C.
Fig. 8: Streamlines inside the square enclosure for a hot wall temperature of 55°C.
Fig. 9: Isotherms inside the square enclosure with Al2O3-water nanofluid inside for a hot wall temperature of 30°C.
Figure 9, 10 and 11 shows the isotherm patterns inside the square enclosure with Al2O3-water nanofluid inside. The initially
random temperature distribution is found to evolve with an increase in temperature and reach a stable state around 50°C. But the
thermal interaction is found to become unstable with increase in hot wall temperature.

6. Heat Transfer Characteristics Inside A Bottom Heated Square Enclosure
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Fig. 10: Isotherms inside the square enclosure with Al2O3-water nanofluid inside for a hot wall temperature of 50°C.
Fig. 11: Isotherms inside the square enclosure with Al2O3-water nanofluid inside for a hot wall temperature of 55°C.
Fig. 12: Streamlines inside the square enclosure with Al2O3-water nanofluid for the hot wall temperature of 30°C.
Figure 12, 13 and 14 shows the streamline pattern for flow inside the square enclosure and with Al2O3 -water nanofluid inside.
The flow develops into a single bulk flow as the bottom wall temperature increases which indicates a continuous heat transfer.
Formation of secondary vortices at higher temperatures indicates instabilities in heat transfer at higher temperatures.

7. Heat Transfer Characteristics Inside A Bottom Heated Square Enclosure
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Fig. 13: Streamlines inside the square enclosure with Al2O3-water nanofluid for the hot wall temperature of 50°C.
Fig. 14: Streamlines inside the square enclosure with Al2O3-water nanofluid for a hot wall temperature of 55°C.
Fig. 15: Isotherms inside the square enclosure for a hot wall temperature of 30°C with air
The figure 15 and 16 shows the isotherms inside the square enclosure when it is filled with air, Al2O3 –water nanofluid for the
smallest temperature difference between the top and bottom walls. For air, it is seen that the heat transfer is concentrated along
the sides where the central portion of the enclosure remains devoid of any thermal interaction. When the air is replaced by
nanofluid, it is evident that the heat transfer is found to spread to the entire area enclosed.

8. Heat Transfer Characteristics Inside A Bottom Heated Square Enclosure
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Fig. 16: Isotherms inside the square enclosure with Al2O3–water nanofluid for a hot wall temperature of 30°C
Fig. 17: Isotherms inside for a hot wall temperature of 50°C the square enclosure with air.
The figure 17 and 18 shows the isotherm pattern inside the square enclosure filled with air, Al2O3-water nanofluid for a hot
wall temperature of 50°C.The thermal interaction between the top and bottom walls is found to establish a bulk flow inside the
enclosure, which is substantiated by the streamlines.
Fig. 18: Isotherms inside the square enclosure with Al2O3–water nanofluid for a hot wall temperature of 50°C.

9. Heat Transfer Characteristics Inside A Bottom Heated Square Enclosure
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Fig. 19: Isotherms inside the square enclosure with air for a hot wall temperature of 30°C.
Fig. 20: Streamlines inside the square enclosure with Al2O3–water nanofluid for a hot wall temperature of 30°C.
The figure 19 and 20 shows streamlines inside the square enclosures for lowest temperature with air and Al2O3–water
nanofluid as conducting mediums. The flow is found to establish a bulk flow when the conducting medium is air. But for the
nanofluids the thermal exchange is found to occur through localized fluid interactions. But as the temperature difference
increases, the nanofluids also tend to exchange heat using bulk flow.
Fig. 21: Streamlines inside the square enclosure with air for a hot wall temperature of 50°C.

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Fig. 22: Streamlines inside the square enclosure with Al2O3–water nanofluid enclosure for a hot wall temperature of 50°C.
Figure 21 and 22 shows streamlines inside the square enclosure with Al2O3–water nanofluid enclosure for a hot wall
temperature of 50°C.Bulk flow is established in the case of Al2O3-water nanofluid whereas the vortices seem to exist for air at a
higher temperature difference.
IV. CONCLUSIONS
The Natural convection heat transfer in an air filled and Al2O3–water nanofluid filled square enclosures heated from the bottom
has been studied numerically. It is found that heat transfer rate is more in case of square enclosure filled with nanofluids than
with air filled square enclosures. As the hot wall temperature increases the flow is found to take place in more arranged manner
which indicates the stability in heat flow case with higher temperature difference, between bottom and top walls.
For air, it is seen that the heat transfer is concentrated along the sides where the central portion of the enclosure remains
devoid of any thermal interaction. When the air is replaced by nanofluid, it is seen that the heat transfer is found to spread to the
entire area enclosed. The fluid interaction inside is found to establish a bulk flow when conducting medium is air. But for
nanofluids, the thermal exchange is found to occur through localized fluid interaction. But as the temperature difference
increases, the nanofluids also tend to exchange heat using bulk flow.
REFERENCES
[1] B. Calcagni, F. Marsili, M. Paroncini, Natural convective heat transfer in square enclosures heated from below, Applied Thermal Engineering 25 (2005)
2522–2531
[2] Massimo Corcione, Effects of the thermal boundary conditions at the sidewalls upon natural convection in rectangular enclosures heate from below and
cooled from above, International Journal of Thermal Sciences 42 (2003) 199–208.
[3] Rajashekhar Pendyala, Yean Sang Wong, SuhaibUmerIlyas, CFD Simulations of Natural Convection Heat Transfer in Enclosures with Varying Aspect
Ratios, Chemical Engineering Transactions • October 2015
[4] Kyo Sik Hwang, Ji-Hwan Lee, Seok Pil Jang, Buoyancy-driven heat transfer of water-based Al2O3 nanofluids in a rectangular cavity, International Journal
of Heat and Mass Transfer 50 (2007) 4003–4010
[5] A. A. Tahery, S. M. Pesteei, A. Zehforoosh , Numerical Study Of Heat Transfer Performance Of Homogenous Nanofluids Under Natural Convection,
International Journal of Chemical Engineering and Applications, Vol. 1, No. 1, June 2010 ISSN: 2010-022.