International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org, editorijaiem@gmail.com
Volume 3, Issue 2, February 2014
ISSN 2319 - 4847
Natural Convection over a Flat Plate from side
to side Enclosures
Pratik Tiwari1 and Vinayak Malhotra2*
1
Undergraduate Student, Dept. of Aerospace Engineering, SRM University, Chennai, Tamil Nadu, India
2
Assistant Professor, Dept. of Aerospace Engineering, SRM University, Chennai, Tamil Nadu, India
Abstract
The study intends physical insight into heterogeneous heat transfer phenomena of laminar free convection over a flat plate
bounded by enclosures. The work aims at understanding the implications of enclosures, with investigation of effects of
parameters ambient temperature, surface roughness and flow velocity on heat transfer coefficient at different surface orientations
and heat source input (voltage). Experiments were performed on an existing natural convection experimental setup and the heat
transfer characteristics were analyzed. Results show that the heat transfer coefficient exhibits a gradual monotonic reducing
behavior with increase in surface inclination under different enclosure conditions. The increase in heat source input increases the
heat transfer rates which primarily govern the enhanced heat losses. However, the change drops at higher power supply and heat
transfer rates converge.
Keywords: Free convection, flat plate, laminar flow, enclosures, heat transfer coefficient.
1. INTRODUCTION
Transfer of heat in our ambiences and in most of engineering expedients is a phenomenon of practical and functional
significance. Convection heat transfer theory directs to predict the energy transfer that takes place between hot body and
the surrounding fluid as a result of temperature difference. The convection heat transfer is broadly classified as: Free and
forced convection. Free convection refers to fluid motion by buoyant forces arising owing to density gradients as a result
of temperature gradients. In forced convection, the flow of the fluid is enhanced by external sources. The free mode of
convection is prominent in nature with applications ranging from the need of cooling to heating at different under
different conditions. The cooling of electronic devices, reactor cores, high voltage power transformers and heating of
houses, heat transfer through chimneys, energy storage systems, to the aircrafts coolant flow path uses natural convection
to aid direction. Here, in this work, heat transfer characteristics are investigated over a square flat plate in the free
convection configuration bounded by enclosures. The interest in this class of problems is primarily driven by the need to
have better understanding of convective heat transfer.
Following the classical work of [1] over laminar free convection on plates, in the last five decades research works have
contributed significantly to the improvement in the understanding of the convective heat transfer. The contributions have
been reported in several reviews like [2]-[8].The works provide an excellent review on the developments up to the end of
the century. Acharya and Tsang [9] showed that the average heat transfer from the enclosure is relatively insensitive to
the inclination angle; however, the local values do exhibit a significant dependence on the inclination of the enclosure.
Rasoul and prinos [10] studied the effect of the inclination angle on steady natural convection in a square enclosure. They
reported that when the hot wall approach the top position (inclination angles greater than 90°), fluid from the hot or cold
wall returns back to the same wall and an almost horizontal flow is observed in the central part of the enclosure.
Lakhal et al., [11] numerically studied natural convection in an inclined rectangular enclosure with perfectly conducting
fins attached to the heated wall. They work stated that the heat losses through the cold wall can be reduced considerably
by using fins attached on the heated wall. This phenomenon becomes more pronounced when the enclosure inclination
angle from the vertical is increased. Islam et al., [12] investigated natural convection in a tilted square enclosure
containing internal energy sources. They noted that the diffusion heat transfer is prominent for the lower value of internal
heat generation whereas the convection outweighs the diffusion for the higher value of internal energy. Furthermore, the
work stated that the convective currents always prevail at the bottom part of the cavity whatever its magnitude is. AbuNada et al., [13] explored the influence of inclination angle for a square enclosure. Inclination angle of the enclosure was
proposed a control parameter for fluid flow and heat transfer. Recently, Tiwari and Malhotra [14] showed that the
convective heat transfer rate for laminar flow over a flat plate exhibits a monotonically decreasing behavior with
increment in plate orientation for a square plate enclosed from two sides. While, there is abundant literature available, but
complexity of the problem had prevented a complete understanding due to interaction between flow, heat and mass
transfer. In the light of above mentioned works, the present work focuses on convective heat transfer coefficient for
varying plate orientation and heat source input. In most of the convection problems, the heat transfer characteristics are
explored on objects (here square plate) open to atmosphere. However, with the presence of an enclosure (i.e. wall), the
heat transfer characteristics are expected to be altered with varying orientation and heat source input. This aspect of
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International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org, editorijaiem@gmail.com
Volume 3, Issue 2, February 2014
ISSN 2319 - 4847
convective heat transfer is yet to be explored. Hence, a systematic study is needed to understand mechanisms controlling
the convective heat transfer under effect of enclosures. The present study was carried out with primary objectives of.
1. Investigating influence of an enclosure on heat transfer coefficient by analyzing effects of parameters ambient
temperature, surface roughness, enclosure effects and flow velocity at different surface orientations.
2. To analyze the role of key controlling parameters.
2. EXPERIMENTAL SETUP AND SOLUTION METHODOLOGY
A simple natural convection apparatus (Fig. 1(a)) was adapted for this study. The apparatus consisted of base made of
mild steel plates which supported the assembly. The smooth plate assembly comprised of a glass enclosure bounded along
the sides but open from both the ends to remove the external influences which can affect heat transfer rate. The aluminum
plate specimen (Fig. 1(b)) is (15 cm x 15 cm) which was heated using electrical power at desired rate for 2 hours prior to
experiments. The rate of heating the plate can be adjusted with the help of a handhold and a digital display.
Thermocouples (5 in numbers) are embedded in plate (Fig. 1(c)) and located equidistance to embark average plate
temperature. In order to facilitate the heat transfer at different orientations, the entire plate assembly can be adjusted with
the help of a handle and an attached protractor.
Figure 1 Pictorial view of the apparatus (a) Front view (b) Top view of square plate (c) schematic of square plate with
location of embedded equidistant thermocouples (shown by circles).
The readings were taken systematically by stepwise increment in plate orientation in proper time interval and repeating
the same for varying power input. It must be noted that all the readings presented here represent the repeatability of
results obtained. The square plate is enclosed from two sides by glass sheets and opens to atmosphere from top and
bottom. The convective heat transfer coefficient is determined as heat power lost due to convection is equated to the
electrical power supplied.
h A T  V I
Where
h
V I
A  T
T  (Tav  T1 )
T  T3  T4  T5  T6
Tav  ( 2
)
5
h 
V
Heat transfer coefficient (W/m2-K)
Voltage supplied (Volt)
I = Current intensity (Ampere)
A = Area of square plate (m2)
Tav = Average thermocouples temperature (K)
T1  Ambient temperature (K)
  Surface orientation (Degrees)
3. RESULT AND DISCUSSION
An experimental parametric study was carried out to study the heat transfer characteristics on a heated flat plate bounded
by enclosures. The effect of variables viz. ambient temperature, surface roughness, enclosure effects and flow velocity on
heat transfer coefficient at different plate orientations and heat source input in laminar flow was investigated. First, we
look at the effect of ambient temperature on convective heat transfer coefficient. Fig. 2 shows variation of heat transfer
rate with varying ambient temperature. The study was carried out for heater input of 100 volt and 0.45 ampere with plate
kept horizontal and smooth surface facing upward.
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Figure 2 Variation of heat transfer coefficient with ambient temperature for horizontal plate orientation and smooth
surface facing upward.
Experiments show that the heat transfer rates are higher with plate kept horizontal and exhibits a monotonically reducing
behavior with increment in ambient temperature. Small increment in ambient temperature (here in range of 29-32
degrees) is seen to result in drastic decrement in heat transfer rate. The reason for this may be attributed to increased
overall linear temperature difference owing to continuous heat power supply resulting in increased average plate
temperature which probably is the reason for significantly reduced rate of heat transfer. The result signifies that
maximum cooling effect comes when the objects are operated at lower ambient temperature in horizontal orientation
whereas, in applications requiring enhanced heating effect, vertical orientation can be more suitable.
Next, we look at the effect of surface roughness on heat transfer rate for selected heater input and varying plate
orientation. Fig. 3 shows variation of heat transfer coefficient with plate orientation for selected voltages of 75, 100, 125,
150 volts respectively. In these reading the effect of enclosure is accounted with top end closed and smooth surface of
plate facing upward (Fig.3) in comparison to rough surface facing upward (Fig.4). Looking at the plots, one can note that
for both cases, the rate of heat transfer increases with increase in voltage at all orientations. For input voltage more than
75 volt the heat transfer rates shows a strong increase. It is interesting to note that the magnitudes of heat transfer
coefficient are higher for rough surface facing upward. The reason for this may be attributed to the circulation region
(strong convection currents coming down) formed by hot gases owing to heat interaction with walls. This results in gases
becoming denser and carrying additional heat in absence of an exit at top. Rough surface generates more heat owing to
friction among the hot buoyant gases and corroborates in carrying additional heat at higher power input. The above
mentioned effect is noted more for plate with low orientation(less than 30o) and recedes with increase in orientation.
Moreover, in case of smooth surfaces, the rate of change in magnitudes at higher input is distinct and confines after 100
volt. But, for the rough surfaces the growth in magnitude drops at higher input (here 125 volts) and beyond that critical
value, the heat transfer rate confines to a close range..
It indicates that though the heat transfer coefficients are effective and higher with rough surfaces. However, beyond a
certain value, the change at higher voltages reduces and it may return with diminishing returns. The results substantiate
the fact that, rough surfaces when placed parallel to surface will yield enhanced cooling effects. However, in case the
requirement demands increased heating effect, any type of surfaces at orientation normal to the surface is sufficient.
Smooth up
Voltage = 75 Volt
Top closed
Voltage = 100 Volt
Voltage = 125 Volt
Voltage = 150 Volt
45
2
Heat transfer coefficient (W/m -K)
50
40
35
30
25
20
0
15
30
45
60
75
90
Surface orientation (Degrees)
Figure 3 Variation of heat transfer coefficient with selected heater input and surface
orientation for smooth surface facing upward with top end closed.
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60
Rough up
Voltage = 75 Volt
Voltage = 100 Volt
Voltage = 125 Volt
Voltage = 150 Volt
Top closed
Heat transfer coefficient (W/m2-K)
55
50
45
40
35
30
25
20
0
15
30
45
60
75
90
Surface orientation (Degrees)
Figure 4 Variation of heat transfer coefficient with selected heater input and surface
orientation for rough surface facing upward with top end closed.
Further, we look at the effect of enclosures on the heat transfer coefficient. The comparison is made for three different
cases with smooth surface facing upward and varying surface orientation and heat source input viz., (a) Top and bottom
ends open (Fig.5) (b) Top end closed (Fig. 3) and (c) bottom end closed (Fig.6). It is worth noting that, the variation of
heat transfer coefficient with orientation for all three cases follows similar trend. With both ends open, the heat transfer
rate and its variation with surface orientation depict a crossover at higher voltages (above 125 volts) and low orientation
(below 30o). With top end closed, the heat transfer rates at higher voltages confine themselves in a closed region and
follow a trend gradually reducing with varying plate orientation. While, when the bottom end is closed, highest heat
transfer rates are obtained for all the orientations and power inputs. Here, in absence of suction created by earth’s gravity,
the surrounding air carries away more amount of heat than the other two configurations. The results signifies that for
enhanced cooling effects, use of a configuration with three sides closed and only top end open may be more beneficial.
However, for greater heating requirements, the system is insensitive to the enclosure effects at higher orientations.
45
75 Volt
Heat transfer coefficient (W/m2-K)
100 Volt
125 Volt
40
150 Volt
35
30
25
0
15
30
45
60
75
90
Surface orientation (Degrees)
Figure 5 Variation of heat transfer coefficient with selected heater input and surface
orientation for smooth surface facing upward with both ends open.
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International Journal of Application or Innovation in Engineering & Management (IJAIEM)
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Volume 3, Issue 2, February 2014
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Bottom closed
Smooth up
Voltage = 75 Volt
Voltage = 100 Volt
Voltage = 125 Volt
Voltage = 150 Volt
80
2
Heat transfer coefficient (W/m -K)
90
70
60
50
40
30
20
0
15
30
45
60
75
90
Surface orientation (Degrees)
Figure 6 Variation of heat transfer coefficient with selected heater input and surface
orientation for smooth surface facing upward with bottom end closed.
Next, the effect of parameter induced flow velocity on the heat transfer rates was explored. Table 1 shows the comparison
of free convection with variable induced velocity of 0.40 m/s and 0.80 m/s respectively. As expected, the value of heat
transfer coefficient is more with assisting flow velocity. Interestingly, though the magnitude of heat transfer coefficient
increases with flow velocity, yet it directs to a critical value above which it starts decreasing as heat transfer coefficient
values are more for flow velocity of 0.40 m/s than 0.80 m/s. The heat transfer coefficient for forced convection follows a
trend similar to free convection with varying plate orientation. However, the change in heat transfer coefficients is more
for flow velocity of 0.80 m/s as the plate orientation changes. This particular study also validates some of the benchmark
studies on forced and free convection. Form the results obtained, one can note that low forced convection yields better
cooling effects when surface is kept horizontal. Besides for enhanced heating effects, it is superior to use surface oriented
normal to surface.
Table 1 Variation of heat transfer coefficient with induced velocity and plate
orientation for smooth surface facing upward.
4. CONCLUSION
An experimental exploration was carried out to understand the implications of parameters, ambient temperature, surface
roughness, enclosures effect and flow velocity on heat transfer coefficient at different orientations and heat source input.
Based on results obtained following conclusions may be drawn: The convection heat transfer is more effective in
horizontal surfaces due to stronger buoyant forces leading to better cooling applications. Increase in ambient temperature
drastically reduces the heat losses. The heat transfer coefficient increases with heater input but it results in diminishing
returns beyond a critical value and thus indicates that a critical power input is adequate to remove sufficient heat and
further increase may be redundant. If application demands enhancing cooling effects, a configuration kept horizontal, at
low ambient temperature, with rough surface, with bottom end closed and low forced flow is proposed. Force convection
is a faster mode of losing heat however it conveys a range where it will be optimum.
References
[1] S. Ostrich, “An analysis of laminar free-convection flow and heat transfer about a flat plate”, NACA, TN 2635,
1952.
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[2] E. M. Sparrow and J. L Gregg, “Laminar free convection from a vertical plate with uniform surface heat flux”,
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[11] E. K. Lakhal, M. Hasnaoui, E. Bilgen and P. Vasseur, “Natural convection in inclined rectangular enclosures,” Heat
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AUTHORS
Vinayak Malhotra received the Bachelor of Engineering in Aeronautical Engineering from The
Aeronautical Society of India and Master of Science degree in Aerospace Engineering from Indian Institute
of Technology. During his Master program, he worked on flame spread in microgravity. He now professes in
Department of Aerospace Engineering, SRM University Chennai.
Pratik Tiwari is an undergraduate student in Department of Aerospace Engineering, SRM University
Chennai. He is interested in broad field of heat transfer and combustion and has worked on convective mode
of heat transfer along with exploring physics in impinging jets and smoldering combustion.
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