1. International Journal of Advanced Research in Engineering RESEARCH IN ENGINEERING
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IJARET
©IAEME
A REVIEW ON NATURAL CONVECTION HEAT TRANSFER THROUGH
INCLINED PARALLEL PLATES
Yogesh Dhote1* and S.B. Thombre2
1
Department of Mechanical Engineering,
Hindustan College of Science & Technology, Farah, Mathura - 281 122 (U.P.) INDIA
2
Department of Mechanical Engineering,
Visvesvaraya National Institute of Technology, Nagpur - 440 011 (M.S.) INDIA
ABSTRACT
Under this study a rigorous literature review has been carried out to observe the research and
development progress in natural convection heat transfer through inclined parallel flat surfaces with
an objective to see the possibilities of research in this direction. The research work carried out by the
various investigators in this respect along with their findings have been discussed and also presented
in tabulated form. The paper is finally concluded with the scope for future work.
Keywords: Natural Convection, Heat transfer coefficient, Lower Plate, Upper Plate, Inclined plate.
1. INTRODUCTION
Considerable interest has been shown by the various investigators in recent years in the
problem of natural convection heat transfer through inclined parallel plates. Such systems are of
practical importance in the field of solar air heating and ventilation applications [1]. In spite of this
there are many engineering applications where the heat transfer through inclined parallel plates is
taking place either through natural or forced convection mode. As far as convection heat transfer is
considered lot of experimental and analytical investigations have already been carried out by the
researchers in forced convection. In case of the research taken place in natural convection heat
transfer it has been observed that there is much difference in the results obtained by different
researchers. Some important investigations are definitely taken place in natural convection still there
is a considerable scope of research in natural convection heat transfer through inclined parallel
plates.
Combined buoyancy forces of heat and mass transfer, resulting from the simultaneous
presence of differences in temperature variations in concentration have significant influences on
momentum, heat and mass in flowing gas mixtures are often encountered in many engineering
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2. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –
6480(Print), ISSN 0976 – 6499(Online) Volume 4, Issue 7, November – December (2013), © IAEME
systems and the natural environment [2]. The study of free convection in inclined parallel plates has
received a great impetus in recent years because several applications of practical interest are working
with the principle like passive solar heating, energy conservation buildings, cooling of electronic
components etc [3].
The prediction of buoyancy induced flow of gases is very difficult due to the complex
relations between the fluid parameters. Although considerable experimental and theoretical research
work has been carried out by various investigators to predict the buoyancy induced flow of gases, in
current situation it is insufficient and there is need to devise more accurate and versatile correlation
for buoyancy induced mass flow and heat transfer.
2. REVIEW OF LITERATURE
The consolidate report of the investigations carried out by the various investigators in
relevance to natural convection heat transfer through inclined parallel plates is tabulated as shown in
Table 1.
N. Onur et al. performed experimental study on the natural convection heat transfer between
inclined parallel plates such that lower plate isothermally heated and the upper plate thermally
insulated as well as unheated. Experiments were carried out for different temperature differences in
air to determine the effect of plate spacing and plate inclination on heat transfer. It is observed that
an opposite wall plays an important heat transfer role in real engineering application. Further
dimensional analysis indicates that natural convection heat transfer between inclined parallel plates
depends on Nusselt Number, ‘Nu’, Rayleigh number, ‘Ra’, and the ratio of plate spacing ‘s’ to plate
length ‘L’ (Aspect Ratio) and plate inclination, ‘θ’.
Table 1. Research review of natural convection heat transfer through inclined parallel plates
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3. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –
6480(Print), ISSN 0976 – 6499(Online) Volume 4, Issue 7, November – December (2013), © IAEME
J. Gryzagoridis et al. also carried out the experimental study on natural Convection from
upper and lower surfaces of an inclined isothermal plate. He reported for inclination angle 0o < θ <
60o there is no change in heat transfer data for the upper and lower surfaces of the inclined plate, and
correlated very well with vertical plate theory. But for inclination θ = 75o, significant changes were
noted in heat transfer data for upper and lower surface of the inclined plate and as expected the upper
surface data indicated higher heat transfer rates.
T. Fujii et al. performed experimental study on natural-convection heat transfer from a plate
with arbitrary inclination. The heat is transferred from one side surface of two plates of 30 cm height,
15 cm width and 5 cm height, 10 cm width for a two dimensional flow. In the laminar region the
expression for the vertical plate is applicable to the inclined plate if only the gravitational term in the
‘Ra’ number is altered to the component parallel to the inclined surface. For the horizontal heated
plate and the slightly inclined heated plate with the horizontal surface both facing downward, ‘Nu’
number is proportional to one fifth power of ‘Ra’ number. For the horizontal heated plate facing
upwards the flow in the boundary layer is turbulent and the ‘Nu’ expression agrees with that in the
turbulent region for the vertical plate. The ‘Nu’ number for the smaller plate is somewhat larger than
that for larger (Lengthwise) plate. The Nusselt number value of 5 cm plate is 23 % larger than 30 cm
plate. For the plate facing downwards the applicable range of angle of inclination in this expression
is extended almost to the horizontal, and for the plate facing upwards it is limited by the occurrence
of flow separation in the boundary layer. The fluid flows into the boundary layer not perpendicularly
to the plate, but almost horizontally. This characteristic is preferred for the horizontal plate too.
Incropera reported, compared with vertical plates, inclined and horizontal plates have reduced
fluid velocities along the plate. One might expect that there is a reduction in convection heat transfer.
On the top of a cold inclined plate the reduction of the gravity that acts in the direction parallel to the
plate reduces the convection heat transfer. However, on the bottom of the same plate gravity moves
fluid from the surface and a boundary layer development is interrupted by the discharge of the
parcels of cool fluid from the surface. The cool fluid close to the lower surface is continuously
replaced by hot fluid by a three dimensional flow, which reduces the effective thermal boundary
layer thickness and increases the convection heat transfer although the gravity component along the
plate is smaller than for a vertical plate. An equivalent discussion can be made for a heated inclined
plate. For the top of the cold plate and the bottom of the heated plate and 0 ≤ θ ≤ 60o, the same
Nusselt number correlations as for vertical plates can be used if ‘g’ is replaced by ‘g cos θ’.
A. S. Lavine investigated the linear stability of mixed and free convection between inclined
parallel plates with fixed heat flux boundary conditions. His results may have significance in low
Rayleigh number natural and mixed convection applications, such as solar collectors, solar cells,
cooling of electronic components and chemical vapour deposition systems. The fixed flux boundary
conditions tend to promote instability more than do fixed temperature boundary conditions.
O. Manca described an experimental analysis for horizontal parallel plates heated with
uniform heat flux, carried out by means of a visualization technique and air temperature
measurements with the help of hot wire probes, to calculate temperature fluctuations and the average
thermal field. The most relevant configurations have been analyzed for different plate distances and
heat flux values in various heating modes as:
a) Both plates heated
b) Upper plate heated and lower plate unheated
c) Lower plate heated and upper plate unheated
The main flow pattern resembles a ‘C’ shape (C loop) for all modes. The flow penetrated
inside the cavity close to the leading edge of the lower plate and exited from the upper part by
reversing its motion between the plates. When the lower plate was heated, flow visualization showed
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4. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –
6480(Print), ISSN 0976 – 6499(Online) Volume 4, Issue 7, November – December (2013), © IAEME
that secondary flows were added to the ‘C’ loop main flow. Such secondary structures arose as
thermals, and then changed into longitudinal vortices and in the upper region of the open ended
cavity a chaotic motion was detected. It is seen that greater the Grashof number, the more chaotic the
flow in the outflow branch of the C loop when the lower plate was heated and upper one was
unheated.
M.A.R. Akhanda et al. described experimental study of natural convection heat transfer
across air layers bounded by lower hot rectangular and square corrugated plates to an upper cold flat
plate. The effect of the angle of inclination, the aspect ratio, the temperature potential and the
Rayleigh number on average heat transfer coefficients are investigated within a range of 0o ≤ θ ≤ 75o,
2.33 ≤ A ≤ 6.33, 10o ≤ T ≤ 35o and 3.29 x 104 < RaL < 2.29 x 106. It is seen that reduction of heat
losses from the absorber plate of a solar collector through the cover plates improves collector
efficiency. Therefore the natural convection heat loss across the air layers bounded by two parallel
plates is of special interest to the designers of solar collectors. The average convective heat transfer
coefficient for rectangular and square corrugations are found to increase with increasing of aspect
ratio
(A = L/H) upto a certain limit and then has a tendency to decrease with further increasing of aspect
ratio. It is seen that for the same aspect ratio but lower Rayleigh number, RaL = 0.40 x 106, the
measured heat transfer coefficients for trapezoidal corrugation at all angles of inclination are about
4% higher than those of square ones. The measured values are also higher than those of square ones
upto an angle of 40o. But beyond this inclination the measured values for square corrugation are
larger than those for both rectangular and trapezoidal corrugation.
W.M. Lewandowski presented research attempts to apply a theoretical model of the natural
convection heat transfer for plates of finite dimensions which would be universal for all angles of
plate inclination (0 < θ < π/2). He suggested model of the phenomenon of convective heat transfer
from real, isothermal, inclined plates exhibits convergence with the results of experimental
investigations. Even the initial results suggested that it is possible to describe all the cases of heating
plate inclination with one criteria relation and then to compare the results on a single graph.
E. Doroodchi et.al investigated the expansion behavior of both the mono-disperse and binary
suspensions by varying the inventories of the solids and the fluidization velocity both theoretically
and experimentally. It has been observed that there is a good agreement between the theoretical
model and the experimental data.
3. DISCUSSION AND CONCLUSION
An opposite wall plays an important heat transfer role in real engineering equipments.
Literature survey indicated that these have been relatively scarce information on the free convection
heat transfer along an inclined plate with an opposite wall [4]. In the literature survey it has been
observed clearly that the buoyancy induced natural convection heat transfer and mass flow of gases
through the inclined parallel plates depends upon various parameters as heating process (isothermal
or adiabatic), heating plate (lower or upper), cooling plate or insulated plate (lower or upper), the
plate inclination and the plate spacing. Mostly the investigations have been carried out for forced
convections and there is some scope for research for natural convection flow thro ugh inclined
parallel plates particularly when the buoyancy induced flow gets developed during varying heat input
to the plates. There is still necessity of investigating the buoyancy induced natural convection heat
transfer and mass flow correlations for gases for a wide range of parameters in this respect.
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5. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –
6480(Print), ISSN 0976 – 6499(Online) Volume 4, Issue 7, November – December (2013), © IAEME
4. FUTURE RESEARCH SCOPE
As already pointed out natural convection heat transfer through inclined parallel plates has
many applications, one of them is solar air heater. The research related to the natural convection heat
transfer through inclined plate(s) applicable to solar air heaters is mostly for plain (absorber) plates.
Though some research literature is available for corrugated (absorber) plates for specific geometry
but again a very wide space is available for research in this direction. Though few investigators
derived the correlations for buoyancy induced flow through the inclined parallel plates either they are
giving different results or not suitable for the complete range of varying parameters.
REFERENCES
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
[14]
[15]
[16]
M. Al-Arabi, M.A.I. El-Shaarawi and M. Khamis, Natural convection in uniformly heated
vertical annuli, International Journal of Heat and Mass Transfer, 30 (7) (1987) 1381-1389.
K.T. Lee, Laminar natural convection heat and mass transfer in vertical-rectangular ducts,
International Journal of Heat and Mass Transfer, 42 (1999) 4523-4534.
C.P. Desai and K. Vafai, Experimental and numerical study of buoyancy induced flow and
heat transfer in an open annular cavity, International Journal of Heat and Mass Transfer, 39,
(10) (1996) 2053-2066.
N. Onur, M. Sivrioglu and M.K. Aktas, An experimental study on the natural convection heat
transfer between inclined plates (Lower plate isothermally heated and the upper plate
thermally insulated as well as unheated), Heat and Mass Transfer, 32 (1997) 471-476.
J. Gryzagoridis and B.E. Klingenberg, Natural convection from upper and lower surfaces of
an inclined isothermal plate, International Community of Heat and mass Transfer, 13 (1986)
163-169.
T. Fujii and H. Imura, Natural convection heat transfer from a plate with arbitrary inclination,
International Journal of Heat and Mass Transfer, 15 (1972) 755-767.
A.S. Lavine, On the linear stability of mixed and free convection between inclined parallel
plates with fixed heat flux boundary conditions, International Journal of Heat and Mass
Transfer, 36 (5) (1993), 1373-1381.
O. Manca, B. Morronea and S. Nardinib, Experimental analysis of thermal instability in
natural convection between horizontal parallel plates uniformly heated, Journal of Heat
Transfer, 122 (2000), 50-57.
M.A.R. Akhanda and F.M. Chowdhury, Natural convection heat transfer from a hot
rectangular and a square corrugated plate to a cold flat plate, Journal of Thermal Science, 9
(3) (2000) 243 – 248.
W.M. Lewandowski, Natural convection heat transfer from plates of finite dimensions,
International Journal of Heat and Mass Transfer, 34 (3) (1991), 875-885.
H.P. Garg, J. Prakash, Solar Energy Fundamentals and Applications, First Revised Edition,
Tata McGraw-Hill Publishing Company Limited, New Delhi, (2000) 46-73.
E.C. Guyer, Hand Book of Applied Thermal Design, Tata McGraw-Hill Publishing Company
Limited, New York, (1989) 1.31-1.47.
J.P. Holman, S. Bhattacharyya, Heat Transfer, Ninth Edition, Tata McGraw-Hill Publishing
Company Limited New Delhi, (2008) 340-344.
C.P. Kothandaraman, S. Subramanyam, Heat and Mass Transfer Data Book, Seventh
Edition, New Age International Publishers New Delhi, (2010) 135-140.
A. Mani, Hand Book of Solar Radiation Data for India, Allied Publishers Private Limited,
New Delhi, (1980) 1-88.
A.F. Mills, Heat Transfer, Irwin Homewood Boston, (1992) 301-308.
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6. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –
6480(Print), ISSN 0976 – 6499(Online) Volume 4, Issue 7, November – December (2013), © IAEME
[17] P.H. Oosthuizen, D. Naylor, Introduction to Convective Heat Transfer Analysis, Tata
McGraw-Hill International Edition, New York, (1999) 403-407.
[18] S.P. Sukhatme, Solar Energy Principles of Thermal Collection and Storage, Second Edition,
Tata McGraw-Hill Publishing Company Limited, New Delhi, (2005) 266-268.
[19] Incropera,
Correlations for natural convection,
Convective heat transfer,
www.tfd.chalmers.se/gr-kurs/MTF112, 66-68.
[20] Dr.N.G.Narve and Dr.N.K.Sane, “Experimental Investigation of Laminar Mixed Convection
Heat Transfer in the Entrance Region of Rectangular Duct”, International Journal of
Mechanical Engineering & Technology (IJMET), Volume 4, Issue 1, 2013, pp. 127 - 133,
ISSN Print: 0976 – 6340, ISSN Online: 0976 – 6359.
[21] Ashok Tukaram Pise and Umesh Vandeorao Awasarmol, “Investigation of Enhancement of
Natural Convection Heat Transfer from Engine Cylinder with Permeable Fins”, International
Journal of Mechanical Engineering & Technology (IJMET), Volume 1, Issue 1, 2010,
pp. 238 - 247, ISSN Print: 0976 – 6340, ISSN Online: 0976 – 6359.
[22] S.K. Dhakad, Pankaj Sonkusare, Pravin Kumar Singh and Dr. Lokesh Bajpai, “Prediction of
Friction Factor and Non Dimensions Numbers in Force Convection Heat Transfer Analysis of
Insulated Cylindrical Pipe”, International Journal of Mechanical Engineering & Technology
(IJMET), Volume 4, Issue 4, 2013, pp. 259 - 265, ISSN Print: 0976 – 6340, ISSN Online:
0976 – 6359.
[23] Yogesh C. Dhote and Dr. S.B. Thombre, “Parametric Study on the Thermal Performance of
the Solar Air Heater with Energy Storage”, International Journal of Mechanical Engineering
& Technology (IJMET), Volume 3, Issue 1, 2012, pp. 90 - 99, ISSN Print: 0976 – 6340,
ISSN Online: 0976 – 6359.
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