In order to enhance the heat transfer rate of solar air heater apparatus, triangular protrusions are provided on the surface of the aluminum absorber plate to act as artificial roughness. Three kinds of absorber plates other than a smooth absorber plate with protrusions of varying apex angles are chosen for this work.

1. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),
ISSN 0976 – 6359(Online), Volume 6, Issue 4, April (2015), pp. 27-34© IAEME
35
NUSSELT NUMBER AND FRICTION FACTOR
CORRELATIONS FOR SOLAR AIR HEATER DUCT
HAVING TRIANGULAR PROTRUSIONS AS ROUGHNESS
ELEMENTS ON ABSORBER PLATE
A. Nagaraju 1
, Prof. B. Uma Maheswar Gowd 2
1, 2
Department of Mechanical Engineering,
Jawaharlal Nehru Technological University, Anantapur, A.P
ABSTRACT
In order to enhance the heat transfer rate of solar air heater apparatus, triangular protrusions
are provided on the surface of the aluminum absorber plate to act as artificial roughness. Three kinds
of absorber plates other than a smooth absorber plate with protrusions of varying apex angles are
chosen for this work. The respective apex angles of protrusions on the three absorber plates are 300
,
450
, and 600
. The mass flow rate is maintained between 0.017-0.0182Kg/sec. The rate of air flow
corresponds to Reynolds number (Re) ranging from 10500-12000, Nusselt number range is 50-110,
friction factor is 4.5-6.7x10-3
, and Stanton number is 6-14x10-5
. The heat transfer rate and thermo-
hydraulic performance obtained is observed to be highest for 450
. Finally comparison of heat transfer
and friction factor from both smooth and roughened plate under the similar condition of air flow is
made. A mathematical correlations is developed in the form Nusselt Number Nu=Rea
.Prb
Tanαc
and
friction factor f = Red
.Tanαe
.
Keywords: Solar Air Heater, Nusselt Number, Friction Factor, Triangular Protrusion, Heat Transfer
Enhancement
I. INTRODUCTION
Solar air heaters are most common type of solar collectors for utilization of solar thermal
energy in industry, household, agriculture, medicine etc. Using solar thermal energy to heat air has
many advantages compared to other sources of energy. But they yield very less heat transfer rate
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2. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),
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because of the formation of laminar sub-layer of air at the surface of absorber plate. The artificial
roughness is used as turbulence promoters on a surface. The surface roughness can be created by
number of methods such as welding, fixing small ribs, fixing small diameter wires, machining and
sand blasting, casting and forming. Many investigations on forced convective heat transfer in smooth
and roughened ducts have been reported in literature. A create artificial roughness on the surface of
absorber plate can be provided ribs, fixing small diameter wires, expanded metal mesh, wire mesh
and dimple shape geometry has been reported by Hans et al. (2009) Varun et al.(2007) and Briz
Bhushan (2010) of different shapes to enhance the heat transfer co-efficient. Experimental
investigations on heat transfer and friction in artificially roughned solar air heater duct have been
reported by Gupta et al. (1993), Jaurker et al. (2006), Karwa (2003), Karmare and Tikekar (2007),
Momin et al.(2002), Prasad and Saini (1988) and Saini and Saini (1997). Nusselt number and friction
factor correlations have been developed by these investigators by using experimental data. As results
there is an increase in frictional losses which cause more power required by blower. To keep friction
losses at a minimum level, the turbulence should be created very close to the duct surface i.e.,
laminar sub-layer. The present investigation is taken up with the objective of experimentation on
triangular protrusions as artificial roughness to the underside of one broad wall of the duct to
evaluate enhancement of heat transfer co-efficient of solar air collector subjected to uniform heat
flux. The experiment encompassed Reynolds number in the range of 10000-12500 relative roughness
height (e/Dh) 0.11, relative roughness pitch (P/e) 8.333, rib height 3mm and angle of attack in the
range of 300
to 600
. The validation test of the apparatus has been done using the smooth plate values
by comparing the experimental values of Nusselt number and friction factor with the values obtained
from Modified Dittus-Boelter equation and Blasius equation. The mathematical correlations for
Nusselt number and friction factor are determined by using MATLAB software. The correlations are
helpful to know how much a parameter affects the heat transfer and friction factor of the apparatus.
II. EXPERIMENTAL APPARATUS
An experimental setup was designed and fabricated in order to carry out experimental
investigation on heat transfer and flow characteristics of smooth as well as roughened duct used in
solar air heaters. The actual experimental setup is as shown in figure 1. A rectangular plywood duct
with interior dimension of 2400 x 150 x 15mm3
is virtually divided into three sections.
Fig.1 Actual setup of experiment

3. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),
ISSN 0976 – 6359(Online), Volume 6, Issue 4, April (2015), pp. 35-44© IAEME
37
They are entry, exit sections with length 800, 600 mm which are more than the ASHRAE
designated minimum standards i.e., WH5 , and WH5.2 respectively and the test section with
length 1000mm. The other dimensions of design are determined by initially fixing the length of the
test section. An aspect ratio of 8-15 is observed to be optimum for maximum heat transfer rate of
solar air heater as per previous researchers. So the aspect ratio of the duct is chosen to be 10.
Calibrated Copper-Constantan 28ASWG thermocouples were used to measure the air and heated
plate temperatures at different locations. A digital micro voltmeter is used to indicate the output of
the thermocouples. An electric heater made of Nichrome wire and Asbestos sheet acts as a substitute
to solar energy. A centrifugal blower is coupled with the shaft of single phase induction motor which
runs at 2800rpm. A by-pass valve is attached between the duct and the centrifugal blower for the
purpose of changing the mass flow rate. The mass flow rate and the pressure difference across the
duct are measured using two U-Tube manometers of least count 0.01mm. The duct is insulated by
using glass wool. A schematic diagram has shown in figure 2 and 3.
Fig.2 Schematic diagram of setup
ABSORBER PLATES
Absorber plate is made up of Aluminium plate of 6mm thickness. Roughness is created by
vertical CNC milling machine with triangular protrusions shape of 3mm rib height on the absorber
plate. Different plates with triangular protrusions having different apex angles and the base of the
protrusions (6mm) are same for all plates.
Fig.3 Cross-sectional view of the solar air heater

4. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),
ISSN 0976 – 6359(Online), Volume 6, Issue 4, April (2015), pp. 35-44© IAEME
38
Fig.4 Rough plates of different apex angles
III EXPERIMENTATION
The setup is checked and instrumentation is fixed. At the beginning of the experiment the
heat input is given and the valve is closed for the natural convection to take place. As the
temperature rise up to the safe working limit, the centrifugal blower is turned on. The temperature
values are collected when the forced convection is taking place at steady state and the mass flow rate
of the air is changed by means of by-pass valve. Likewise the experiment is repeated again for
different plates.
The following parameters were measured during the experiments as shown in Table-1
1. Pressure drop across the orifice plate by inclined U-tube manometer.
2. Pressure drop across the duct by using manometer.
3. Inlet air temperature of collectors by using digital milivoltmeter and thermocouples.
4. Outlet air temperature of collectors
5. Temperature of plate.
TABLE-1 EXPERIMENTAL CONDITION
Parameter Values
Reynolds Number (Re)
Roughness height (e)
Relative roughness height (e/Dh)
Relative roughness pitch (p/e)
Heat Flux (1)
Plate Material
Thickness of Plate
Channel Aspect ratio (W/H)
Test Length
Hydraulic Diameter
10500 – 12000
3 mm
0.11
8.333
1000 W/m2
Aluminium plate
6 mm
10
1000mm
40mm

5. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),
ISSN 0976 – 6359(Online), Volume 6, Issue 4, April (2015), pp. 35-44© IAEME
39
IV. DATA REDUCTION
Mean air and plate temperature
Tfav = (ti+t0av)/2
Pressure drop calculation
∆p = ∆h x 9.81 x ∆m x 1/5
Mass flow rate
])1/0(1/([2 2
0 AAPAm −∆= ρ
Velocity measurement
V = m/ρwH
REYNOLDS NUMBER
Re=VDh/v
HEAT TRANSFER COEFFICIENT
Qa = mcp (t0-ti)
Qa - Heat transfer rate
H = Qa/Ap (tpav/tfav)
NUSSELT NUMBER
Nu = hDh/k
FRICTION FACTOR
f=δp Dh/2ρLV2
THERMO HYDRAULIC PERFORMANCE
ε=(Nur/Nus) / (fr/fs)
VALIDATION TEST
Nusselt number and Friction factor determined from the expermental data and smooth duct
were compared with those obtained from the modified Dittus-Boelter equation (1) and modified
Blasius equation (2) for Nusselt number and friction factor respectively and found satisfactory.
MODIFIED DITTUS BOELTER EQUATION
2.0
4.08.0 2
.Pr.Re.023.0
−






=
h
av
s
D
R
Nu (1)
Where = (1.156+H/W-1)/(H/W)
MODIFIED BLASIUS EQUATION
25.0
Re.085.0 −
=sf (2)

6. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),
ISSN 0976 – 6359(Online), Volume 6, Issue 4, April (2015), pp. 35-44© IAEME
40
Fig.5 Comparison of experimental and predicted values of Nusselt number for smooth duct
Fig.6 Comparison of experimental and predicted values of Friction factor for smooth duct
V. DEVELOPMENT OF NUSSELT NUMBER AND FRICTION FACTOR
CORRELATIONS
The mathematical correlations for the Nusselt number and the friction factor are determined
by using MATLAB software. The correlation is a functional relation containing all the independent
parameters which affect the heat transfer rate and friction factor. These correlations help us to predict
the heat transfer rate and friction factor at any other values of the affecting parameters. The
correlations obtained are:
Nu = Rea
Prb
Tan αc
Where a = 1.1853, b = 19.3005, c = -0.0955
f = Red
Tan αe
Where d = 0.1961, e = 0.0040
0
10
20
30
40
50
60
70
80
90
10800 11000 11200 11400 11600 11800
Nu(experimental)
Nu(theoretical)
NusseltNumber
Reynolds number
0
0.001
0.002
0.003
0.004
0.005
0.006
10900 11000 11100 11200 11300 11400 11500 11600 11700 11800
f(experimental)
f(theoretical)
ReynoldsNumber
FrictionFactor

7. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),
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VI RESULTS AND DISCUSSION
Fig. 7 Plate and Air Temperature difference Vs Length of the plate at Mass flow rate 0.0176kg.s-2
Fig. 8 Plate and Air temperature difference Vs Length of the plate at Mass flow rate 0.0176 kg.s-2
Fig. 9 Plate and Air temperature difference Vs Length of the plate at Mass flow rate 0.0182kg.s-2
Fig. 7, 8 and 9 graphs are drawn by taking Tplate – Tair on y-axis and length of the absorber
plate on x-axis. From graphs it can be observed that the temperature difference is high for the plate
with 450
apex angle protrusion and 600
plate has next highest temperature difference values.
Temperature difference increases with increase in length of absorber plate. For better efficiency the
length of the plate is taken as 1m. If it is more than 1m the temperature difference would not raise
and if less than 1m, we may lose heat and flow.

8. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),
ISSN 0976 – 6359(Online), Volume 6, Issue 4, April (2015), pp. 35-44© IAEME
42
NUSSELT NUMBER VS REYNOLDS NUMBER
Fig. 10 Nusselt number Vs Reynolds number
Fig.10 Shows the variation of Nusselt number with Reynolds number for smooth plate and
for the plates with different apex angle protrusions like 30, 45 and 600
. Generally Nusselt number
increases with increase in Reynolds number. Nusselt number for 300
and 600
are nearly same.
However, in exceptional case it is seen that Nusselt number for 300
plate is 7% higher when
compared to 600
plate. From graph it is seen that Nusselt number is highest for the plate with 450
apex angle protrusion and least for the smooth plate.
FRICTION FACTOR VS REYNOLDS NUMBER
Fig. 11 Friction factor Vs Reynolds number
Fig.11 shows the variation of friction factor with Reynolds number for smooth plate and for
the plates having 300
, 450
and 600
apex angle protrusions. From graph it can be seen that friction
factor is highest at lower Reynolds number and decrease with an increase in Reynolds number values
for all plates. The frictional factor seems to be highest for the plate with protrusions of an apex angle
600
.

9. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),
ISSN 0976 – 6359(Online), Volume 6, Issue 4, April (2015), pp. 35-44© IAEME
43
THERMO-HYDRAULIC PERFORMANCE VS REYNOLDS NUMBER
Fig. 12 Reynolds number Vs Thermo-Hydraulic Performance
Fig.12. It is observed that the 450
plate has highest Thermo-Hydraulic Performance. The
Thero-Hydraulic Performance is least for the 600
plate. The Thermo-Hydraulic Performance of the
300
plate is slightly more than that of 600
plates.
VII CONCLUSION
1. It is concluded that the 450
plate has given maximum Heat Transfer rate of 109 which is 42%
higher than that of the smooth plate. While the enhancement of heat transfer rate is minimum
for 600
plate whose lease Nusselt Number value is 81.
2. The maximum value of friction factor is obtained for the 450
plate which is 6.7x10-3
while
that of the smooth plate 5.4x10-3
.
3. The Thermo-hydraulic performance value of 450
plates is maximum that is 1.73 and
minimum for the 600
plate which is 1.2.
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