Applied Thermal Engineering 116 (2017) 100–109

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Applied Thermal Engineering

journal homepage: www.elsevier.com/locate/apthermeng

Research Paper

Experimental investigation and optimization of impinging jet solar

thermal collector by Taguchi method
Ranchan Chauhan a,⇑, Tej Singh b, Nitin Kumar a, Amar Patnaik c, N.S. Thakur d
a
Faculty of Engineering and Technology, Shoolini University, Solan, HP 173229, India
b
Department of Mechanical Engineering, Manav Bharti University, Solan, HP 173229, India
c
Department of Mechanical Engineering, M.N.I.T. Jaipur, Rajasthan 302017, India
d
Centre for Energy and Environment, N.I.T. Hamirpur, HP 177005, India

h i g h l i g h t s

Taguchi optimization of control factors is implemented in solar thermal collectors.

Contribution ratio of each control factor has been evaluated.

Performance index is evaluated as a quality index measure of energy delivered.

Effective energy delivery in solar collectors decreases beyond Re of 14,000.

Taguchi method is powerful tool for parametric optimization based upon MCDM.

a r t i c l e i n f o a b s t r a c t

Article history: In this paper, an experimental investigation has been carried out to study the influence of geometrical
Received 2 September 2016 variations of impinging air jets on heat transfer and fluid friction in a solar thermal collector. Taguchi
Revised 27 November 2016 based design of experiment approach has been applied to optimize the parameters which is apposite
Accepted 9 January 2017
for an optimal design towards efficient energy conversion. In total sixteen experimental runs have been
Available online 10 January 2017
performed on three main control factors viz. jet diameter ratio, streamwise and spanwise pitch ratio each
having three levels of operation. The heat transfer and fluid friction behaviour have been studied along
Keywords:
with the thermohydraulic performance in terms of performance index which plays simultaneously both
Solar thermal collector
Taguchi
these criteria. The results show that the geometric variations significantly affect the performance of
Performance Index impinging jet solar thermal collector. The investigation reveals that the jet diameter ratio contributes
Optimization the most towards overall performance with contribution ratio of 48.86% followed by spanwise pitch ratio
and streamwise pitch ratio with contribution ratio of 41.61% and 9.53% respectively. Finally, an optimal
design combination of an impinging jet solar thermal collector has been obtained with an improvement
of 37–48.3% at Reynolds number in the range 4000–16,000.
Ó 2017 Published by Elsevier Ltd.

1. Introduction Some of the major applications include heating and cooling in food
industries, cooling of heated components in gas turbine engines,
Single phase heat transfer has been an area of great importance solar heat absorbers, drying in paper industries, annealing metal-
which demands an extensive research attention. Several cooling lurgy, steel or glass industry to temper the products after rolling.
techniques have been investigated to dissipate the undesired accu- The literature suggests that the flow required from an impinging
mulation of heat flux in several applications such as electronic jet device for a required heat transfer coefficient may be two orders
equipments [1], solar collectors [2], nuclear power [3] and boiler of magnitude smaller than that required for a cooling approach
industry [4]. The impinging air jets are extensively being used in using free wall parallel flow [5]. Several authors have studied the
many industrial and commercial applications in order to enhance heat transfer characteristics of single/multiple jet arrays. Wang
the rate of heat transfer in cooling, heating, drying processes, etc. et al. [6] performed an experimental investigation to study the
effect of vortex generators on heat transfer placed in the cross flow
channel upstream of the jet exit. Hosain et al. [7] studied the heat
⇑ Corresponding author. transfer by turbulent water jets impinging on hot flat steel plates
E-mail address: ranchanc85@gmail.com (R. Chauhan).

http://dx.doi.org/10.1016/j.applthermaleng.2017.01.025
1359-4311/Ó 2017 Published by Elsevier Ltd.
 R. Chauhan et al. / Applied Thermal Engineering 116 (2017) 100–109 101

Nomenclature

Aom area of orifice meter (m2) DPd pressure drop across test section (Pa)
Aap surface area of absorber plate (m2) DPom pressure drop across orifice meter (Pa)
Cd coefficient of discharge Qu useful heat gain (W)
Cp specific heat of air (J/kg K) Tfi temperature of fluid at inlet (K)
Dhd hydraulic diameter (m) Tfo temperature of fluid at outlet (K)
Dj diameter of jet (m) Tpm mean temperature of absorber plate (K)
fc friction factor for conventional solar thermal collector Tfm mean temperature of fluid (K)
ffij friction factor for solar thermal collector with impinging V velocity of air in the channel (m/s)
air jets X streamwise pitch (m)
h heat transfer coefficient (W/m2 K) Y spanwise pitch (m)
kf thermal conductivity (W/m K)
Ld length of the test section (m) Greek symbols
^
m mass flow rate (kg/s) qair density of air (kg/m3)
Nuc Nusselt number for conventional solar thermal collector b ratio of orifice diameter to pipe diameter
Nuij Nusselt number for solar thermal collector with imping-
ing air jets

at temperature lower than the boiling point so as to understand the inserts using Taguchi grey relation analysis. Investigation of heat
convective heat transfer phenomenon. Chauhan and Thakur [8,9] transfer from a surface equipped with rectangular blocks has been
developed heat transfer and friction factor correlations in a solar reported by Bilen et al. [17] using Taguchi method to study the
air flow channel with jet impingement air flow. Huang et al. [10] effect of geometric position of wall mounted rectangular blocks
studied the effect of Reynolds number varied between 800 and on heat transfer and concluded that the most efficient parameter
1700 of mixture of air / butane and the distance between nozzle is Reynolds number followed by angular disposition. Wang et al.
and plate on heating performance of the flame. Craft et al. [11] mod- [18] optimized the structure of H-type finned tube heat exchanger
eled flow and heat transfer from a row of round jets impinging onto using Taguchi method and also the influence of geometric param-
a concave semicircular surface to reproduce important flow fea- eters was reported. The parametric optimization of overlapped
tures found in internal turbine blade cooling applications. In the helical baffled heat exchangers as reported by Du et al. [19] using
entire above research studies the objectives have been concerted Taguchi method concluded that the overlap size has the most sig-
in investigating the characteristics of heat transfer and friction nificant effect on the comprehensive performance among all other
behaviour related to the particular application. The enhancement parameters. Sholahudin and Han [20] used simplified dynamic
in heat transfer is accompanied by generous increase in frictional neural network model to predict heating load of a building using
losses inside the fluid flow channel and both of these factors depend Taguchi and analysis of variance (ANOVA) method which reduced
upon the geometric configuration and operating flow Reynolds the number of input parameters. Aghaie et al. [21] proposed a
number. Where the first factor i.e. the rate of heat transfer is desir- general optimized geometry of angled ribs for enhancing the
able for the efficient output from the system, the other factor is thermo-hydraulic behaviour of a solar air heated channel using
unpleasant and needs to be at its lowest possible value. This very Taguchi approach. The results concluded that the rib relative pitch,
objective of determining the set of conditions where the desired rib height, rib tip width and rib front projection have the most
value is placed at its highest level and the undesired at its lowest, influence on thermohydraulic performance of the solar air flow
confronts a study which lay down the set of parameters that deliv- channel.
ers maximum energy output from the energy conversion system The present study is intended to investigate the effect of
and proves its superiority. The selection of such an optimal param- diameter of the jet, streamwise and spanwise pitch between the
eter set demands an uncomplicated, procedural and practical jets on the performance of the impingement air flow in impinging
method to steer the design engineers to consider a number of per- jet solar thermal collector. The influence of the individual parame-
formance defining criterions and their interrelationships. ters on the comprehensive performance is also discussed so as to
The Taguchi approach is a statistical approach pioneered by Dr. come out with an optimum geometrical configuration which will
Genichi Taguchi which specified three situations (i) larger the bet- place the desirable heat transfer at its higher level corresponding
ter, (ii) smaller the better and (iii) on-target, minimum variation. to the lowest of frictional losses inside the channel. Since, the
Taguchi is being used extensively in many engineering applications quantitative estimation of the above factors is quite extensive,
to go for best experimental design and optimize the parameters which amplify the experimental cost and time, thus the design of
based upon the above specified conditions. Studies have reported experiments is carried out using Taguchi approach followed by
the supremacy of the Taguchi method in number of engineering the percentage contribution of the parameter influence over
applications. Singh et al. [12] studied tribological properties of performance criterions. Also, the investigation is extended to carry
nanoclay filled friction composite materials using Taguchi design out the confirmation of the experimental results. Being affirmed of
of experiment approach. The techno-economic appraisal of ground the experimental results, the validation of the optimal combination
source heat pump has been carried out by Esen et al. [13,14] for of the control factors has been carried out at an entire Reynolds
space heating using Taguchi approach. Turgut et al. [15] optimized number range of operation of solar thermal collectors.
the concentric heat exchanger with injector turbulators using
Taguchi method to study the effect of heat transfer and pressure
loss of injector shaped turbulator having different angle, diameter 2. Experimental details
and number and found optimal operating conditions for heat
transfer and pressure loss. Chamoli et al. [16] carried optimization The experimental test set up used in the present study is a
studies inside the heat exchanger tubes with perforated disc rectangular channel employing impinging air jets with forced
102 R. Chauhan et al. / Applied Thermal Engineering 116 (2017) 100–109

convection flow. The total length of the rectangular channel is and optimization in impinging jet solar thermal collector. These
2.4 m which is alienated into the entrance segment, test segment parameters have been optimized in order to obtain the set of jet
and the exit segment measuring 0.6 m, 1.4 m and 0.4 m respec- plate parameters which suggest the maximum heat transfer with
tively [22]. The experimental set up comprises of rectangular woo- minimum friction losses inside the impinging jet air flow passage.
den air flow channel, micro-manometer, electric heater, variable During experimentation four values of air flow rate was used for
transformer, ammeter, thermocouples, GI pipe, orifice meter, U- each set of jet plate parameters. The experimental value of the
tube manometer, control valves and blower as its main compo- parameter was recorded once the system attained a steady state
nents, shown in Fig. 1a. The location of spanwise and streamwise condition. The parameters recorded for the set of readings were:
pitch on the jet plate is shown in Fig. 1b. A consistent heat flux is
provided by an electric heater, fabricated by uniting the series (a) Pressure drop across the test section (DP).
and parallel loops of nichrome wire of size 1.4  0.29 m placed (b) Pressure drop across the orifice plate (DP). Temperature of
on top side of the test segment and other three sides insulated. the absorber plate (Tpm). Temperature of air at inlet (Tft)
To maintain a specific voltage, a variable transformer and an and outlet (Tfo) of the test segment.
ammeter is connected to measure the current flowing through
the circuit. A 0.5 mm thick mica sheet is sandwiched between The values of the essential parameters were used to figure out
the nichrome wire and the asbestos sheet of 5 mm thickness so the values of fundamental process parameters based upon which
as to prevent back heating from the heater. To minimize the ther- the performance defining criterions were evaluated. The process
mal losses from the electric heater, its backside was insulated with parameters viz. the mass flow rate of air through the channel, use-
75 mm thick glass wool. The heater was placed 25 mm above ful heat gain, convective heat transfer coefficient, Nusselt number
absorber plate with help of wooden spacers. For measuring the and friction factor were determined as follows:
temperature of the absorber plate over which the radiations are

0:5
being concentrated, fifteen thermocouples were attached by dril- 2qair;0 DPom
ling grooves over it. Also, to measure the temperature of the air ^ ¼ C d Aom
The mass flow rate; m ð1Þ
1  b4
at inlet and outlet, three thermocouples both at entry and exit seg-
ment were suspended at midway of the channel height. In totality,
21 thermocouples were used to measure the temperatures at dif- ^ p ðT fo  T fi Þ
The useful heat gain; Q u ¼ mC ð2Þ
ferent locations. The thermocouples are attached to the tempera-
The convective heat transfer coefficient,
ture scanners to display the temperature having least count of
0.1 °C. The micro-manometer (DP-Calc 5825) having a least count h ¼ Q u =½Aap ðT pm  T fm Þ ð3Þ
of 0.1 Pa is used to measure the pressure drop transversely of the
test segment which ensures the power penalty from the centrifugal
blower attached at the other end. To record the mass flow rate of hDhd
The Nusselt number; Nu ¼ ð4Þ
the air inside the channel, the orifice meter is used attached with kf
U-tube manometer which contains iso-propyl alcohol as a mano-
metric fluid. Gate valves at inlet and outlet of the blower were
DPd Dhd
placed to control the flow Reynolds number. The friction factor; f ¼ ð5Þ
2qair Ld V 2air
2.1. Experimental modus operandi For computation of the above process parameters, the thermo-
physical properties of the air flowing through the channel such as
The system parameters viz. jet diameter, streamwise pitch density, viscosity, and specific heat were obtained from the text of
spacing, spanwise pitch spacing are apposite experimental design Duffie and Beckman [23] at mean bulk fluid temperature.

Fig. 1a. Schematic diagram of the experimental test rig.

 R. Chauhan et al. / Applied Thermal Engineering 116 (2017) 100–109 103

Fig. 1b. Spanwise and streamwise pitch on the jet plate.

2.2. Experimental uncertainty 4. Mass flow rate of air

" 2  2  2  2 #0:5
dm^ dC d dAom dqa dðDPÞom
The experimental value obtained during investigation may dif- ¼ þ þ þ ð12Þ
m^ Cd Aom qa ðDPÞom
fer from its true value because of presence of lot of factors which
come into play while evaluation and recording. The deviation of 5. Useful heat gain
the measured value from the true value is the uncertainty in mea- "   2  2 #0:5
surement. The measurement uncertainty of various important dQ u dm_ 2 dC p dðDT f Þ
¼ þ þ ð13Þ
quantities has been evaluated and is in control limits. The proce- Qu _
m Cp DT f
dure for computation of uncertainty is discussed below [24]:
6. Heat transfer coefficient
The uncertainty in measurement of ‘‘y” when the parameter is " 2  2   #0:5
calculated using specific measured quantities is given by: dh dQ u dAap dðDT f Þ 2
¼ þ þ ð14Þ
" 2  2  2  2 #0:5 h Q Aap DT f
@y @y @y @y @y
¼ @x1 þ @x2 þ @x3 þ   þ @xn
y @x1 @x2 @x3 @xn 7. Nusselt number
" 2  2  2 #0:5
ð6Þ dNuij
¼
dh
þ
dDhd
þ
dkf
ð15Þ
Nuij h Dhd kf
where dx1, dx2, dx3, . . . , dxn are the possible errors in measurement of
x1, x2, x3, . . . , xn. The term dy is absolute uncertainty and dy/y the rel- 8. Reynolds Number (Re)
ative uncertainty. The uncertainty associated with various instru- "   2  2  2 #0:5
2
dRe dV dqa dDhd dl
ments used in measurement is shown in Table 1. The uncertainty e¼ þ þ þ ð16Þ
in measurement of various quantities is computed as: R V qa Dhd l
9. Friction factor (frs)
1. Area of absorber plate, flow and orifice meter "   2  2  2  2 #0:5
" 2  2 #0:5 2
df ij dV dqa dDhd dL dðDPÞd
dAap W  dL L  dW ¼ þ þ þ þ
¼ þ ð7Þ f ij V qa Dhd L ðDPÞd
Aap W L W L
ð17Þ
" 2  2 #0:5
dAflow dW dH The uncertainty analysis has been carried out for complete test
¼ þ ð8Þ run for single geometry and the range of uncertainty of each quan-
Aflow W H
tity obtained in presented in Table 2.
P
dAo d0  dd0
¼ 2
P 2 ð9Þ 3. Experimental design
Ao d0
4

2. Hydraulic diameter The Taguchi based approach is one of the most healthy design

 2  2 0:5 and optimization method, which evaluated the control factors dis-
dDhd
dH
 dH þ dDhd
dW
 dW cretely to achieve the optimal design values. The Taguchi method
dDhd
¼ ð10Þ paves its way firstly by selecting the objectives which are to be
Dhd 2  ðW  HÞðW þ HÞ1
accomplished such as the performance defining criterions (PDCs)
3. Density which specify the desired system output. Based upon the
" 2   #0:5
dqa dPatm dT fo 2 objectives, the control factors are then determined which may
¼ þ ð11Þ affect the objectives being set. The control factors are assured with
qa Patm T fo
varying levels of operation. These specified control factors and

Table 1
Uncertainty intervals of various measurements. Table 2
Range of uncertainty in the measurement of essential parameters.
Measurement Instrument Uncertainty
S. No. Parameters Error range, %
Dimensions Vernier calliper ±0.02 mm
Steel rule ±1 mm 1. Mass flow rate ±1.73
2. Useful heat gain ±2.23
Pressure loss Micro-manometer ±0.1 Pa
3. Heat transfer coefficient ±2.29
U-tube manometer ±1 mm
4. Nusselt number ±2.42
Temperature Thermocouple ±0.1 °C 5. Friction factor ±3.06
104 R. Chauhan et al. / Applied Thermal Engineering 116 (2017) 100–109

Table 3
Levels for various control factors used in the experiment.

Control factor Level

I II III IV
A: Jet diameter ratio (Dj/Dh) 0.043 0.065 0.087 0.109
B: Streamwise pitch ratio (X/Dh) 0.435 0.869 1.304 1.739
C: Spanwise pitch ratio (Y/Dh) 0.435 0.652 0.869 1.304

their levels undergo the numerical tests which are arranged in an 3.2. Control factors and levels
orthogonal array followed by the signal to noise ratio (SNR) analy-
sis. The influence of the control factors on the objectives are then The control factors pertaining to the impinging jet solar thermal
evaluated on the main-effect plots so as to determine the optimal collector are characterized as: jet diameter ratio, streamwise pitch
location of the control factors. Finally the confirmation tests are ratio and spanwise pitch ratio. The levels for various control factors
performed which prove that the interactive effect among the con- used in the experiment are illustrated in Table 3. These levels are
trol factors is negligible. selected consistently within the rational series of the control fac-
tors where the performance variation can be affected in terms of
3.1. Performance defining criteria (PDCs) performance index.

In the very first step of Taguchi method, PDCs are specified

which are to be optimized (maximized or minimized). The heat 3.3. Analysis of signal to noise ratio (SNR)
transfer from the heated absorber surface and the fluid friction
inside the channel are both pertinent to evaluate the performance In order to enhance the statistical properties for the purpose of
of solar thermal collectors. Thus, these two quantities specified as optimization, the experimental data is transformed into SNR based
Nuij and ffij are employed as the main targets to quantify the heat upon logarithmic data transformations which are then interpreted.
transfer and the friction behaviour of the impinging jet solar ther- The orthogonal array has been customized which helps in reducing
mal collector. As a noteworthy, it is well known that the heat trans- the number of experimental runs by compounding diverse levels of
fer increases with increasing fluid flow rate. However, this increase the diverse control factors and thus is a vital part of the Taguchi
in heat transfer is escorted with high increase in fluid friction too. method. The set of orthogonal arrays stipulates the way of per-
Thus, it becomes a very tedious task to intensify simultaneously forming the minimal number of experiments which give full infor-
both the objectives. A dimensionless number viz. the performance mation of all the factors affecting performance parameter and
index evaluates the overall thermal-hydraulic performance, in thereby saves the time and the resources. The crux of the orthogo-
which both Nuij and ffij is taken into account simultaneously. This nal arrays method lies in choosing the level combinations of the
dimensionless number is expressed as: input design variables for each experiment. In the present study,
the impact of three control factors has been studied using L16
Nuij =Nuc orthogonal design. In conventional full factorial experiment design,
PI ¼ ð18Þ
0:333
ðffij =ffc Þ it would require 34 = 81 runs to study three different factors each
with four levels, whereas, Taguchi’s factorial experiment approach
where Nuc and ffc are Nu and ff of the conventional solar thermal reduces it to only 16 runs offering a great advantage in terms of
collector respectively. Thus, in all, the three objectives are selected experimental cost and time. This is because in the orthogonal array
so as to facilitate the optimization of flow and geometric parame- the levels corresponding to each control factor are equally com-
ters in an impinging jet solar thermal collector using Taguchi based bined with the levels of other factors. As per the specific situations
approach. Where Nuij and ffij describes the thermal and hydraulic of Taguchi method, the transformations are; higher-the-better,
components and aids to elucidate how the heat and flow character- lower-the-better and nominal-the-best. Higher-the-better and
istics of solar thermal collector are influenced by various factors, PI lower-the-better are applicable where the objective is desired to
optimizes the overall thermal and hydraulic performance as a inclu- be as large as possible and as small as possible respectively
sive performance evaluation criterion. whereas nominal-the-best is applicable where the objective is

Table 4
Experimental design with SNR.

Ex. Run A B C Nuij SNR ffij SNR PI SNR

1 0.043 0.435 0.435 72.8654 37.2504 0.0120 38.3853 1.5251 3.6660
2 0.043 0.869 0.652 88.0686 38.8964 0.0198 34.0614 1.5617 3.8721
3 0.043 1.304 0.869 103.6004 40.3072 0.0258 31.7741 1.6829 4.5212
4 0.043 1.739 1.304 110.4224 40.8611 0.0336 29.4749 1.6424 4.3095
5 0.065 0.435 0.652 81.5879 38.2325 0.0135 37.3850 1.6434 4.3149
6 0.065 0.869 0.435 80.8121 38.1495 0.0166 35.5916 1.5196 3.6348
7 0.065 1.304 1.304 116.6664 41.3389 0.0272 31.3149 1.8621 5.4000
8 0.065 1.739 0.869 111.8296 40.9711 0.0286 30.8712 1.7548 4.8845
9 0.087 0.435 0.869 76.3097 37.6516 0.0152 36.3902 1.4796 3.4028
10 0.087 0.869 1.304 91.2155 39.2014 0.0222 33.0679 1.5571 3.8462
11 0.087 1.304 0.435 83.1619 38.3985 0.0190 34.4336 1.4959 3.4981
12 0.087 1.739 0.652 94.1602 39.4773 0.0232 32.6843 1.5839 3.9944
13 0.109 0.435 1.304 77.4564 37.7811 0.0110 39.1619 1.6702 4.4553
14 0.109 0.869 0.869 82.0437 38.2809 0.0187 34.5574 1.4828 3.4217
15 0.109 1.304 0.652 80.8121 38.1495 0.0201 33.9443 1.4266 3.0862
16 0.109 1.739 0.435 79.2825 37.9835 0.0179 34.9294 1.4535 3.2483
 R. Chauhan et al. / Applied Thermal Engineering 116 (2017) 100–109 105

Table 5 contribution of each factor on the performance parameters was cal-

Response table for signal to noise ratios of Nuij. culated by using following steps:
Level A: (Dj/Dh) B: (X/Dh) C: (Y/Dh) Step-I: Calculation of SNR ratio - In this step the SNR is calcu-
1 39.33 37.73 37.95
lated for experimental results.
2 39.67 38.63 38.69 Step-II: Determination of overall mean SNR - In this step the
3 38.68 39.55 39.30 overall mean SNR (SNR) is determined by using following equation:
4 38.05 39.82 39.80
Delta 1.62 2.09 1.85
Rank 3 1 2 1 X16
SNR ¼ ðSNRÞi ð21Þ
16 i¼1

Table 6 Step-III: Determination of sum of squares - Here, the sum of

Response table for signal to noise ratios of ffij. squares (a) due to variation about the SNR is determined as
Level A: (Dj/Dh) B: (X/Dh) C: (Y/Dh) follows:
1 33.42 37.83 35.83
2 33.79 34.32 34.52 X
16
2
3 34.14 32.87 33.40
a¼ ððSNRÞi  SNRÞ ð22Þ
i¼1
4 35.65 31.99 33.25
Delta 2.22 5.84 2.58
For the ith process parameter, the sum of squares due to varia-
Rank 3 1 2
tion about the mean (ai) is

X
4
2
expected to be kept as a specific value to gain the best perfor- ai ¼ ððSNRÞij  SNRÞ ð23Þ
mance. In solar thermal collectors, Nuij and PI are desired to be j¼1
as large as possible whereas ffij should be at its minimum possible
Step-IV: Contribution percentage: Finally the percent contribu-
value. Thus, Nuij and PI are defined by higher-the-better character-
tion of individual process parameter can be calculated as:
istic and the ffij by lower-the-better characteristic and expressed
as: ai
Higher the better characteristic: Contribution; %i ¼  100 ð24Þ
a
 X 
1 1
SNR ¼ 10log10 ð19Þ
n h2
4. Results and discussion

Lower the better characteristic : SNR

 X  The experimental tests have been conducted in total of sixteen
1 runs to calculate the SNR each for higher and lower characteristics
¼ 10log10 h2 ð20Þ
n of Nuij, ffij and PI as shown in Table 4. The discerning analysis and
the ANOVA have been performed to finally reach out with an opti-
2
where n is the number of test runs and 
h represent the experimen- mized geometric configuration of impinging jet solar thermal
tal data obtained for optimization of control factors. Further, the collector.

Main Effects Plot for SN ratios

Data Means
Jet diameter ratio Streamwise pitch ratio
40.0
39.5
39.0
Mean of SN ratios

38.5
38.0

0.043 0.065 0.087 0.109 0.435 0.869 1.304 1.739

Spanwise pitch ratio
40.0
39.5
39.0
38.5
38.0

0.435 0.652 0.869 1.304

Signal-to-noise: Larger is better
Fig. 2. Effect of control factors on Nuij.
106 R. Chauhan et al. / Applied Thermal Engineering 116 (2017) 100–109

Main Effects Plot for SN ratios

Data Means

Jet diameter ratio Streamwise pitch ratio

38

36

34
Mean of SNratios

32
0.043 0.065 0.087 0.109 0.435 0.869 1.304 1.739
Spanwise pitch ratio
38

36

34

32
0.435 0.652 0.869 1.304
Signal-to-noise: Smaller is better
Fig. 3. Effect of control factors on ffij.

Table 7 Table 8
Contribution of process parameters on Nuij. Contribution of process parameters on ffij.

Process parameter SNR ai a % Contribution Process parameter SNR ai a % Contribution

(Dj/Dh) 38.9332 1.5490 6.1765 25.08 (Dj/Dh) 34.2517 2.8597 27.0066 10.59
(X/Dh) 2.7119 43.91 (X/Dh) 19.8468 73.49
(Y/Dh) 1.9156 31.01 (Y/Dh) 4.3001 15.92

4.1. Optimization of Nuij and ffij Table 9

Response table for signal to noise ratios of PI.

The intuitive analysis in a Taguchi based optimization studies Level A: (Dj/Dh) B: (X/Dh) C: (Y/Dh)
the response effects besides the contributing ratios of each control 1 4.092 3.960 3.512
factor under consideration. Based upon the experimental data and 2 4.559 3.694 3.817
the SNR characteristic equations, the response effects on Nuij and 3 3.685 4.126 4.058
ffij are evaluated as shown in Tables 5 and 6 respectively. The tables 4 3.553 4.109 4.503
Delta 1.006 0.433 0.991
show the output response of each factor at that specific level which
Rank 1 3 2
is the average the arithmetic mean value of SNR for each level of
each factor. The heat transfer and fluid flow behaviour inside the
impinging jet solar thermal collector fluid flow channel are charac-
terized by Nuij and ffij, where it becomes essential to study the [25,26]. The control factors viz. A, C also possesses great influence
influence of control factors on the PDC’s. The main effects plots on the PDCs. This can be explained on the basis of interference
for Nuij and ffij are shown in Figs. 2 and 3 respectively. The main effects that are created in the vicinity of the heat transferring sur-
effect plots are drawn based upon the average values of SNR for face. With increase in factor A up to 0.065 the interference is unli-
each PDC. It can be seen that both the PDCs have different depen- kely but beyond 0.065 the interference effects between the
dence on the control factors. Therefore it becomes essential to adjacent/surrounding jet aperture are significant which affects
determine the contribution of each control factor towards their the heat transfer and thereby the Nuij characteristics [27]. How-
respective PDCs. The contribution ratio of each control factor on ever, the effect on ffij characteristics is less because of decrease in
the PDCs is presented in Tables 7 and 8 respectively. From the blockage area towards decreasing values of factor A. The same
tables it is clear that the dependence of the control factors is differ- decreasing trend is observed for factor C with respect to ffij.
ent on different PDCs. Where the contribution ratio follows the Higher the value of SNR suggests the optimal level for the con-
order B > C > A in case of Nuij and is the same for ffij, the criterion trol factor. The optimal combination of the control factors with
Nuij is desirable whereas the criterion ffij is undesirable. Stream- respect to Nuij characteristics as visualized by the contribution
wise pitch ratio has the most significant effect on Nuij and ffij with ratio is A2B4C4. On the same table, the optimal combination of fac-
contribution ratio of 43.91% and 73.49% respectively. The main rea- tors with respect to ff is A4B1C1. The results here clarify that both
son is because of turbulence created inside the rectangular channel Nuij and ffij characteristics cannot be optimized simultaneously
which enhances the heat transfer and thereby the Nuij gets for the best overall optimum combination of the control factors.
enhanced. Also, with increase in turbulence the friction effects Therefore, PI has been finally targeted to be optimized which
are increased which thereby increases ffij to a large extent simultaneously evaluates Nuij and ffij characteristics so as to
 R. Chauhan et al. / Applied Thermal Engineering 116 (2017) 100–109 107

Main Effects Plot for SN ratios

Data Means
Jet diameter ratio Streamwise pitch ratio
4.50

4.25

4.00

3.75
Mean of SN ratios

3.50
0.043 0.065 0.087 0.109 0.435 0.869 1.304 1.739
Spanwise pitch ratio
4.50

4.25

4.00

3.75

3.50
0.435 0.652 0.869 1.304

Signal-to-noise: Larger is better

Fig. 4. Effect of control factors on PI.

Table 10 Table 11
Contribution of process parameters on PI. Results of the confirmation experiments.

Process parameter ai a % Contribution Optimum control parameters Error

SNR
Prediction Experimental
(Dj/Dh) 3.9723 0.6163 1.2614 48.86
(X/Dh) 0.1203 9.53 Nuij
(Y/Dh) 0.5249 41.61 Level A2B4C4 A2B4C4 %
Nu achieved 116.8011 118.0601 1.08
ffij
achieve an optimal design configuration for impinging jet solar Level A4B1C1 A4B1C1 %
ff achieved 0.0056 0.0058 3.57
thermal collector.
PI
Level A2B3C4 A2B3C4 %
4.2. Optimization of PI PI achieved 1.827 1.8621 1.92

The PI serves a basis of comparison based upon overall perfor-

mance of the solar thermal collectors because of its simultaneous Estimated value of Nuij, ffij and PI at optimum condition was calcu-
consideration of thermal and hydraulic effects taking place inside lated by adding the average performance to the contribution of
the fluid flow channel [28]. The response effects of PI are presented each parameter at the optimum level using the following equations
in Table 9. The mean effects plot for PI is shown in Fig. 4 which [29]:
shows the dependence of each control factor on PI. Also, the contri-   
bution ratio of each factor on PI is presented in Table 10. It is clear gNu ¼ T Nu þ ANu Nu Nu
2  T Nu þ B4  T Nu þ C 4  T Nu ð25Þ
from Table 10 that the jet diameter ratio and the spanwise pitch
ratio have the most significant effect on PI with 48.86% and   
41.61% respectively. The streamwise pitch has low contribution gff ¼ T ff þ Aff4  T ff þ Bff1  T ff þ C ff1  T ff ð26Þ
towards PI with 9.53%. Thus, the ranking of parameters follows
  
the following order based upon PI as: A > C > B. These geometric
gPI ¼ T PI þ API2  T PI þ BPI3  T PI þ C PI4  T PI ð27Þ
parameters are therefore necessary to consider their effects
towards optimization of impinging jet solar thermal collector.
where gNu, gff and gPI are the predicted average values and T Nu , T ff
and T PI are average experimental values for Nuij, ffij and PI respec-
4.3. Confirmation experiments
tively. ANu Nu Nu
2 ; B4 and C 4 are the average Nuij values for parameter

In design of experiment, the confirmation experiment is the A, B and C at their optimum levels. Aff4 ; Bff1 and C ff1 are the average
final step conducted to validate the interference drawn during ffij values for parameter A, B and C at their optimum levels.
the analysis phase. It is performed by considering the new set of API PI PI
2 ; B3 and C 4 are the average PI values for parameter A, B and C
factor settings A2B4C4 to predict Nuij, A4B1C1 to predict ffij and at their optimum levels. The experiments were performed on factor
A2B3C4 to predict PI. The results of confirmation tests conducted settings A2B4C4 to calculate Nuij, A4B1C1 to calculate ffij and A2B3C4
with the optimum design parameters are presented in Table 11. to calculate PI. The values of Nuij, ffij and PI obtained from these
108 R. Chauhan et al. / Applied Thermal Engineering 116 (2017) 100–109

Fig. 5. Validation of PI with Reynolds number at different combination of control factors.

experiments were then compared with their predicted values (Eqs. (Nuij) and minimize the losses due to friction (ffij). The control fac-
(25)–(27)) as shown in Table 11. It can be seen that the difference tors have been characterized as jet diameter ratio; streamwise
between experimental results and the predicted values is only pitch ratio and the spanwise pitch ratio. Following conclusions
1.259 for Nuij, 0.0002 for ffij and 0.0351 for PI indicating that the have been drawn based upon the results of the investigation.
experimental results are very close to the predicted results. This
corroborates the experimental results with the predicted results, 1. The heat transfer and fluid friction characteristics are very
with an error of 1.08% for Nuij, 3.57 for ffij and 1.92% for PI. much influenced by the geometric parameters (control factors)
viz. jet diameter ratio, streamwise pitch ratio and spanwise
4.4. Validation of optimal combination of control factors pitch ratio. The contribution ratio of each of these parameters
on heat transfer is 25.08%, 43.91% and 31.01% respectively and
The optimal combination of the control factors as investigated that of friction factor is 10.59%, 73.49% and 15.92% respectively.
using Taguchi approach is A2B3C4. This combination is compared 2. The order of factors which dominate the performance index, in
with other closely associated and randomly selected combinations terms of which the overall performance is assessed, is jet diam-
so as to prove its reliability over other combination sets. The clo- eter ratio > spanwise pitch ratio > streamwise pitch ratio. Each
sely associated combination A2B4C2 (Design 8) is selected which of these parameters is necessary to be determined towards
ranks just next to the optimal combination besides two randomly optimization of the overall system performance employing
selected combinations A2B3C4 and A1B3C3. All these combination impinging air jets. The contribution ratio of the order is
sets are validated at different Reynolds number values ranging 48.86%, 41.61%, 9.53% respectively.
4000–16,000. The variation in PI with Re at different combinations 3. An optimal geometric combination based upon heat transfer
of control factors is shown in Fig. 5. The figure represents that the and friction characteristics is A2B4C4 and A4B1C1 respectively,
optimal combination set has the highest value at all values of Rey- while the optimal configuration corresponding to thermohy-
nolds number. Compared to the conventional solar thermal collec- draulic performance in terms of performance index (PI) is
tor, an increase of 37–48.3% is achieved in a Reynolds number A2B3C4. Thus, it is necessary to determine the optimal perfor-
range from 4000 to 16,000. Also, the figure represents that at mance index pertaining to any system which involves the con-
higher Reynolds number (more than 14,000), the performance sideration of two or more criteria (heat transfer and fluid
index degrades which is due to the fact that at higher values of friction in this case) so that an efficient energy conversion
mass flow rate of air, the friction factor increases abruptly while may take place.
the increase in heat transfer is not too significant. It can be con- 4. The range of operation for impinging jet solar thermal collectors
cluded that with increase in Reynolds number beyond 14,000 the for high overall performance should be limited to flow Reynolds
useful thermal energy output is less compared to the increase in number of 14,000, beyond which the system will consume
pumping power requirement to maintain that desired mass flow more energy to propel the air through the channel and will deli-
rate. Thus, the operation of solar thermal collectors may be limited ver less thermal energy output.
to lower Reynolds number range; however the range of operation 5. Compared to the conventional solar thermal collector, an
may slightly vary from variation in system to system. increase in the thermohydraulic performance of 37–48.3% in
impinging jet solar thermal collector is achieved in a Reynolds
5. Conclusions number range from 4000 to 16,000.

In the present study an experimental design has been carried The Taguchi based optimization can be successfully applied to
out using Taguchi design of experiments upon which the Taguchi solar energy conversion processes where optimal control factors
analysis has been performed to come out with the optimal set of may be evaluated which maximizes the desired factor and mini-
control factors which would maximize the useful energy delivery mizes the undesired factor with simultaneous consideration.
 R. Chauhan et al. / Applied Thermal Engineering 116 (2017) 100–109 109

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