Journal of Power and Energy Engineering, 2013, 1, 53-57
http://dx.doi.org/10.4236/jpee.2013.15008 Published Online October 2013 (http://www.scirp.org/journal/jpee)
53
Optimum Inclination Angles of Booster Mirrors and Solar
Radiation Availability on the Horizontal and Inclined Box
Type Solar Cookers
V. P. Sethi1, K. Sumathy2, D. S. Pal3
1Department of Mechanical Engineering, Punjab Agricultural University, Ludhiana, Punjab India; 2Department of Mechanical Engi-
neering, North Dakota State University, Fargo, USA; 3Department of Mathematics, Statistics and Physics, Punjab Agricultural Uni-
versity, Ludhiana, Punjab India.
Received October 2013
ABSTRACT
Mathematical relations are developed to compute optimum inclination angle of booster mirror for horizontally placed
cooker (λ) and for optimally inclined cooker (ψ) during all months (selected day) of the year at 30˚N latitude for max-
imizing the reflected component of solar intensity onto the absorber plate of the cooker. A solar radiation model is also
developed and used to compute the ratio of various solar intensities on horizontal, inclined and normal surface of the
absorber plate for all months at 30˚N latitude. These ratios give a clear indication of greater solar rad iation availability
on the optimally inclined cooker as compared to the horizontally placed cooker for faster cooking especially during
winter months when solar radiation capture is small. Experimental validations have also been performed to access the
accuracy of the developed relations and model.
Keywords: Solar Radiation; Solar Cooker; Optimum Inclination; Booster Mirror
1. Introduction
Many important modular studies have been performed on
box type solar cookers till date to optimize their perfor-
mance. Transient analysis was performed to get the over-
all thermal performance of the box type solar cooker by
[1]. A box type solar cooker which could perform well in
clear sunny d ays was developed [2]. An obliqu e pan was
also designed for putting the food material in tilted posi-
tion. Parametric study of box type solar cooker was also
performed with and without booster mirrors called ref-
lectors [3]. Thermal performance of box type solar cook-
er was tested and a test procedure was developed to test
its performance using two figures of merit F1 and F2 [4].
An improved box type solar cooker with tilted absorb-
ing surface was developed but the problem of placing the
food material could not be solved [5]. Methods of testing
and evaluating the advanced version of the box-type so-
lar cooker were also developed [6]. A model for predic-
tion of the cooking power of a solar cooker based on
three controlled parameters (solar intercept area, overall
heat loss coefficient, and absorber plate thermal conduc-
tivity) and three uncontrolled variables (insolation, tem-
perature difference, and load distribution) was developed
[7]. The performance of solar cookers by analyzing the
previously collected data was also evaluated [8]. The role
of cooking vessel inside the cooker was established tak-
ing into consideration its lid and the bottom surface [9,
10]. Cooking vessel design in cylindrical shape of box
type was also improved and its heat transfer from the lid
was also made faster to the food material placed inside
the vessel [11,12]. A comparative experimental study of
a box type solar cooker with two different cooking ves-
sels was made [13]. Fins are shown to improve the heat
transfer from the internal hot air of the cooker towards
the interior of the vessel where the food to be cooked is
placed. An optimally inclined box type solar cooker with
modified cooking vessel design was presented [14]. The
performance of optimally inclined cooker was consis-
tently better as compared to conventional horizontally
placed cooker in terms of higher solar radiation availabil-
ity, absorber plate temperature, higher chamber tempera-
ture and lesser cooking time.
The review reveals that various researchers around the
world have developed many improved solar cooker de-
signs either by increasing the aperture (solar interception
area), by using multiple reflectors, by changing the incli-
nation of the solar cookers, by reducing the overall heat
transfer coefficient, by increasing the conductive heat
transfer of absorber plate and by modifying the cooking

Optimum Inclination Angles of Booster Mirrors and Solar Radiation Availability
on the Horizontal and Inclined Box Type Solar Cookers
54
vessel design. In this study, a mathematical model is de-
veloped to compute the optimum inclination angle of the
booster mirror for horizontally placed and inclined cook-
er for maximizing the reflected component of the solar
radiation for better performance during all months and
selected latitudes.
2. Description of Horizontal and Inclined
Box Type Solar Cookers
Two identical box type solar cookers of length 580 mm,
width 300 mm and height 155 mm each were fabricated
using galvanized iron sheet of 0.8mm thickness. One
cooker was kept in horizontal position on ground (Figure
1) while the other cooker was kept on an optimally in-
clined frame (Figure 2) in inclined pos ition. Each cooker
has two top glass covers of 4 mm thickness and a booster
mirror with a provision of altering the angle of inclina-
tion. A round shape cylindrical cooking vessel of 175 mm
diameter and 52 mm depth was placed inside the hori-
zontally placed cooker. The designed parallelepiped cook-
ing vessel was placed horizontally inside the inclined
cooker for greater heat transfer to the food material.
3. Mathematical Model for Optimum Tilt
Angle of the Booster Mirrors
3.1. Horizontally Placed Cooker
Optimum tilt angle of the booster mirror is computed for
all months and given latitude for maximizing the reflect-
ed radiation component onto the absorber plate.
In Figure 1, at the top edge A of the booster mirror
Figure 1. Horizontal cooker with booster mirror at opti-
mum inclined angle λ.
Figure 2. Inclined cooker with booster mirror at optimum
inclined an gle ψ.
λ + θz + i = 90˚ (1)
also
90CAB r∠ +=
(2)
from Equations (1) and (2)
z
CAB
λθ ∠=+
(3)
If ray Ir1 strikes the top of the inclined reflector mirror
at an angle λ + θz, then the line AC formed by reflected ray
Rr1 reac hi ng t h e ed ge of t he uppe r gl ass c ove r al so ha s the
same internal angle λ + θz, then in triangle ABC;
, 90
90 2
z
z
CAB ABC
and ACB
θλ λ
λθ
°
°
∠=+∠= ±
∠= −−
Also mathematically we know that
sin() sin(902)sin(90)
zz
BC ABAC
θλ λθ λ
°°
= =
+−− ±
(4)
Since AB= BC = W (width of the absorber plate)
sin() sin(90 2)
zz
WW
θλ λθ
°
=
+−−
(5 )
Equation (5) gi ves the value of optimum tilt angle of the
booster mirror λ for horizontally placed cooker ;
90 2
3
z
θ
λ
°
−
=
(6)
3.2. Optimum Tilt Angle of the Booster Mirror
for Inclined Cooker
Optimum tilt of the booster mirror (ψ) in case of north
facing reflector (Figure 2) of inclined solar water heater
was give n by [ 15] and is used for inclined cooker as
ψ = (π – β - 2ϕ + 2δ)/3 (7)
The declination angle “δ” is computed using the given
Equation (8)
360(284 )
23.45sin 365
n
δ
+

=

(8)
Booster
mirror angle λ
15.5 cm
8cm
43 cm
W=58cm
90±λ
λ
θz
θ
z
+λ
i
r
N o rmalto
t hep l aneof
reflection
Incident
ray,I
ri
R ef lecte
dray, R
ri
C
A
B
W
Glass wool
insulation
-λ+λ
North facing booste r
mirror
Ab so rbe r
plate
Parallelepiped
cooking v esse l
Double glass
co ve r
ψ
+ψ
-ψ
Inc ident
radiation
Ii
β, Inclined stand
Double ste p
frame

Optimum Inclination Angles of Booster Mirrors and Solar Radiation Availability
on the Horizontal and Inclined Box Type Solar Cookers
55
where “n” is the number of days starting from January 1.
4. Solar Radiation Model
Variation of effective width of the sun rays intercepted
by the absorber plate in horizontal and inclined position
of the cooker is shown in Figures 3(a) and (b).
In ΔABC
90
s
A α ∠= −
cos(90 )
hs
WW α =×−
(9)
Where αs can be computed using Equation (15).
Hourly solar radiation incident on the inclined surface
of the absorber plate depends upon the time of the day i.e.
the hour angle ω (zero at noon, negative in the morning
and positive in afternoon, varies by 15˚ after each hour),
nth day of the year (starts from Januar y 1) i.e. declination
angle δ, altitude angle αs with horizontal or zenith angle
θz with vertical and surface azimuth angle γ (in northern
hemisphere, it is zero for south facing surfaces, 180˚ for
north facing surfaces, −90˚ for east facing and +90 for
west facing surfaces), latitude angle
φ of a place and tilt
angle β of the s urface with horiz ont a l.
Zenith angle of sun on the inclined absorber plate θi is
given by [ 1 6]
1
cos[sin (sin coscos cos cossin )
cos (coscoscossin cos sin )
cos sinsinsin]
ifg
fg
g
θδ βδωβ
δωβ δβ
δ ωβ
−
= +
+−
+
(10)
Zenith angle of the sun with vertical (θz) and solar al-
titude angle (αs) with horizontal at any time of the day
and for any day of the year can be determined at any
specific latitude location is given b y [16].
(a) (b)
Figure 3. Variation of effective width of the sun rays inter-
cepted by the absorber plate in (a) horizontal and (b) in-
clined position.
1
cos(cos .cos .cossin.sin)
z
θφδ ωδφ
−
= +
(11)
ω = 15˚ (tsolar – 12) (12)
The hour angle is 15˚ times the number of hours from
solar noon. It is negative before noon, zero at noon and
positive after 12.
Intensity of extra terr es trial radiatio n Iext measure d on a
plane normal to the radiation on the nth day of the year,
360
10034cos365
ext sc
n
II .


= +



(13)
Value of direct normal solar radiation in terrestrial re-
gion depe nds upon t urbidity fa c tor Tr of atmosphere [17].
exp 0.9 9.4sin
r
n exts
T
II
α

−
= ×
+

(14)
Tr is known for different months and for different re-
gions [18].
αs = 90 − θz (15)
'cos
bn i
II θ =
(16a)
cos
hb nz
II θ =
(16b)
The amount of diffuse radiation available on the in-
clined surface can be known as (Tiwari, 2006)
''
'2
cos 1cos/ 2
sin
bi b
dd
ext sext
II
II
II
θβ
α


= +−
 



(17)
1( )cos
3
dext nz
I II θ = −
The reflected component of total radiation is then com-
puted as
'2
sin/2
R gh
I rI β =
(1 8)
Where “r” is the ground reflectivity (0.3)
gh
I
bd
II= +
(1 9)
On the horizontal surface of the absorber plate at solar
noon.
Total solar radiation falling on the inclined surface of
the absorber plate at solar noon is given by
Ii = Ib' + Id' + IR' (20)
A computer program in C++ is developed and used for
comput i ng the solar r adiati on flux on various surfa c e s.
5. Results and Discussion
5.1. Optimum Tilt Angles
Optimum tilt angles computed for winter and summer
months at 30˚N latitude are shown in Table 1. It shows
W
W
Absorber
plate in
inclined
position
β
Wh
h
W
i
Beam radiation
on inclined
surface (Iib)
Beam radiation
on normal
surface (In)
α
s
A
B
C
9
0
°
Beam radiation
on horizontal
surface (Ih)

Optimum Inclination Angles of Booster Mirrors and Solar Radiation Availability
on the Horizontal and Inclined Box Type Solar Cookers
56
that for horizontal cook er, optimum inclination angle λ is
3.3˚, 1.2˚ and 8.2˚ outwards (+) from the vertical position
(λ = 0˚) in October, February and March. It becomes
2.08˚, 5.6˚ and 4.2˚ inwards (−) from the vertical position
during November, December and January due to greater
solar zenith angle (θz). During summer, optimum inclina-
tion angle λ is 20.8 ˚, 11.2˚, 6.8˚, 8.9 ˚, 16.7˚ and 27.6˚. In
the case of inclined cooker, the optimum inclination an-
gle ψ in winter months is 18.5˚, 12.1˚, 9.4˚, 11.0˚ 16.3˚
and 23.3˚. This variation is much higher in summer
months as 41.5˚, 47.6˚, 50.6˚, 49.2˚, 44˚ and 36.2˚ for
maximization of reflected component.
5.2. Solar Radiation Capture Ratios
The ratio Wh/Wi is 0.62, 0.73, 0.84, 0.76, 0.65 and
0.60 during January, February, March, October,
November and December which shows that inter-
cepted width for solar radiation capture is much
smaller for horizontal cooker as compared to in-
clined cooker. The ratio of solar radiation intensity
available on inclined to horizontal cooker (Ii/Igh) is
1.51, 1.33, 1.15, 1.26, 1.45 and 1.66 during January,
February, March, October, November and Decem-
ber which sho ws that in clined cook er receives much
higher solar radiation intensity as compared to ho-
rizontal cooker in winter months. The variation of
horizontal versus normal surface and inclined ver-
sus normal surface also shows that inclined cooker
receives almost maximum possible radiation during
all months of t he year as the ratio is al ways close to
one. Whereas for horizontal cooker this variation is
0.59 to 1.00 during winter and summer months.
5.3. Experimental Validation
The Figure 4 shows that the measured and predicted
values of solar radiation intensities match well for hori-
zontal as well as for inclined surface of absorber plate
within 5% of the standard deviation. It shows that the
developed model is accurate enough for making correct
predictions for solar radiation availabilities at optimized
inclination angles.
Finally it can be concluded that inclined cooker has
much better solar radiation capture during winter months
for efficient cooking as compared to horizontally placed
cooker at 30˚N latitude.
Table 1. Optimum tilt angles computed for horizontal (λ) and inclined cooker (ψ) at 30˚N latitude during all months of the
year.
Winter Month and date, (n) Latitude (˚ N) 30 Summer Month and date, (n) Latitude (˚N) 30
θz λ ψ θz λ ψ
Oct. 15, (288) 40.1 03.3 18.5 Apl, 15, (105) 20.8 16.1 41.5
Nov. 15, (319) 49.3 −2.08 12.1 May 15, (135) 11.2 22.5 47.6
Dec. 15, (349) 53.5 −5.6 9.4 June 15, (166) 6.8 25.5 50.6
Jan. 15, (15) 51.3 −4.2 11.0 July 15, (196) 8.9 24.0 49.2
Feb. 15, (46) 43.2 1.2 16.3 Aug. 15, (227) 16.7 18.8 44.0
Mar. 15, (74) 32.7 8.2 23.3 Sept. 15, (258) 27.6 11.4 36.2
Table 2. Shows the ratios of intercepted widths for horizontal (Wh) and inclined cooker (Wi) and solar radiation intensities on
Horizontal (Igh), Inclined (Ii) and normal (In) surfac es for horizontal and incli ned cookers at 30˚N latitude during all months
of year.
Month and date, (Tr) Latitude 30˚N Month and date,(Tr) Latitude 30˚N
Wh/Wi Ii/Igh Ihb/In Ib׳/In Wh/Wi Ii/Igh Ihb/In Ib׳/In
Jan. 15, (3.1) 0.62 1.51 0.62 0.99 July 15, (4.3) 1.00 1.00 0.99 0.99
Feb. 15, (3.2) 0.73 1.33 0.73 1.00 Aug. 15, (4.2) 0.95 1.04 0.96 0.99
Mar. 15, (3.5) 0.84 1.15 0.84 1.00 Spt. 15, (3.9) 0.88 1.08 0.88 0.97
Apl, 15, (3.9) 0.93 1.05 0.93 1.00 Oct. 15, (3.6) 0.76 1.26 0.76 0.98
May 15, (4.1) 0.98 1.02 0.98 1.00 N ov. 15, (3.3) 0.65 1.45 0.65 0.99
June 15, (4.2) 1.00 1.00 0.99 0.99 Dec. 15, (3.1) 0.60 1.66 0.59 0.99

Optimum Inclination Angles of Booster Mirrors and Solar Radiation Availability
on the Horizontal and Inclined Box Type Solar Cookers
57
Figure 4. Measured and predict ed sol ar r adi ation i nte nsit ie s
on the horizontal and inclined surfaces of absorber plate on
15th March, 2012.
REFERENCES
[1] Y. S. Yada v and G. N. Tiwari, “Transient Analytical St u-
dy of Box-Type Solar Cooker,” Energy Conversion and
Management, Vol. 27, No. 3, 1987, pp. 121-125.
http://dx.doi.org/10.1016/0196-8904(87)90064-1
[2] P. C. Pande and K. P. Thanvi, “Design and Development
of a Solar Cooker for Maximum Energy Capture in
Stationary Mode,” Energy Conversion and Management,
Vol. 27, 1987, pp. 117-120.
http://dx.doi.org/10.1016/0196-8904(87)90062-8
[3] B. A. Jubran and M. A. Alsaad, “Parametric Study of
Box-Type Solar Cooker,” Energy Conversion and Mana-
gement, Vol. 32, 1987, pp. 223-234.
http://dx.doi.org/10.1016/0196-8904(91)90126-4
[4] S. C. Mullick, T. C. Khandpal and A. K. Saxena, “Ther-
mal Test Procedures for Box Type Solar Cooker,” Solar
Energy, Vol. 39, 1987, pp. 353-360.
http://dx.doi.org/10.1016/S0038-092X(87)80021-X
[5] N. M. Nahar, “Performance and Testing of an Improved
Hot Box Solar Cooker,” Energy Conversion and Mana-
gement, Vol. 30, 1990, pp. 9-16.
http://dx.doi.org/10.1016/0196-8904(90)90051-Y
[6] M. Grupp, P. Montagne and M. Wackennagel, “A Novel
Advanced Box Type Solar Cooker,” Solar Energy, Vol.
47, 1991, pp. 107-113.
http://dx.doi.org/10.1016/0038-092X(91)90041-T
[7] P. A. Funk and D. L. Larson, “Parametric Model of Solar
Cooker Performance,” Solar Energy, Vol. 62, No. 1, 1998,
pp. 63-68.
[8] P. A. Funk, “Evaluating the International Standard Pro-
cedure for Testing Solar Cookers and Reporting Perfor-
mance,” Solar Energy, Vol. 68, No. 1, 2000, pp. 1-7.
[9] R. A. V. Narasimha and S. Subramanyam, “Solar Cookers-
Part I: Cooking Vessel on Lugs,” Solar Energy, Vol. 75,
No. 3, 2003, pp. 181-185.
[10] R. A. V. Narasimha and S. Subramanyam, “Solar Cookers-
Part II: Cooking Vessel with Central Annular Cavity,”
Solar Energy, Vol. 78, No. 1, 2005, pp. 19-22.
[11] A. R. Reddy and R. A. V. Narasimha, “Prediction and
Experimental Verification of Performance of Box Type
Solar Cooker-Part I. Cooking Vessel with Central Cylin-
drical Ca vity,” Energy Conversion and Management, Vol.
48, No. 7, 2007, pp. 2034-2043.
[12] A. R. Reddy and R. A. V. Narasimha, “Prediction and
Experiemental Verification of Performance of Box Type
Solar Cooker-Part II. Cooking Vessel with Depressed
Lid,” Energy Conversion and Management, Vol. 49, 2008,
pp. 240-246.
http://dx.doi.org/10.1016/j.enconman.2007.06.020
[13] A. Harmim, M. Boukar and M. Amar, “Experimental Stu-
dy of a Double Exposure Solar Cooker with Finned
Cooking Vessel,” Solar Energy, Vol. 82, No. 4, 2008, pp.
287-289.
[14] V. P. Sethi and S. Kumar, “Inclined Box Type Solar
Cooker Using Modified Absorber Plate and Ne w Cooking
Vessel Design,” Proceedings of International Conference
on Recent Innovations in Technology, Kottayam, Kerala,
12-14 January 2012, pp. 233-237.
[15] S. P. Sukhatme, “Solar Energy, Principles o f Thermal Col-
lection and Storage,” 6th Edition, Tata McGraw-Hill Pub-
lishing Company Limited, New Delhi, 1990.
[16] J. A. Duffie and W. A. Beckman, “Solar Engineering of
Thermal Processes,” John Wiley and Sons, New York,
1991.
[17] G. N. Tiwari, “Solar Energy Fundamentals, Design, Mo-
delling and Applications,” Narosa Publishing House, New
Delhi, 2006.
[18] N. K. Bansal, M. Kleeman and M. Meliss, “Renewable
Energy Sources and Conversion Technology,” Tata Mc-
Graw Hill Publishing Co., New Delhi, 1990.
0
200
400
600
800
1000
1200
Solar Intensity (W/m
2
)
Time of the day
Measured intensity on horizontal surface
Predicted intensity on horizontal surface
Measured intensity on inclined surface
10:00 10:30 11:00 11:30 12:00 12:30 1 :00 1 :30 2 :00 2 :30 3 :00 3 :30 4 :00