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71
MIT International Journal of Mechanical Engineering Vol. 1 No. 2 Aug 2011, pp 71-78
ISSN No. 2230 – 7699 © MIT Publications
Parametric Studies of Top Heat Loss Coefficient of
Double Glazed Flat Plate Solar Collectors
Anand Bisen
P.P. Dass
Department of Mechanical Engineering,
Govt. Kalaniketan Polytechnic College,
Jabalpur (M.P.), India
Department of Mechanical Engineering,
Jabalpur Engineering College,
Jabalpur (M.P.), India
Rajeev Jain
Department of Mechanical Engineering,
Govt. Kalaniketan Polytechnic College,
Jabalpur (M.P.), India
Abstract: The performance of any solar collector is largely
affected by various parameters. Estimation of various heat losses
in the flat plate solar collector is important for their thermal
performance evaluation and upward heat losses have a major
contribution in the total heat losses in flat plate collectors. The
top heat loss coefficient is a function of various parameters which
includes the temperature of the absorber plate Tp, ambient
temperature Ta and glass cover temperatures Tg1 and T g2, wind
heat transfer coefficient hw, emissivity of absorber plate Îp and
glass cover Îg, spacing between the absorber plate and glass
cover L1, L2, tilt angle of the collector b, number of glass covers
N and thickness of glass covers Lg1, Lg2.The present work aims
at the studies of effect of estimation of air properties by two sets
of correlation on the estimation of top heat loss coefficient of
double glazed flat plate solar collector by estimating glass cover
temperatures by using numerical solution technique. This
comparison of air properties effects on top heat loss coefficient
(Ut) has been studied for the given range of absorber plate
temperature (Tp), Ambient temperature (T a) and wind heat
transfer coefficient (hw) using MATLAB.
Keywords: flat plate collector, top heat loss coefficient, absorber
plate temperature, ambient temperature and wind heat transfer
coefficient.
(Fig. 1) is a special kind of heat exchanger which converts
solar radiation energy to heat energy by using usually air,
water or oil. Flat-plate collectors can be designed for
applications requiring moderate temperature (T < 100 0C).
They are relatively inexpensive, easily constructed, require
little maintenance and use both beam and diffuse radiation of
the sun. They are well suited to the drying of agricultural
crops. The major applications of these units are in solar water
heating, building heating, air conditioning, and industrial
process heat.
A review of correlations quantifying heat transfer has been
carried out by Holland et.al (1976). They described equation
to calculate the Nusselt number for natural convection
between parallel plates. Correlations suggested to calculate
Nusselt number (Nu) are
Nu
If
È
1 1.44 É1 È Ra Ø
É
Ù 1,
Ê 5830 Ú
Ê
then, N u
1708 Ø
R a ÙÚ
ËÈ R a Ø
Û
ÌÉ
Ù 1Ü
Ê
Ú
Í 5830
Ý
È 1708 Ø
Ù
Ê Ra Ú
1 1.44 É
Buchberg et.al (1976) have given correlation to calculate
the Nusselt number for natural convection between parallel
Solar energy is the most clean energy source in the world. plates. Buchberg et al., (4) has suggested correlations to
The sun emits approximately 1353 (W/m2) on to a surface of calculate Nusselt number (Nu) are,
earth if there is no atmospheric layer.(Thekaekara and If R < 1708, then, N = 1
a
u
Drummond 1971).The world receives 170 trillion (kW) solar
If (Ra < 1708) & (R a1 < 5900), then,
energy and 30% of this energy is reflected back to the space,
1708 Ø
È
47% is transformed to low temperature heat energy, 23% is
N u 1 1.44 É1 R a ÙÚ
used for evaporation/rainfall cycle in the Biosphere and less
Ê
than 0.5% is used in the kinetic energy of the wind, waves If (R < 5900) & (R < 9.23 × 10 4), then,
a
a
and photosynthesis of plants (Duffie and Beckman 1991,
Kalogirou 2004).Thus Solar Energy option has been identified
N u 0.229 – R 0.252
a
as one of the promising alternative energy source for If (R < 9.23 × 10 4) & (R < 10 6), then,
a
a
future. Various devices (i.e. Solar Collector) are used for
N u K – R a0.285
thermal collection and storage of this energy. A solar collector
I. INTRODUCTION
72
MIT International Journal of Mechanical Engineering Vol. 1 No. 2 Aug 2011, pp 71-78
ISSN No. 2230 – 7699 © MIT Publications
A Malhotra et.al. (1981) have suggested that Nusselt number
correlations of a single gap are extended to a two cover system.
It is found by using two covers there is an overall saving of
more then 50% in convective losses yielding better result. N.
Akhtar (1999) reported that for evaluating the top heat loss
factor it is adequate to calculate the individual heat transfer
coefficients based
Figure 1: Cross section of basic flat plate solar collector
on mean temperature of glass cover rather than two separate
relations for inner and outer surfaces. He has suggested
correlations for calculating top heat loss coefficient of
corresponding enclosed space, three correlations are, Upward
heat loss from the absorber plate to the first glass cover is
given by,
Qt = (hcpg1+ hrpg1) (TP – Tg1)
From the first glass cover to the second glass cover by,
Qt = (hcg1g2 + hrg1g2) (Tg1 – Tg2)
and from the second glass cover to the atmosphere by ,
Qt = (hw + hrg2a) (Tg2 – Ta)
T.P. Woodman (1977) has provided the basic equations for
calculating collector performance as a function of design and
operating parameters. This equation is used to investigate the
sensitivity of collector output to ambient air temperature,
absorber plate temperature and heat transfer coefficient of
wind. He suggested that use of two cover plates instead of
one is shown to be nearly always beneficial.
heat balance equations.An additional advantage of the
proposed technique over the semi-empirical equations is that
results can be obtained for different values of sky temperature,
using any given correlation for convective heat transfer in
the air gap spacing, and for any given values of fluid (air in
the present case) properties.
Sekhar et. al. (2009) have found that the emissivity of the
absorber plate has a significant impact on the top loss
coefficient and consequently on the efficiency of the Flat plate
collector. The efficiency of FPC is found to increase with
increasing ambient temperature. There is no significant impact
of tilt angle on the top loss coefficient.
Need of the present work: To find effect of estimation of
air properties by two sets of correlations for the estimation of
top heat loss coefficient of double glazed flat plate solar
collector by estimating glass cover temperatures. Nusselt
number (Nu) can be calculated by the correlations suggested
by Holland et al. [6] and Buchhberg et al. [4] to estimate the
convective heat transfer coefficient This is required to show
the variations in results obtained by the above said
correlations.
Objective of Present study: The present work aims at the
studies of effect of estimation of air properties by two set on
the estimation of top heat loss coefficient of double glazed
flat plate solar collector by estimating glass cover temperatures
by using numerical solution technique. This comparison of
thermo-physical air properties effects on top heat loss
coefficient (U t) has been studied for the given range of
absorber plate temperature (Tp), Ambient temperature (T a) and
wind heat transfer coefficient (h w) using MATLAB. The range
of variables for which the proposed equations have been
evaluated in given Table 1.
Table 1: Range of Variables
Variables
Range
Ambient Temperature (Ta)
288K to 318K
Absorber Plate temperature (Tp)
Heat Transfer coefficient of wind (hw)
373K to 423K
5w/m2-K to
25 w/m2-K
Emissivity of Absorber Plate (T p)
0.9
Kutscher, et al., (1993) have showed that the radiation heat
loss is determined by considering losses to both the sky and
0.88
Emissivity of glass (Tg)
the ground and Convective heat losses are obtained by
Thickness of first glass cover (L g1)
0.004 m
integrating the product of the temperature and velocity profiles
)
0.004
m
Thickness
of
second
glass
cover
(L
g2
in the boundary layer at the downwind edge of the collector.
Space between Absorber plate &
This convective heat loss is then expressed in terms of the
First glass cover (L1)
0.098 m
thermal equivalent length of irradiated absorber, and analysis
shows that this loss can be very low for large collectors even
Space between first and second
under windy conditions. Mullick and Samdarshi (1994) have
0.012 m
glass cover (L2)
presented a generalized analytical equation for the top heat
loss factor of a flat-plate collector with one or more glass
covers. The maximum computational errors resulting from II. METHODOLOGY
the use of the analytical equation with several simplifications
Estimation of air properties by two sets of correlation on
are ±5 percent compared to numerical solution of the set of the estimation of top heat loss coefficient of double glazed
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MIT International Journal of Mechanical Engineering Vol. 1 No. 2 Aug 2011, pp 71-78
ISSN No. 2230 – 7699 © MIT Publications
flat-plate solar collector by estimating glass cover temperatures
Q t (h cpg1 h rpg1 ) (Tp Tg1)
(1)
by using numerical solution technique. This comparison of
air properties effects on top heat loss coefficient (U t) has been and from the first glass cover to the second glass cover by
studied for the given range of absorber plate temperature (T p),
Q t (h cg1g2 h rg1g2 ) (Tg1 Tg2)
(2)
Ambient temperature (Ta) and wind heat transfer coefficient
and from the second glass cover to the atmosphere by
(hw) using MATLAB.
Q t (h w h rg2a ) (Tg2 Ta )
(3)
Energy balance equations of flat-plate collectors
In steady state, the performance of a flat-plate solar collector
can be described by the useful gain from the collector, Qu,
which is defined as,
Qu=Ac[S-UL(Tp-Ta)]+
where Ac is gross area of the collector, the first term is the
absorbed solar energy and second term represents the heat
loss from the collector, TP and Ta or Plate temperature and
ambient temperature.
Heat loss from the collector
In solar collectors, the solar energy absorbed by the absorber
plate is distributed to useful gain and to thermal losses through
the top, bottom, and edges.
Top heat loss through the cover system
To evaluate the heat loss through the cover systems, all of
the convection and radiation heat transfer mechanisms
between parallel plates and between the plate and the sky
must be considered as shown in Figures 1, 2 and 3. In this
study the net radiation method is applied to obtain the
expression for the heat loss for the general cover system of
flat-plate solar collectors.
Figure 3: Thermal network for a two cover flat plate
collector (a) in terms of conduction, convection and
radiation (b) in terms of resistances between plates.
Where,
h cpg1
h rpg1
h cg1g2
Figure 2: Heat transfer mechanisms through a
cover system with two glass cover
Calculation of top heat loss coefficient
The top loss co-efficient is evaluated by considering
convection and re-radiation losses from the absorber plate in
the upward direction.
Upward heat loss from the absorber plate to the first glass
cover
h cg1g2
h rg2a2
K1 – N u1
L1
(4)
V
Î
Þ 2 2
Ñ 1 1 Ñ (Tp Tg1 ) (Tp Tg1 )
Ï 1ß
ÑÐ °p °g Ñà
K 2 Nu 2
L2
V
È 2 1Ø
ÉÊ °g ÙÚ
V · °g
(5)
(6)
2
(Tg1
2
) (Tg1 Tg2 )
Tg2
(Tg2 4 Tsky 4 )
Tg2 Ta
Measurable input variables in a solar collector.
TP = Plate temperature
Ta = Ambient temperature
(7)
(8)
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MIT International Journal of Mechanical Engineering Vol. 1 No. 2 Aug 2011, pp 71-78
ISSN No. 2230 – 7699 © MIT Publications
Îg = Emissivity of the glass
Îp = Emissivity of absorber plate
Buchberg (4) equation to calculate Nusselt number (N u1)
(19)
If Ra1 < 1708, then N u1 = 1
L2 = Spacing between absorber plate and glazing
L1 = Spacing between first and second glazing
If (Ra1 > 1708) & (R a1 < 5900), then
È
N u1
Lg = Thickness of glass covers
k = Thermal conductivity of air
1 1.446 É1 Ê
1708 Ø
R a1 ÙÚ
(20)
If (Ra1 > 5900) & (R a1 < 9.23 × 10 4), then,
Using numerical solution method programming in MATLAB
N u1 0.229 – R 0.252
has been done. The properties of air with mean temperature as
a1
independent variable is evaluated.
4
6
If (Ra1 < 9.23 × 10 ) & (Ra1 < 10 ), then,
Air properties
(21)
0.285
K1 – R a1
(22)
For accurate prediction of collector performance it is
Arithmetic mean temperature of space between first glass
necessary to evaluate properties of the working fluid (air) to
cover and second glass cover,
calculate the convective heat transfer coefficient. Properties
Tg1 Tg2
of air evaluated at the arithmetic mean of the corresponding
Tm
(23)
surface temperatures
2
N u1
Tp Tg1
Tm
(9)
2
Following correlations for air properties are used to calculate
Raleigh number (Ra)
Air properties correlation-I [7]
K1
3 – 108 Tm2 104 Tm 4 – 105
(10)
V1
[9 – 105 Tm 2 0.040 Tm 4.17] – 106
(11)
Pr1
1.057 0.06 log Tm
(12)
Air properties correlation- II [10,11]
K1 = 0.0002067 Tm0.85
V1 = 9(10 ) Tm
Pr1 = 1.0602 – 0.602 log Tm
–10
(13)
(14)
(15)
1.72
Raleigh number (Ra) of enclosed space can be calculated
by using air properties of corresponding enclosed space
R a1
9.8 (TP Tg1 ) (L1 )3 (Pr )
V12
È TP Tg Ø
ÉÊ
Ù
2 Ú
(16)
N u1
1
if
È R a1 Ø 3
É
Ù 1,
Ê 5830 Ú
then N u1
È 1708 Ø
Ù
Ê R a1 Ú
1 1.44 É
9.8 (Tg1 Tg2 ) (L 2 )3 (Pr 2 )
(24)
(Tg1 Tg2 )
2
V2
2
The natural convection heat transfer coefficient for the
enclosed space between the first glass cover and second glass
cover is calculated by correlations suggested by Holland et.al.
(6) and Buchberg et.al.(4) as discussed earlier (Eqn. 17 to
22).The convective heat transfer coefficients (h cpg1, hcg1g2,) and
Radiative heat transfer coefficients (h rpg1, hrg1g2 and hrg2a)
can be evaluated by equations discussed earlier. (Eqn. 4 to 8).
Ra2
Calculation of top heat loss coefficient
UPg1, Ug1g2, and Ug2a are given by correlations [5]
Between Plate and First Glass Cover (U pg1)
U pg1
(17)
(18)
(h cpg1 h rpg1)
(25)
Between first glass cover and second glass cover (U g1g2)
U g1g2
A review of correlations quantifying heat transfer has been
carried out by Holland. et.al. (6) and Buchberg et.al.(4). They
recommended use of the following correlations to calculate
Nusselt number (Nu)
For (Nu1) Space between the absorber plate and first glass
cover is calculated by Holland et.al.(6) Equation to calculate
Nusselt number (Nu1)
1
Ë
Û
1708 Ø ÌÈ R a1 Ø 3
È
Ü
É
1 1.44 É1 Ù 1Ü
R a1 ÙÚ ÌÍÊ 5830 Ú
Ê
Ý
Raleigh number (Ra2) of enclosed space can be calculated
by using air properties of corresponding enclosed space
(source: Duffie and Beckman)
(h cg1g2 h rg1g2 )
(26)
Between second glass cover & ambient air (U g2a)
U g2a
(h w h rg2a )
(27)
and Top heat loss coefficients may be given by,
Ut
(h cpg1 h rpg1 ) 1 (h cg1g2 h rg1g2 ) 1
(h w h rg2a )1 2L g / k g
(28)
where, Lg = Thickness of the glass cover
kg = Thermal conductivity of glass
Overall heat transfer loss coefficient (U L) can be calculated
by following correlation
Ul
U t U b Us
(29)
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MIT International Journal of Mechanical Engineering Vol. 1 No. 2 Aug 2011, pp 71-78
ISSN No. 2230 – 7699 © MIT Publications
K
L1
by Holland and Buchberg. The comparison of air properties
effects on top heat loss coefficient (U t) has been studied for
the given range of absorber plate temperature (T p), Ambient
If side heat loss co-efficient (U s) is assumed to be constant.
Temperature (Ta) and wind heat transfer coefficient (h w)
UL Ut Ub
(31) using MATLAB. The present study will help in calculating
upward heat losses for a flat plate solar collector with double
cover system.
III. RESULTS AND DISCUSSION
where,
Ub
(30)
A way to describe the top heat loss coefficient of double
glazed flat plate solar collector using numerical computing
environment MATLAB the results have been presented in
a graphical manner. In the present study effects of three
important parameters Ambient temperature (Ta) Absorber
plate Temperature (Tp) and heat transfer coefficient of wind
(hw), on over all heat transfer coefficient has been discussed.
In the present study, top heat loss coefficient (U t) is
calculated from equation 28. Convective heat transfer
coefficients (hcpg1, hcg1g2) are calculated from equations 4 to
6. For natural convection, Nusselt number (Nu) is calculated
from correlations suggested by Holland et al., (6) and
Buchberg et al., (4) from equations 17 to 22.
The comparison of top heat loss coefficient (U t) evaluated
by Holland et al., (6) and Buchberg et al., (4), result as
shown in Tables 2 and 3. Percentage change or variation in
Ut is 0.35% to 0.33% [by Holland et al., (6)] and percentage
change or variation in Ut is 0.42 % to 0.40% [by Buchberg
et al., (4)]. It shows as plate temperature increases
percentage change in Ut decreases.The effect of ambient
temperature (Ta) on top heat loss coefficient (U t) with
variable absorber plate temperature (Tp), results shown in
(Graphs 4, 5 and 6), shows that loss factor increases as the
ambient temperature also increases. This trend implies that
collector losses will be minimum in the early hours in the
morning and maximum at higher absorber plate temperatures.
The effects of absorber plate temperature (Tp) on top heat
loss coefficient (U t) with variable heat transfer coefficient
of wind (hw) (Graphs 1, 2 and 3) indicates that the heat
transfer coefficient of wind can contribute to losses in the
collector. The loss coefficient increases as the heat transfer
coefficient of wind also increases and this is attributed to
the increased convective and radiative losses from the
glazing cover to the surrounding.
IV. CONCLUSION
REFERENCES
[1]
Akhtar, N., (1999). “Upward Heat Losses in Solar Thermal
Collectors”, Ph.D. Thesis, CES, I.I.T. Delhi.
[2]
ASHRAE, (1986). Standard 93-86, Methods of Testing to
determine the thermal performance of solar collectors,
American society of Heating, Refrigeration and Air
Conditioning Engineers.
[3]
Malhotra, H.P. Garg and Usha Rani (1980). “Minimizing
convective heat losses in flat plate solar collector”. Solar
energy, volume 25, Issue 6, pp. 521-526.
[4]
Buchberg, H., I. Catton and D.K. Edwards (1976). Natural
convection in enclosed spaces, A review of application to
solar energy collector, J. Heat Transfer, Trans. ASME, 98 (2):
182-188.
[5]
Duffie, J.A. and W.A. Beckman (1991). Solar Engineering
of Thermal Processes, 2nd edition, Wiley Interscience,
New York.
[6]
Hollands, K.G.T., T.E. Unny, G.D. Raithby and L. Konicek,
(1976). Free convective heat transfer across inclined air layers.
J. Heat Transfer, Trans. ASME, Ser. C 98 (2), 189–193.
[7]
Holman, J.P., “Heat transfer” Tata Mcgraw Hill, Delhi, 9th
edition 2004.
[8]
Kalogirou, S.A. (2004). “Solar Thermal Collectors and
Applications”, Progress in Energy and Combustion Science,
No. 30 pp. 231-295.
[9]
Malhotra, A., H.P. Garg and A. Patil (1981). Heat loss
calculation of flat plate solar collector. J .Thermal Engg. Vol.
2: 59-62.
[10] Mullick, S.C. and Samdarshi, S.K. (1988). “An Improved
Technique for Computing the Top Heat Loss Factor of Flat
Collector with Single Glazing”. ASME Journal of Solar
Energy Engineering, Vol. 110 : 262-267.
[11] Mullick, S.C. and Samdarshi, S.K. (1991). “An analytical
equation for Top Heat Loss Factor of Flat Plate Collector with
Double Glazing.’’ASME. Journal of Solar Energy
Engineering, Vol.113:117-122.
An analytical study has been conducted to evaluate the
top heat loss coefficient of a flat plate solar collector. In the [12] Sekhar Y. Raja, Sharma, K.V. and Rao M. Basaveswara (2009)
evaluation of heat loss from the solar collector, two sets of
“Eevaluation of heat loss coefficients in solar flat plate
correlations have been used for estimating air properties.
collectors”ARPN journal of engineering and applied sciences,
For natural convection heat transfer between configuration
Vol. 4, no. 5.
correlations of Holland nd Buchberg was used. The effects [13] Woodman, T.P. (1977). “The effect of design and operating
of absorber plate temperature (Tp), ambient temperature (Ta)
parameters on the performance of flat plate solar collectorand wind heat transfer coefficient (hw) on top heat loss
Calculation method and detailed appraisal”. Solar Energy, Vol.
transfer coefficient are evaluated by correlations suggested
19(3):263-270
76
MIT International Journal of Mechanical Engineering Vol. 1 No. 2 Aug 2011, pp 71-78
ISSN No. 2230 – 7699 © MIT Publications
V. NOMENCLATURE
A
: Collector area,m
Tp
Ta
: Plate temperature,0C
: Air temperature, 0C
Tg1
Tg2
: Temperature of first glass cover, 0C
: Temperature of second glass cover, 0C
Îg
Îp
: Emissivity of the glass
: Emissivity of the absorber plate
L2
L1
: Spacing between absorber plate and first glazing
: Spacing between first and second glazing
Lg
Tm
: Thickness of the glass cover
: Mean temperature between two heat transfer
surfaces
2
Tp
Ut(h)
Ut(b)
% change
383
3.8912
3.9070
0.404402
384
3.9019
3.9176
0.400756
385
3.9127
3.9283
0.397118
386
3.9236
3.9391
0.393491
387
3.9346
3.9500
0.389873
388
3.9456
3.9609
0.386276
389
3.9566
3.9719
0.385206
390
3.9678
3.9829
0.379121
391
3.979
3.9940
0.375563
392
3.9902
4.0052
0.374513
393
4.0015
4.0158
0.356093
Upg1 : Over all heat transfer co-eff. between absorber
plate and first glass cover (U1 )
Ug1g2 : Overall heat transfer co-eff. between first and
second glass cover (U 2 )
394
4.0129
4.0272
0.355085
395
4.0243
4.0386
0.354083
396
4.0358
4.0500
0.350617
Ug2a : Overall heat transfer co-eff. between second glass
cover and Ambient air (U3 )
hrpg1 : Radiative heat transfer co-eff. between plate and
first glass cover
397
4.0474
4.0615
0.347162
398
4.0581
4.0731
0.36827
399
4.0698
4.0847
0.364776
400
4.0815
4.0964
0.363734
hcpg1 : Convective heat transfer co-eff. between plate and
first glass cover
hcg1g2 : Convective heat transfer co-eff. between first and
second glass cover
401
4.0933
4.1081
0.360264
402
4.1052
4.1199
0.356805
403
4.1171
4.1318
0.355777
hrg2a : Radiative heat transfer co-eff. between second
glass cover and ambient air
hrg1g2 : Radiative heat transfer co-eff. between first and
second glass cover
404
4.129
4.1437
0.354755
405
4.141
4.1556
0.351333
406
4.153
4.1676
0.350322
407
4.1651
4.1797
0.349307
408
4.1773
4.1918
0.345913
409
4.1894
4.2039
0.344918
410
4.2017
4.2161
0.341548
Table 2: Comparison of Top Heat Loss Co-efficient by
Holland and Buchberg Equation with Air Property
Correlation - I
L1 = 0.098 m; L2 = 0.012 m; Tp = 373:1:423K;
Ta = 303K; hw =5 w/m2-K
411
4.214
4.2284
0.340554
412
4.226
4.2406
0.344291
Tp
Ut(h)
Ut(b)
% change
413
4.2384
4.2530
0.343287
373
3.7915
3.8050
0.354796
414
4.2508
4.2654
0.342289
374
375
3.8012
3.8111
3.8148
3.8247
0.356506
0.355583
415
4.2633
4.2779
0.341289
416
4.2758
4.2904
0.340295
376
377
3.8211
3.8312
3.8347
3.8448
0.354656
0.353725
417
4.2884
4.3029
0.336982
418
4.301
4.3155
0.335998
4.3136
4.3282
0.337323
378
379
3.8413
3.8516
3.8550
3.8652
0.355383
0.351858
419
420
4.3263
4.3409
0.336336
380
381
3.8619
3.8723
3.8755
3.8860
0.350922
0.352548
421
4.3391
4.3537
0.335347
422
4.3519
4.3665
0.334364
382
3.8805
3.8964
0.408069
423
4.3647
4.3793
0.333387
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MIT International Journal of Mechanical Engineering Vol. 1 No. 2 Aug 2011, pp 71-78
ISSN No. 2230 – 7699 © MIT Publications
Table 3: Comparison of Top Heat Loss Co-efficient by
Holland and Buchberg Equation with Air Property
Correlation - II
L1 = 0.098 m; L2 = 0.012 m; Tp = 373:1:423K;
Ta = 303K; hw =5 w/m2-K
Tp
Ut(h)
Ut(b)
% change
408
4.1301
4.1471
0.409925
409
4.1423
4.1593
0.408723
410
4.1545
4.1715
0.407527
411
4.1667
4.1837
0.406339
Tp
Ut(h)
Ut(b)
% change
373
3.7446
3.7605
0.422816
412
4.1790
4.1960
0.405148
374
3.7544
3.7703
0.421717
375
3.7643
3.7802
0.420613
413
4.1914
4.2084
0.403954
376
3.7743
3.7902
0.419503
414
4.2038
4.2208
0.402767
377
3.7844
3.8003
0.418388
415
4.2162
4.2332
0.401587
378
3.7945
3.8105
0.419892
416
4.2287
4.2457
0.400405
379
3.8048
3.8207
0.416154
417
4.2412
4.2583
0.401569
380
3.8151
3.8310
0.415035
418
4.2538
4.2709
0.400384
381
3.8255
3.8414
0.413912
419
4.2662
4.2835
0.403875
382
3.8360
3.8519
0.412783
420
4.2789
4.2963
0.405000
383
3.8465
3.8625
0.414239
421
4.2916
4.3090
0.403806
384
3.8572
3.8731
0.410524
422
4.3044
4.3218
0.402610
385
3.8679
3.8838
0.409393
423
4.3172
4.3347
0.403719
386
3.8787
3.8946
0.408258
387
3.8895
3.9054
0.407129
388
3.9004
3.9163
0.405995
389
3.9098
3.9273
0.445599
390
3.9209
3.9383
0.441815
391
3.9321
3.9494
0.438041
392
3.9433
3.9606
0.436803
393
3.9546
3.9718
0.433053
394
3.9660
3.9831
0.429314
395
3.9774
3.9945
0.428089
396
3.9889
4.0059
0.424374
397
4.0004
4.0173
0.420681
398
4.0120
4.0289
0.419469
399
4.0236
4.0401
0.408406
400
4.0353
4.0518
0.407226
401
4.047
4.0635
0.406054
402
4.0588
4.0753
0.404878
403
4.0706
4.0871
0.403709
404
4.0825
4.0990
0.402537
405
4.0939
4.1110
0.415957
406
4.1059
4.1230
0.414747
407
4.1180
4.1350
0.411125
MIT International Journal of Mechanical Engineering Vol. 1 No. 2 Aug 2011, pp 71-78
ISSN No. 2230 – 7699 © MIT Publications
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