experimental investigations on top loss coefficients

8/4/2019 Experimental Investigations on Top Loss Coefficients

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Abstract—The flat plate collector is one of the most widely used

device for harnessing the solar energy. The measurement of the flat

plate collector performance is the collector efficiency. The collector

efficiency is the ratio of the useful energy gain to the incident solar

energy over a particular period of time. The useful energy gain in

turn depends on the energy loss from the top surface of the collector

both due to convective & radiative heat transfer processes. The losses

from the bottom and from the edges of the collector do exist but their contribution is not as significant as the losses from the top. Hence

investigations are carried out to study the losses by changing the

collector tilt to determine the top loss coefficient.

Keywords—Collector, Tilt angle, Losses, Top loss coefficient

I. I NTRODUCTION

HE technology of harnessing the solar energy has reached

to the state of commercialization on mass scale. The

greatest advantage of using solar energy is that it is an

inexhaustible and pollution free source of energy. The Lord

Sun gives approximately 1.8 x 1011 MW power, which is

many thousand times higher than the present consumption rateon earth. This makes it one of the most promising of the

unconventional sources of energy.

II. NOMENCLATURE

A p Area of absorber plate, m2

Qs Losses of heat from sides, W

Q b Losses of heat from bottom, W

Qt Losses of heat from top, W

Ein Energy input, W

β Collector tilt angle, degrees

N No. of covers

σ Stefan Boltzmann constant 5.67 x 10-8 W/m2K -4

∈ p Emissivity of plate

∈c Emissivity of cover

T b Temperature of bottom cover of collector, K

Tc1 Mean temperature of 1st cover, K

Tc2 Mean temperature of 2nd cover

Tc Thickness of cover, m

M. K. Bhatt is with the S. V. National Institute of Technology, Surat,

Gujarat State, India (Phone: 91-9898082293, Fax: 91-261-2227334, email:

[email protected] )

S. N. Gaderia is with the S. V. National Institute of Technology, Surat,

Gujarat State, India (email: [email protected] )

S. A. Channiwala is with the S. V. National Institute of Technology, Surat,

Gujarat State, India (email: [email protected])

Ut Top heat loss co-efficient, W/m2K

UL Over all heat loss co-efficient of collector, W/m2K

Th Temperature of heater plate, K

T p Temperature of absorber plate, K

hw wind induced convective heat transfer co-efficient,

W/m2K

hC1-2 Convective heat transfer co-efficient between 1st and

2nd

cover, W/m2K

K c Thermal conductivity of cover, W/m2K

h p-c Convective heat transfer co-efficient between

absorber plate & cover, W/m2K

hc-a Convective heat transfer co-efficient between cover &

atmosphere, W/m2K

F p-c Radiation shape factor between plate & cover

∈g Emmisivity of glass cover

Qu Useful energy gain, W

S Flux absorbed by collector, W/m2

III. FLAT PLATE COLLECTOR

The flat plate collector shown in Fig. 1 is one of the most

widely used device for harnessing solar energy. In any solar collection device, the principle usually followed is to expose a

dark surface to solar radiation so that the radiation is

absorbed. A part of the absorbed radiation is then transferred

to a fluid like air or water. When no optical concentration is

done; the device in which the collection is achieved is called

the flat plate collector. The flat plate collector is the most

important type of solar collector because it is simple in design,

has no moving parts and requires little maintenance. It can be

used for a variety of applications in which temperature

ranging from 40 °C to 100 °C is required.

Fig. 1 Solar flat plate collector

IV. PERFORMANCE ANALYSIS OF FLAT PLATE COLLECTOR

An energy balance on the absorber plate yields the

Experimental Investigations on Top Loss Co-

efficients of Solar Flat Plate Collector atDifferent Tilt AngleM. K. Bhatt, S. N. Gaderia, and S. A. Channiwala

T

World Academy of Science, Engineering and Technology 79 2011

432



following equation for steady state:

qu = A p S - q1 (1)

where, qu = useful heat gain, i.e., the rate of heat transfer to

the working fluid; S = incident solar flux absorbed in the

absorber plate; A p = area of the absorber plate and q1= rate of heat loss.

In order to determine the flux, ‘S’ absorbed by the absorber

a term called the transmitivity absorptivity product (τα)

which is defined as the ratio of the flux absorbed in the

absorber plate to the flux incident on the cover system, is

evaluated and is given by ‘S’.

S= I b R b (τα) b + Id R d (τα)d+ (I b + Id) R r . (τα)d (2)

Where

τ = transmitivity of glass cover system.

α = absorptivity of absorber plate.

(τα) b = transmitivity absorptivity product for the beam

radiation falling on the collector.

(τα)d = transmitivity absorptivity product for the diffuse

radiation falling on the collector.

Now, rate of the heat loss is given by,

ql = Ul A p (T pm – Ta) (3)

Where,

Ul= overall loss coefficient

A p= area of absorber plate.

T pm= average temperature of the absorber plate, andTa= temperature of surrounding air.

The heat loss from the collector is the sum of the heat loss

from the top, the bottom and the sides.

Ql = qt + q b + qs (4)

Where,

Qt = Ut A p (T pm – Ta) (5)

Q b = U b A p (T pm – Ta) (6)

Qs = Us A p (T pm – Ta) (7)

Ul = Ut + U b + Us (8)

Here, Ut , U b and Us are the top, the bottom and the side

loss co-efficients respectively.

V. TOP LOSS COEFFICIENT

The top loss co-efficient Ut is evaluated by considering the

convection and the radiation loss from the absorber plate in

the upward direction. For the purpose of calculation, it is

assumed that

1) The transparent covers and the absorber plate constitute a

system of infinite parallel surface and flow of the heat isone dimensional and steady.

2) Temperature across the thickness of the cover is

negligible and that the interaction between the incoming

solar radiation absorbed by the covers and the outgoing

loss may be neglected

A schematic diagram of two-cover system is shown in theFig. 2.

Fig. 2 schematic diagram of two-cover system

In steady state the heat is transferred by convection and

radiation between the following:

1) The absorber plate and the first cover.

2) The first cover and the second cover and

3) The second cover and the surrounding must be equal.

( )( )

( )1

4 4

1

1 1/1/ 1/ 1

pm c

p p c pm c

p c

T T q A h T T

σ

−

−= − +

∈ + ∈ −

(9)

( )( )

( )2

4 4

1 2

1 21/ 1/ 1

c c

p c c c

p c

T T h T T

σ

−

−= − +

∈ + ∈ −(10)

( ) 4 4

2 2 2( )

w c a c skyh T T T T σ = − + ∈ −(11)

Eqs. 9 to 11 constitute a set of three nonlinear equations,

which can be solved iteratively by assuming Tc1 and Tc2 for

which qt/A p is same by all these equations.

There exists few correlations for calculating h p-c, hw, and Ut

which have been derived based on different experiments andtechniques which may not be representative of real life

collector.

The present work is an attempt to present the comparative

assessment of these correlations, based on systematic

experiments, on an experimental research collector which is a

representative of real life collector and to study the effect of

collector tilt angle on top losses and top loss co-efficient.

VI. EXPERIMENTAL SET-UP & METHODOLOGY

An experimental research collector as shown in Fig. 3 is the

representative of real life collector developed during the

course of this work. It essentially consists of a cover plate of 5

mm thick glass, powder coated black absorber of copper [∈ p


433



= 0.9] having size as 1210 mm x 710 mm x 1 mm, two

reflective electric heaters of 0.5 kW capacity, kept below the

absorber to produce uniform heat flux, and wooden housing

filled with cerwool insulation (K=0.03 W/m-k) at the back

and glass wool (K = 0.04, W/m-k) at the sides.

Fig. 3 photograph of research collector

The experiments are conducted in a laboratory with black

curtains on the windows so as to avoid any infiltration of

external radiation. The electricity is supplied to the two

heaters by two variacs at a predecided controlled rates varying

from 200 to 700 W through double stabilized power sources

and the collector is allowed to reach to its steady state which

takes nearly 4 to 5 hours for each heat input. The steady state

temperature levels are measured by 48 calibrated chromel

alumel thermocouples of 26 gauge mounted on the bottom of

the glass cover, absorber plate, heater plate, bottom, sides,

edges and covers of housing. The wind is created by three

adjustable height pedestal fans whose input is also controlled

by variacs for creating different speeds. The wind velocity is

measured by vane type anemometer over six different points

on the collector, Fig. 3 gives the photographic view of

experimental set-up.

VII. EXPERIMENTAL DETERMINATION OF VARIOUS PARAMETERS

Once the steady state is achieved the top loss, the overallloss and the convective heat transfer coefficients are evaluated

from the energy balance equation as follows:

Qin = Qt + Q b + Qs + Qc + Qe + Qsl (12)

Qin is the total energy supplied to the heaters which is same

as the heat losses from collector under steady state. The

bottom losses, Q b, side losses, Qs, edge losses, Qe, corner

losses, Qc are calculated as per the method suggested by

Channiwala. Sealing losses are assumed as 1% and hence top

losses are calculated by subtracting all these losses from input

energy Qin. Once Qt is obtained U1, Ut, h p-c and hw may be

evaluated as follows:

4 4

4 4

( )

( )

( )

( ) ( )

( )

( ) ( )

int

t

t

p ct p c

t cw c a

QU

Ap Tp Ta

Q

U Ap Tp Ta

F Tp TcQh

Ap Tp Tc Ap Tp Tc

Q Tc Tah h

Ap Tc Ta Ap Tc Ta

σ

σ

−

−

−

=−

= −

−= −

− −

∈ −= = −

− −

VIII. INVESTIGATION STAGES

Effect of Plate Temperature:

In this stage, the effect of plate temperature on the wind loss and the top loss coefficient

of solar flat plate collector is investigated with different heat

inputs, keeping collector in horizontal position under zero

wind velocity. For each set of experiments the steady state

conditions were obtained and all the temperature and power

inputs were recorded, based on which h p-c, hw, Ut and U1 are

evaluated.

Effect of Collector Tilt Angle: In second stage the effect of

tilt angle (β) is studied keeping the collector at various angles

varying from 0° to 90°, with respect to horizontal under zero

wind velocity.

Effect of Wind Velocity: In this stage, the effect of wind

velocity at zero degree of yaw angle has been studied with

different wind velocities varying from 0 to 5 m/s. For this,

three pedestal fans were used to generate necessary wind.

Anemometer was used to measure wind velocity at six

different points and the average velocity was used in

calculation.

Effect of Wind Direction: In final stage of this project work,

the effect of yaw angle was studied. The readings were taken

at various yaw angles like 0°, 45°, and 90° with respect to the

principle axis of solar collector. Further, for each yaw angle

observations have been made at different wind velocitiesranging from 0 to 5 m/s.

IX. R ESULTS AND DISCUSSION

The salient features of the results obtained are discussed

below:

It is apparent from the graphs 1 to 3 that there is an increase in

top loss at different tilt angles, which supports the fact that at

higher absorber plate temperature levels both radiative &

convective losses will increase, resulting in increase in top

losses. Both Ut and Ul are found to be increasing due to

increased convective & radiative losses. The graphs 4 to 6

shows that there is an increase in % top loss as tilt angle

increases.

(13)

(14)

(15)

(16)


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Graph. 1

Graph. 2

Graph. 3

Graph. 4

Graph. 5

Graph. 6

X. CONCLUSION

The tilt angle has very marginal effect of wind induced

convective heat transfer at a given constant absorber plate

temperature. The top loss co-efficient correlations in general

over predict the value of Ut by 5-15%. Samdarshi and

Mullick, Agrawal and Larson correlation seems to correlate

present experimental work by 10%. For any collector, tilt

between zero to ninety the top loss coefficient may be

evaluated as,


435



Utβ = Uth [1 – 0.0006β]

Where

Utβ = top loss coefficient at angle of β degree

Uth = top loss coefficient for horizontal collector

With the increase in absorber plate temperature,

simultaneously the value of Ut and Ul increases at different tilt

angle. Thus the value of Ut and Ul are found increasing due to

increased convective and radiative losses.

R EFERENCES

[1] J. A. Duffie and W. A. Beckman, "Solar Engineering of Thermal

Processes", 2nd Ed: John Willey and Sons, Inc., New York, 1991.

[2] Sukhatme, S.P., "Solar Energy-Principle of Thermal Collection and

Storage", Tata McGraw Hill Pub, Co., Delhi, 1984.

[3] Hollands, K.G.T., Unny, T,E., Raithby G.D., and Konicek, L., "Free

Convective Heat Transfer Across Inclined Air Layers" ASME J. of Heat

Transfer, Vol., 98, No.2, p.p. 189-193, May 1981.[4] Jurges I. W., "Der Warmeubergang an Einer Ebnen Wand", Biehefte

Zum Gesundheits- Ingenieur, Rehihe-I Beihfte 19, 1924.

[5] Mc Admas, W.H., "Heat Transmission", 3rd Ed. McGraw Hill. New

York, 1954

[6] Wattmuff, J. H, Charters, W. W. S., and Proctor, D., "Solar and Wind

Induced External Coefficients for Solar Collectors", Int. Revue d' Hellio-

technique 2, 56. 1977.

[7] Sparrow, EM, and Tien, K.K. "Forced Convection Heat Transfer at an

Inclined and Yawed Square Plate -Application to Solar Collectors",

ASME J. of Heat Transfer, pp. 507-512., Nov. 1977.

[8] Test, F.L., Lessmann, R C. and Johary, A., "Heat Transfer during Wind

Flow Over Rectangular Bodies in the Natural Environment", ASME

Trans, of Heat Transfer, Vol. 103, pp. 262-267, May, 1981.

[9] Shakerin, S., "Wind Related Heat Transfer Coefficient for Flat Plate

Solar Collectors", ASME Trans., J. of Solar Energy Engineering, Vol.

109. pp. 108-111 May 1987.[10] Sharples, S, and Charlesworth, P.S., "Full Scale Measurements of Wind

Induced Convective Heat Transfer from a Roof Mounted Flat Plate

Collector", J. Solar Energy, Vol., 62, No.2, pp. 69-77, 1998.

[11] Hottel H.C. and Woenz, B.B., "Performance Of Flat Plate Heat Solar

Collector". Trans. ASME, Vol. 64, pp. 94 -102, Feb. 1942.

[12] Klein S.A, "The Effect of Thermal Capacitance upon the Performance of

Flat Plate Solar Collector", M.Sc. Thesis, Univ. of Wisconsin, 1973.

[13] Klein, S.A., "Calculation of Flat Plate Collector Loss Coefficients",

Solar Energy, Vol. 17, pp. 79-80, 1975

[14] Rabl, A" "Active Solar Collectors and Their Applications", Oxford

Univ. Press. 1985.

[15] Agarwal, V.K. and Larson, D.C., "Calculation of the Top Loss

Coefficient of A Flat Plate Collector", Solar Energy, Vol. 27, pp. 69-71.

1981.

[16] Malhotra, A., Garg, H.P. and Palit, A., "Heat loss Calculation of Flat

Plate Solar Collector". J. Thermal Engineering, Vol. 2; No.2... pp. 59-62,1981.

[17] Mullick, S.C. and Samdarshi, S.K. "An Improved Technique For

Computing The Top Heat Loss Factor Of A Flat Plate Collector With A

Single Glazing", ASME Journal of Solar Energy Engineering, Vo... 110,

pp. 262.267, Nov.1988.

[18] Swinbank, W.C., "Long -wave Radiation from Clear Skies", Quarterly

Journal of Royal Meteorological Society, Vol. 89, 1963.

[19] Mullick, S.c. and Samdarshi, S.K., "Analytical Equation For The Top

Heat Loss Factor Of A Flat Plate Collector With Double Glazing",

ASME Journal of Solar Energy Engineering, Vol. 113, pp. 117·122, May

1991.

[20] Samdarshi, S.K. and Mullick, S.C... "Generalised Analytical Equation

for the Top Loss Factor of a Flat Plate Solar Collector with N Glass

Covers", Personnel Communications, 1993.

[21] Channiwala, S.A, and Doshi, N.I., "Heat Loss Coefficients for Box Type

Solar Cooker", J. of Solar Energy, Vol. 42, No.6, pp. 495·501, 1981.

[22] Sam, R,G., Lessmann, R.C, and Test F, L.. "An Experimental Study of

Flow Over a Rectangular Body", ASME J. of Fluid Mechanics, Vol.

101. pp. 443·448, 1979.


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