performance evaluation of corrugated absorber double … · solar air heater has the important...

International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:17 No:01 63

172201-3535-IJMME-IJENS © February 2017 IJENS I J E N S

Abstract— In this paper the mathematical model of double

flow flat plate and corrugated absorbers solar air heater having

various configurations are presented. A computer program in

C++ language has been developed to solve the mathematical

model. The energy, effective and exergy performance of

collectors are analyzed on the basis of effective parameters such

as mass flow rate, insolation and flow channel depth. Comparison

of present mathematical model results with the results of other

researchers show a good agreement. The results of corrugated

absorber have been compared with flat plate absorber solar air

heater for similar operating conditions and its indicate that there

is significant enhancement in efficiency of corrugated absorber to

that of the flat plate absorber solar air heater with double flow

configurations. It is observed that the exergy efficiency become

negative at higher mass flow rate (i.e. m > 0.072 kg/s) for all types

of solar air heater. The results also show that the optimum

channel depth of AH-1 solar air heater is 0.02 m at which all

efficiencies have the highest values for entire range of mass flow

rate and insolation investigated.

Index Term— Corrugated absorber, double flow, energy

efficiency, exergy efficiency, solar air

NOMENCLATURE

area of collector (m2)

half height of v-groove (m)

specific heat of air at constant pressure (J/kg K)

hydraulic diameter (m)

energy gain by air (W)

exergy (W)

friction coefficient

height of air flow channel (m)

height of glass cover (m)

convective heat transfer coefficient (W/m2 K)

radiative heat transfer coefficient (W/m2 K)

specific enthalpy (J/kg)

insolation (W/m2)

thermal conductivity (W/m K)

collector length (m)

thickness (m)

mass flow rate (kg/s)

Nusselt number

fluid pressure (N/m2)

universal gas constant (J/kg K)

Reynolds number

resistance factor

specific entropy (J/kg K)

temperature (K)

loss coefficient (W/m2 K)

velocity of wind (m/s)

velocity of air (m/s)

collector width (m)

work rate or power (W)

Greek symbols

absorptivity

emissivity

fraction of mass flow rate

pressure drop (N/m2)

efficiency

density of air (kg/m3)

Stefan-Boltzmann constant (W/m2 K

4)

transmissivity

angle of v-groove absorbing plate (˚)

angle of trapezoidal absorbing plate (˚)

specific exergy (J/kg)

Subscripts

ambient

air flow

air flow above the absorber plate

air flow under the absorber plate

absorber plate

bottom

bottom plate

channel

destruction

environment

effective energy

entrance

energy

effective thermal energy gain

exit

exergy

glass cover

lower glass cover

upper glass cover

heat

inlet

Performance Evaluation of Corrugated Absorber

Double Flow Solar Air Heater Based on Energy,

Effective and Exergy Efficiencies

Som Nath Saha*, S. P. Sharma

National Institute of Technology, Jamshedpur - 831014, India * Corresponding Author, Tel: +918582094184, [email protected]



insulation

overall

mean

maximum

minimum

outlet

pipe

sun

top

thermal energy gain

work

I. INTRODUCTION

Now a days, among all renewable energy sources, one of the

most suitable energy source is solar energy. Demand of

application of solar energy is increasing day by day because of

its sustainability, abundantly and cleanness. Its main

application is in thermal energy utilization system like solar

water heater, air heater, cooker, pump, power generation etc.

Solar air heater has the important place among all thermal

energy system due to its use in low to medium grade thermal

energy, simple in design, easy to install, eco-friendly, low cost

of manufacturing as well as operation and maintenance. These

are the benefits of solar air heater however, its efficiency is

low due to adverse thermo physical properties of air which

leads to low rate of heat transfer between absorber plate to

flowing air.

In recent decades, many researchers have developed various

design and configurations of solar air heater to improve their

performance. It has been shown that one of the effective ways

to increase the convective heat transfer rate between absorber

plate and flowing air is to increase the heat transfer surface

area and to increase turbulence inside the flow channel by

using fins or corrugated surfaces [1-2]. Different design and

configurations of solar air heaters like fins and baffles on

absorber, corrugated absorber, roughened absorber and packed

bed have been developed to improve their performance by

various authors [3-10].

The first law of thermodynamic analysis is based on energy

balance method and it is used to calculate the energy and

effective efficiency of energy systems. The second law of

thermodynamics analysis involves the reversibility or

irreversibility of process which is very significant for exergy

analysis of an energy system. Exergy (or availability) is an

important technique to optimize and performance evaluation

of energy system. Both the analysis are very important to

study the performance of a system. Many researchers have

been looked into the exergy analysis for performance

evaluation of solar air heaters.

Kalaiarasi et al. [11] investigated experimentally energy and

exergy analysis of a flat plate solar air heater having copper

tubes with extended copper fins as absorber. They found

maximum energy and exergy efficiency 49.4 % to 59.2 % and

18.25 % to 35.53 % respectively and also observed that solar

air heater with sensible heat storage have better than the

conventional flat plate solar air heater without storage.

Exergetic performance evaluation of solar air heater with arc

shaped wire rib roughened absorber plates have been

investigated analytically by Mukesh et al. [12] and found the

maximum enhancement in exergetic efficiency as compared to

smooth absorber solar air heater is 56 % at relative roughness

height (e/d) = 0.0422. Mahdi et al. [13] studied the exergetic

analysis based on exergy loss of a double pass/glazed v-

corrugated plate solar air heater and also optimized exergy

efficiency for different parameters of distance between two

glass covers, height of v-corrugations, area of the heater and

total mass flow rate. Abhishek et al. [14] analytically

investigated the energy and exergy performance of wavy fin

solar air heater and a mathematical model have been

developed for the evaluation of the effect of various complex

geometries of wavy fin. Bahrehmand et al. [15] studied the

energy and exergy analysis of single and two glass cover solar

air collector and effect of depth, length, fin shape and

Reynolds number. Their study showed that the system with fin

and thin metal sheet are more efficient than other systems. A

detailed parametric studied have been done by Sabzpooshani

et al. [16] to study the exergetic performance of a baffled type

solar air heater and also investigated the effect of variation of

fin and baffle parameters, number of glass covers, bottom

insulation thickness and inlet air temperature at different mass

flow rates. Salwa et al. [17] proposed a packed bed solar air

heater with PCM spherical capsules as packing material. They

used first and second laws of thermodynamics to obtain the

energy and exergy efficiency for optimization. Experimentally

they found energy efficiency 32% to 45% and exergy

efficiency 13% to 25%. Golneshan and Nemati [18] derived

exergy efficiency for unglazed transpired solar collector and

proposed correlation to predict the optimum working

temperature. Huseyin [19] experimentally investigated the

efficiency and exergy analysis of five different types of air

solar collectors and reported that heat transfer coefficient and

pressure drop increases with shape of absorber surface. Fatih

Bayrak et al. [20] performed experiment on the five types of

solar air heaters with porous baffles insert and compared the

energy and exergy efficiencies with each other for mass flow

rates of 0.016 kg/s and 0.025 kg/s. The results showed that

higher efficiency for mass flow rate of 0.025 kg/s with

aluminium foam of 6 mm thickness. Farzad and Emad [21]

compared performance of design parameters for flat plate

collectors with energy and exergy analysis. Lalji et al. [22]

developed correlations for heat transfer coefficient and friction

factor for packed bed solar air heater and also they have done

exergy analysis. Akpinar and Kocyigit [23] investigated the

first and second laws efficiency of flat plate solar air heaters

having several obstacles on absorber plate and without

obstacles. The investigation carried out for two mass flow

rates 0.0074 and 0.0052 kg/s and obtained the first law

efficiency 20 % to 82 % and second law efficiency 8.32 % to

44.00 %. Nwachukwu [24] employed exergy analysis to

optimized the sizing of pin fin to improve the heat absorption

and dissipation potential of a solar air heater. A comparative

study have been presented by Gupta and Kaushik [25] for

various types of artificial roughness geometries in the absorber

plate of solar air heater and evaluate the performance in terms

of energy, effective and exergy efficiency. Mohseni et al. [26]

analyzed the optimum mass flow rate for maximum exergy

efficiency of a flat plate collector by using second law of

thermodynamics and found that the optimum mass flow rate is

0.0011 kg/s for tested conditions. Hikmet [27] experimentally



presented the energy and exergy analysis of a flat plate solar

air heater with different obstacles and without obstacles. He

concluded that double flow collector with obstacles is better

than that without obstacles. Ucar and Inalli [28] conducted an

experimental investigation of five different air collector with

staggered fins attached below the absorber plate. They

presented the exergy relations for all collectors and found that

the largest irreversibility occurred at conventional solar

collector. Ozturk [29] experimentally evaluated energy and

exergy efficiency of a solar air heater with paraffin wax as

thermal energy storage. The system efficiencies were

evaluated by energy and exergy analysis and found average

energy efficiency 40.4% and exergy efficiency 4.2%. Ozturk

and Demirel [30] experimentally investigated the thermal

performance of packed bed solar air heater packing with

Raschig rings and found that the energy and exergy

efficiencies increases as the outlet air temperature increases.

It is evident from the literature survey that no detailed

investigation on energy, effective and exergy based

performance of double flow corrugated absorber solar air

heater with different configurations is carried out. In this

paper, mathematical model have been presented for the

evaluation of energy, effective and exergetic performance of

double flow flat and corrugated absorber solar air heaters. The

influence of performance parameters such as mass flow rate,

air flow channel depth and solar radiation intensity on energy,

effective and exergy efficiencies are investigated. From the

results the optimum mass flow rate and air flow channel depth

have been found at which solar air heaters give the best

performance for a set of system parameters. This study help to

predict the performance on the basis of energy, effective and

exergy efficiencies of double flow solar air heater. The use of

double flow configuration with corrugated absorber improves

the performance with less pressure drop penalty. Further, the

double glass cover reduces the heat loss from the top surface

to the surrounding.

Fig. 1 shows the different configuration of double flow

corrugated and flat plate absorber solar air heaters. AH-1 (Fig.

1a) and AH-3 (Fig. 1c) are v-corrugated absorber and v-

corrugated bottom plate, having different air flow channels.

AH-2 (Fig. 1b) and AH-5 (Fig. 1e) are trapezoidal absorber

and trapezoidal bottom plate, with different air flow

configurations. AH-4 is v-corrugated absorber with flat

bottom plate (Fig. 1d). AH-6 is the flat plate (plane) absorber

solar air heater (Fig. 1f). Each of the solar air heaters have

1.25 m length and 0.80 m width. The height of corrugated

absorber is 0.0125 m and the range of different parameters

such as mass flow rate is 0.035 – 0.083 kg/s, air flow channel

depth is 0.01 – 0.05 m and insolation is 200 – 1000 W/m2 have

been considered for the investigation.

(a) AH-1

(b) AH-2

(c) AH-3

(d) AH-4

(e) AH-5

(f) AH-6

Fig. 1. The double flow type solar air heaters for different design of

absorbing plates.

II. MATHEMATICAL MODELING

The different configuration of double flow corrugated

absorber solar air heaters are analytically studied in this work.

Fig. 2 shows the equivalent flow diagram of double flow solar

air heater of different configurations. The analysis is based on

analytical solutions for energy balance equations. In order to

formulate the energy balance equations, the following

assumptions are made:

The temperatures of the absorbing plate, bottom plate

and bulk fluids are functions of the flow directions

only.



The systems operate under quasi steady state.

There is no temperature gradient across the thickness

of lower and upper glass covers, absorbing plate and

back plate.

Both the glass covers and fluid (air flow 1 and air

flow 2) do not absorb radiant energy.

The inlet air temperature is equal to the ambient

temperature.

Fig. 2. The equivalent flow diagram of double flow solar air heater of

different configurations.

A. Energy Balance Equations

To formulate the energy balance equations, considered a

differential element of length dx at a distance x from the inlet.

For studied systems, the energy balance equations are written

as:

Glass cover 1 (lower glass cover)

( ) ( )

( ) (1)

Absorber plate

( ) ( )

( ) ( )

(2)

Bottom plate

( ) ( )

( ) (3)

Air flow 1 (air flowing over the absorbing plate)

( )

( )

(4)

Air flow 2 (air flowing under the absorbing plate)

( )

( ) (5)

Solving Eqs. (1) and (2), we have

( ) ( ) (6)

[( )( )

( ) ] (7)

where,

(8)

(9)

(10)

(11)

Solving Eqs. (2) and (3), we have

( ) ( ) (12)

[( )( )

( ) ] (13)

where,

(14)

(15)

(16)

Substitution of Eq. (6) and Eq. (7) into Eq. (4), yields ( )

( ) ( ) (17)

where,

(18)

(19)

(20)

Substitution of Eq. (12) and Eq. (13) into Eq. (5), we have ( )

( ) ( ) (21)

where,

(22)

(23)

(24)

Solving Eqs. (17) and (21) with the boundary condition:

At,

We obtains the temperature distributions of air flow 1 and air

flow 2 as

*

+

*

+

(

)

(25)

(26)



The outlet temperature of air flow 1, can be obtained from

Eqs. (25), for,

*

+ *

+

(

)

(27)

The outlet temperature of air flow 2, can be obtained from

Eqs. (26), for,

(28)

where,

*(

) √(

)

+ (29)

*(

) √(

)

+ (30)

*(

) ( ) (

) (

)

+ (31)

(

) ( ) (

) (

)

(32)

B. Heat Transfer Coefficients

An empirical equation, derived by Klein [31], is used to

calculate top loss coefficient, , and is given by

[ ( ⁄ )

{( )

( ) } ( ⁄ )

]

( )(

)

*( )

{ ( ) } ⁄ +

(33)

The bottom loss coefficient, , is given by

(34)

The convective heat transfer coefficient from the outer glass

cover (g2) due to wind is calculated by the expression given

by McAdams [32].

(35)

The heat transfer coefficient between two glass covers, inner

glass cover (g1) and outer glass cover (g2) is expressed by

Hottel and Woertz [33] empirical equation as

( )

(36)

The convective heat transfer coefficients between the

absorbing plate and air flow 1 is assumed to be equal to the

convective heat transfer coefficient between air flow 1 and

inner glass cover, and the convective heat transfer coefficients

between the absorbing plate and air flow 2 is assumed to be

equal to the convective heat transfer coefficient between air

flow 2 and bottom plate.

(37)

and, (38)

The radiation heat transfer coefficients between the

absorbing plate and inner glass cover and between the

absorbing plate and bottom plate may be expressed by

assuming mean radiant temperature equal to the mean fluid

temperature as,

(39)

and

(40)

The radiation heat transfer coefficients between the two

glass cover inner glass cover and outer glass cover and outer

glass cover and air are respectively as

(41)

and

(42)

For flat plate absorber (AH-6),

The convective heat transfer coefficient for air.

(43)

For laminar flow, the equation presented by Heaton et al.

[34],

⁄

⁄ (44)

For turbulent flow the correlation derived from Kays [35],

data with the modification of McAdams [32],

[ ⁄ ] (45)

For AH-4 collector,

The construction of the corrugated plate solar air heater is

similar to the flat plate solar air heater except the flat plate is

replaced by a corrugated plate. The energy balance equations

are same only heat transfer coefficient between absorber plate

and flowing fluid are different. The developed area of the

corrugated plate is greater than the flat plate by a factor of

⁄ ⁄ [36] thus the heat transfer coefficient between

absorbing plate to fluid is

(

) (46)

Hollands and Shewen [37] developed the correlation of

Nusselts number ( ) and modified by Karim et al. [36] can

be expressed as:

If

(47)

If

(48)



If

(49)

Huseyin [19] presented the correlation of Nusselts number

as:

For AH-1 collector,

(50)

For AH-2 collector,

(51)

The heat transfer coefficient between absorbing plate to fluid

is

(52)

For AH-3 collector,

(53)

For AH-5 collector,

(54)

C. Mean Temperature

The mean air temperatures in the ducts can be found by

integrating Eqs. (25) and (26) from to and the

expressions are

*

+

*

+

(

)

(55)

(56)

The overall loss coefficient is the sum of top and bottom loss

coefficients:

(57)

The mean absorbing plate temperature can be calculated by

(58)

The mean temperature of inner glass cover (g1)

(59)

The mean temperature of outer glass cover (g2)

( )

(60)

D. Pressure Drop

The pressure drop is calculated from the following

expression;

(61)

The pressure drop through the upper and lower channel

is calculated by the relation [38 - 40];

⁄ (62)

Huseyin [19] present the correlation of friction coefficient

for turbulent flow as:

For AH-6 collector,

(63)

For AH-1 collector,

(64)

For AH-2 collector,

(65)

For AH-3 collector,

(66)

For AH-5 collector,

(67)

The sum of the inlet and outlet pressure drop ( )

can be determined by Hegazy [41];

(68)

where the sum of the entrance and exit resistance factor

is taken 1.5 [42].

E. Energy, effective and exergy efficiencies

The thermal energy gain ( ) is calculated as

(69)

where, ( ) (70)

and ( ) (71)

The energy efficiency ( ) can be calculated by

( )

(72)

The effective thermal energy gain ( ) is calculated as

⁄ (73)

where, is the work energy lost in friction in the heater

channel, given by

⁄ (74)

is the conversion factor to transform different efficiencies

(thermal to mechanical) and is taken 0.2 [15].

The effective energy efficiency ( ) is calculated by

(75)

The general exergy balance equation can be expressed in

rate form as [23]

∑ ∑ ∑ (76)

The Eq. (76) can be written as

(77)

The rate form of the general exergy balance equation can

also be written as:

∑(

) ∑ ∑ (78)

where

(79)

(80)

On substitution of Eqs. (79) and (80) in Eq. (78),

(

) [ ] (81)

where, is the solar energy absorbed by the absorber plate.

(82)

The change in enthalpy and entropy is given as:

( ) (83)

(84)

By substituting Eqs. (82) – (84) into Eq. (81), we have

(

)

( )

(85)



The exergy efficiency of a solar air heater is defined

as the ratio of exergy gain of the system to the exergy of

absorbed solar radiation.

(

)

(86)

III. CALCULATION PROCEDURE

Numerical calculations have been carried out to calculate

the energy, effective and exergy efficiencies for different solar

air heater systems with system, operating and meteorological

parameters given in Table 1. In order to obtain the results

numerically, a computer program in C++ language was

developed. TABLE I

SYSTEMS, OPERATING AND METEOROLOGICAL PARAMETERS USED WITH

PRESENT INVESTIGATION

= 0.5

The physical properties including density, specific heat, the

dynamic viscosity and the thermal conductivity of air have

been taken at mean temperature.

The procedure followed for determination of energy,

effective and exergy efficiencies are briefly explained as,

(i) First assumed the values of Taf1,m, Taf2,m, Tap,m, Tg1,m

and Tg2,m.

(ii) By using assumed values and using Eqns. (36) –

(54); calculate the heat transfer coefficients.

(iii) To check the assumed temperature values Taf1,m,

Taf2,m, Tap,m, Tg1,m and Tg2,m use Eqs. (55) – (60) and

obtained new temperature values. If the calculated

values of temperatures are different from the assumed

values continued calculation by iteration method.

These new temperatures will be use as the assumed

temperatures for next iteration and the process will be

repeated until all the newest temperatures obtained

are their respective previous values.

(iv) After completing the iteration the mean temperature

values were obtained and thermal energy gain and

energy efficiency can be calculated by Eqns. (69) and

(72).

(v) By using Eqn. (61) calculate pressure drop including

channel pressure drop, entrance and exit pressure

drop, then calculate effective thermal energy gain and

effective energy efficiency by Eqns. (73) and (75)

respectively.

(vi) The exergy efficiency calculated via Eq. (86).

Flow chart for iterative solution of governing equations is

shown in Fig. 3.

Fig. 3. Flow chart for iterative solution of governing equations.

IV. RESULTS AND DISCUSSION

In this section, the results of energy, effective and exergy

performance have been obtained through the present

mathematical model for various system and operating

parameters. A comprehensive study are followed to examine

the effect of mass flow rate, insolation and flow channel depth

on the performance of collectors.



0.03 0.04 0.05 0.06 0.07 0.08 0.09

680

700

720

740

760

780

800

AH-1

AH-2

AH-3

AH-4

AH-5

AH-6

= 0.5

I = 1000 W/m2T

he

rma

l e

ne

rgy g

ain

, E

teg

(W

)

Mass flow rate (kg/s)

Fig. 4. Effect of mass flow rate on thermal energy gain.

0.03 0.04 0.05 0.06 0.07 0.08 0.09

675

690

705

720

735

750 AH-1

AH-2

AH-3

AH-4

AH-5

AH-6

= 0.5

I = 1000 W/m2

Effe

ctive

th

erm

al e

ne

rgy g

ain

(W

)


Fig. 5. Effect of mass flow rate on effective thermal energy gain.

Figs. 4 and 5 depict the effect of mass flow rate of air on the

thermal energy gain and effective thermal energy gain for

different corrugated and flat plate absorber solar air heaters for

I = 1000 W/m2. Fig. 4 shows that thermal energy gain

increases continuously with increase in mass flow rate of air,

whereas Fig. 5 shows the effective thermal energy gain

increases upto a particular value of mass flow rate, attains

maxima and then decreases sharply. It is noticed that there

exists an optimum value of mass flow rate at which effective

thermal energy gain attained the maximum value for each

solar air heater, which is due to the fact that the mass flow rate

is a strong parameter that effect the pumping power there by

affecting the effective thermal energy gain. It is seen from Fig.

5 that effective thermal energy gain of flat plate solar air

heater (AH-6) reaches maximum value at m= 0.058 kg/s,

whereas for other collectors maximum values shifted towards

lower mass flow rates. This type of trends is observed due to

increase in pressure drop of flowing air in corrugated absorber

solar air heaters.

0.03 0.04 0.05 0.06 0.07 0.08 0.09

0.675

0.700

0.725

0.750

0.775

0.800

AH-1

AH-2

AH-3

AH-4

AH-5

AH-6

= 0.5

I = 1000 W/m2

En

erg

y e

ffic

ien

cy (

en

e)


Fig. 6. Effect of mass flow rate on energy efficiency.

0.03 0.04 0.05 0.06 0.07 0.08 0.09

0.650

0.675

0.700

0.725

0.750

AH-1

AH-2

AH-3

AH-4

AH-5

AH-6

= 0.5

I = 1000 W/m2

Effe

ctive

en

erg

y e

ffic

ien

cy (

efe)


Fig. 7. Effect of mass flow rate on effective energy efficiency.

Figs. 6 and 7 show the variation of energy and effective

energy efficiencies with mass flow rate of air for different type

of corrugated and flat plate absorbers for I = 1000 W/m2.

From the Fig. 6, it is seen that energy efficiency increases with

increase in mass flow rate of air, this is due to increase in

thermal conductance from absorber to flowing air. Whereas

from Fig. 7, effective energy efficiency increases upto a

certain value of mass flow rate, attains maxima and there after

decreases sharply. This may be attributed to the fact that lower

amount of energy spent in overcoming the friction losses at

the lower mass flow rates. The energy required to overcome

the friction losses increases sharply with the increase in mass

flow rate; the rate of increase of heat transfer and friction

losses are, in fact, not proportional, i.e. the heat transfer

coefficient increase being proportional to a power less than

one of the mass flow rate, while the friction losses increasing

with the square of the mass flow rate. Consequently, at the

higher mass flow rate, the rate of increase of heat transfer is

lower in comparison to the rate of increase of the friction



losses, i.e. a region where the actual gain are not

commensurate with the expenditure in power losses.

0.03 0.04 0.05 0.06 0.07 0.08 0.09

-0.01

0.00

0.01

0.02

0.03

0.04

AH-1

AH-2

AH-3

AH-4

AH-5

AH-6

= 0.5

I = 1000 W/m2

Exe

rgy e

ffic

ien

cy (

exe)


Fig. 8. Effect of mass flow rate on exergy efficiency.

Fig. 8 shows the variation of exergy efficiency with mass

flow rate for double flow corrugated and flat plate solar air

heaters, for I = 1000 W/m2. It is seen that corrugated absorber

leads to exergy efficiency increase compared to flat plate solar

air heater for the total range of mass flow rate considered. The

improvement is due to enhanced heat transfer surface area and

also creation of turbulence which results in higher heat energy

gain. It is also seen from the figure that corrugated absorbers

are more efficient at low mass flow rate and the percentage of

exergy efficiency enhancement reduces with increase in mass

flow rate, this is because of at higher mass flow rate the outlet

temperature of air is almost equal for all type of solar air

heater. It can also observed that the exergy efficiency become

negative at higher mass flow rate (i.e. m > 0.072 kg/s),

because exergy of required pump work exceeds the exergy of

energy gain collected by the solar air heater.

0.03 0.04 0.05 0.06 0.07 0.08 0.09

0

100

200

300

400

500

600

700

800

900

AH-1

I = 1000 W/m2

I = 800 W/m2

I = 600 W/m2

I = 400 W/m2

I = 200 W/m2

Th

erm

al e

ne

rgy g

ain

(W

)


Fig. 9. Effect of mass flow rate on thermal energy gain at different insolation.

0.03 0.04 0.05 0.06 0.07 0.08 0.09

0

100

200

300

400

500

600

700

800

AH-1I = 1000 W/m

2

I = 800 W/m2

I = 600 W/m2

I = 400 W/m2

I = 200 W/m2

Effe

ctive

th

erm

al e

ne

rgy g

ain

(W

)


Fig. 10. Effect of mass flow rate on effective thermal energy gain at different

insolation.

Figs. 9 and 10 show the effect of mass flow rate on thermal

energy gain and effective thermal energy gain respectively for

different insolation, for AH-1 solar air heater. It is found that

as mass flow rate increases the rate of increase of thermal

energy gain is very low, whereas effective thermal energy gain

decreases for a specific insolation. Increasing the mass flow

rate increases the pumping power which leads to increase the

pressure drop. It is also found from the figures that, for a

specific mass flow rate the thermal energy gain as well as

effective thermal energy gain increases with increase in

insolation, this is due to increased rate of energy gain per unit

area.

0.03 0.04 0.05 0.06 0.07 0.08 0.09

0.72

0.73

0.74

0.75

0.76

0.77

0.78

0.79

I = 200 W/m2

I = 400 W/m2

I = 600 W/m2

I = 800 W/m2

I = 1000 W/m2

= 0

En

erg

y e

ffic

ien

cy (

en

e)


Fig. 11. Effect of mass flow rate on energy efficiency at different insolation.



0.03 0.04 0.05 0.06 0.07 0.08 0.09

0.2

0.3

0.4

0.5

0.6

0.7

0.8

I = 200 W/m2

I = 400 W/m2

I = 600 W/m2

I = 800 W/m2

I = 1000 W/m2

= 0.5

AH-1Effe

ctive

en

erg

y e

ffic

ien

cy (

efe)


Fig. 12. Effect of mass flow rate on effective energy efficiency at different insolation.

Figs. 11 and 12 present the variation of energy and effective

energy efficiency as a function of mass flow rate of air

respectively for AH-1 collector, for the range of insolation 200

– 1000 W/m2. Fig. 11 reveals that the energy efficiency

increases with increase in mass flow rate for all insolation

considered, whereas it can be seen from Fig. 12 that at lower

insolation effective energy efficiency decreases drastically as

mass flow rate increases however, at higher insolation

effective energy efficiency curve flow less steeper fall with

increase in mass flow rate. This type of trend is observed

because, at lower insolation heat gain by the flowing air is low

and at higher insolation heat gain is high. Also, for higher

mass flow rate pumping power loss is high, which increase

pressure drop. It is also observed from the both figures, for a

specific mass flow rate energy efficiency and effective energy

efficiency increases with increase in insolation even so,

percentage enhancement of both efficiencies decrease with

increase in insolation. This is probably because of increase in

insolation, increases the thermal radiation heat losses from the

absorbing plate to bottom plate and to the glass cover but

monotonically reduced the thermal radiation heat loss from the

glass cover to the sky.

0.03 0.04 0.05 0.06 0.07 0.08 0.09

-0.15

-0.12

-0.09

-0.06

-0.03

0.00

0.03

I = 200 W/m2

I = 400 W/m2

I = 600 W/m2

I = 800 W/m2

I = 1000 W/m2

= 0.5

AH-1

Exe

rgy e

ffic

ien

cy (

exe)


Fig. 13. Effect of mass flow rate on exergy efficiency at different insolation.

The effect of mass flow rate on exergy efficiency for

different solar radiation for AH-1 air heater is shown in Fig.

13. As seen from the figure exergy efficiency continuously

decreases with increase in mass flow rate and when the

radiation is maximum exergy efficiency is also maximum for a

specific mass flow rate. At lower mass flow rate the exergy

efficiency is high because of exergy efficiency is the function

of outlet temperature of air. The outlet temperature of air is

high for lower mass flow rate and low for the higher mass

flow rate. This behavior may be explained by longer contact

times of air with the absorber. It is also seen that for higher

radiation exergy efficiency become negative at higher mass

flow rate and for lower radiation at which exergy efficiency

become negative shifted towards lower mass flow rates. This

type of trend is observed due to outlet temperature of air is

high at higher radiation for a specific mass flow rate.

0.03 0.04 0.05 0.06 0.07 0.08 0.09

700

720

740

760

780

800

H = 0.01 m

H = 0.02 m

H = 0.03 m

H = 0.04 m

H = 0.05 m

I = 1000 W/m2

AH-1

Th

erm

al e

ne

rgy g

ain

(W

)


Fig. 14. Effect of mass flow rate on thermal energy gain at different channel

depth.



0.03 0.04 0.05 0.06 0.07 0.08 0.09

0.70

0.72

0.74

0.76

0.78

0.80

H = 0.01 m

H = 0.02 m

H = 0.03 m

H = 0.04 m

H = 0.05 m

I = 1000 W/m2

AH-1

En

erg

y e

ffic

ien

cy (

en

e)


Fig. 15. Effect of mass flow rate on energy efficiency at different channel depth.

Figs. 14 and 15 illustrate the effect of mass flow rate on

thermal energy gain and energy efficiency respectively for

different channel depth for AH-1 solar air heater. The channel

depth varies from 0.01 – 0.05 m. From the results, it is found

that the thermal energy gain and energy efficiency increases

with increase in mass flow rate. When channel depth

decreases the thermal energy gain and energy efficiency

increases upto a certain depth then there after start decreasing

with further decreasing the channel depth. This type of trends

are mainly due to enhance heat transfer rate and thermal losses

to the surroundings, when channel depth move towards the

critical value. It is seen from the figures that, for 0.02 m

channel depth the thermal energy gain and energy efficiency

have the maximum value throughout the mass flow rate

investigated and for 0.01 m depth its value decreases because

of increase in top losses.

0.03 0.04 0.05 0.06 0.07 0.08 0.09

640

660

680

700

720

740

760

H = 0.01 m

H = 0.02 m

H = 0.03 m

H = 0.04 m

H = 0.05 m

I = 1000 W/m2

AH-1

Effe

ctive

th

erm

al e

ne

rgy g

ain

(W

)


Fig. 16. Effect of mass flow rate on effective thermal energy gain at different

channel depth.

0.03 0.04 0.05 0.06 0.07 0.08 0.09

0.64

0.66

0.68

0.70

0.72

0.74

0.76 H = 0.01 m

H = 0.02 m

H = 0.03 m

H = 0.04 m

H = 0.05 m

I = 1000 W/m2

AH-1

Effe

ctive

en

erg

y e

ffic

ien

cy (

efe)


Fig. 17. Effect of mass flow rate on effective energy efficiency at different

channel depth.

The effect of variation of mass flow rate and channel depth

on the effective thermal energy gain and effective energy

efficiency are presented in Figs. 16 and 17 respectively for

AH-1 solar air heater. It is seen that trend of both graphs are

same i.e. effective thermal energy gain and effective energy

efficiency first increases with increase in mass flow rate,

attains the maximum value then there after start decreasing

with increase in mass flow rate. It is also noted that for a

particular mass flow rate as the channel depth increases,

effective thermal energy gain and effective energy efficiency

initially increasers attains an optimum value at 0.02 m and

then start decreasing, this is due to the fact that as the channel

depth increases the pumping power reduces at higher rate as

compared to thermal energy gain there by increasing the

effective thermal energy gain and effective energy efficiency

but after a certain depth the thermal energy gain is not

substantial as compared to pumping power. It is perceived that

for lower channel depths maximum effective energy efficiency

obtained is higher due to higher convective heat transfer

coefficient which increases the thermal energy gain. However,

the increase in the mass flow rate associated with decrease in

channel depth cause an increase in pressure drop due to which

the drop in effective energy efficiency is more predominant

for higher mass flow rate and shallower depth.



0.03 0.04 0.05 0.06 0.07 0.08 0.09

-0.02

-0.01

0.00

0.01

0.02

0.03

0.04

H = 0.01 m

H = 0.02 m

H = 0.03 m

H = 0.04 m

H = 0.05 m

I = 1000 W/m2

AH-1

Exerg

y e

ffic

ien

cy (

exe)


Fig. 18. Effect of mass flow rate on exergy efficiency at different channel

depth.

Fig. 18 shows the variation of exergy efficiency as a

function of mass flow rate for different channel depth of AH-1

solar air heater. Exergy efficiency decreases with increase in

mass flow rate and become negative at higher mass flow rate

(m > 0.07 kg/s) for all values of channel depth considered. It

has been found that the optimum channel depth is 0.02 m at

which exergy efficiency has the maximum value. Actually the

outlet temperature of air is an important parameter of exergy

efficiency and it is seeing that channel depth affects pumping

operating power, air velocity and consequently heat transfer

coefficient and outlet air temperature. The outlet temperature

of air increases with decrease in channel depth due to increase

in heat transfer rate and attains maximum value at the channel

depth of 0.02 m and then further decrease in channel depth

decreases the outlet temperature of air due to increase in heat

loss to the environment.

V. VALIDATION OF MATHEMATICAL MODEL

0.035 0.040 0.045 0.050 0.055 0.060 0.065

0.50

0.55

0.60

0.65

0.70

0.75

0.80

0.035 0.040 0.045 0.050 0.055 0.060 0.065

0.50

0.55

0.60

0.65

0.70

0.75

0.80

En

erg

y e

ffic

ien

cy (

en

e)


El Sebaii Flat plate

El Sebaii v-corrugated plate


Present work AH-1

Present work AH-2

Present work AH-3

Present work AH-4

Present work AH-5

Present work AH-6

Fig. 19. Comparison of analytical energy efficiency data with available experimental data.

The numerically calculated energy efficiency of different

solar air heaters have been compared with the experimental

values obtained from El Sebaii et al. [43]. Fig. 19 shows the

comparison of analytical results of present work with

experimental values of energy efficiency of El Sebaii et al. of

double flow flat plate (AH-6) and corrugated absorber (AH-4)

solar air heater. The maximum deviation of theoretical values

of energy efficiency for flat plate collector (AH-6) is found to

be and for corrugated collector (AH-4) . Figure

also shows the comparison of energy efficiency of various

types of corrugated collectors with flat plate collector for the

same parameters and found there is considerable enhancement

in energy efficiency for AH-1, AH-2 and AH-3 collectors. The

efficiency enhancement for AH-1 collector is found to be

20.66 % and 15.47 % at the mass flow rate of 0.04 kg/s and

0.06 kg/s respectively with respect to flat plate collector (AH-

6). This shows good resemblance of theoretical and

experimental values which makes validation of calculated

numerical data with mathematical modelling.

VI. CONCLUSIONS

A detailed analytical study has been carried out on the

energy, effective and exergy performance of flat and various

configurations of corrugated absorber double flow solar air

heater under various system and operating conditions. The

important conclusions of this study could be summarized as

follows:

i) A mathematical model for double flow solar air

heater have been developed to study the energy,

effective and exergy performance of collector.

ii) A computer program in C++ language has been

developed to solve the mathematical model and

obtained the results of thermal and effective

thermal energy gain; energy, effective and

exergy efficiencies to analyze the effect of

system and operating parameters.

iii) It is observed that thermal energy gain and

energy efficiency increases while exergy

efficiency decreases with increase in mass flow

rate however effective thermal energy gain and

effective energy efficiency increases upto a

certain limiting value of mass flow rate and then

there after decreases sharply.

iv) It has been found that effective thermal energy

gain of flat plate solar air heater (AH-6) reaches

maximum value at mass flow rate of 0.058 kg/s,

whereas for other collectors maximum values

shifted towards lower mass flow rates. This type

of trends is observed due to increase in pressure

drop of flowing air in corrugated absorber solar

air heaters.

v) There is significant enhancement in efficiency of

corrugated absorber to that of the flat plate

absorber solar air heater with double flow

configurations. The enhancement in energy,

effective and exergy efficiencies at mass flow

rate of 0.035 kg/s for AH-1 collector with respect



to AH-6 collector (flat plate collector) are found

to be 7.12%, 7.20% and 15.43% respectively.

vi) The percentage enhancement of exergy

efficiency reduces with increase in mass flow

rate, because of at higher mass flow rate the

outlet temperature of air is almost equal for all

type of solar air heater. It can also observed that

the exergy efficiency become negative at higher

mass flow rate (i.e. m > 0.072 kg/s), because

exergy of required pump work exceeds the

exergy of energy gain collected by the solar air

heater.

vii) For a specific mass flow rate energy gain;

energy, effective and exergy efficiency increases

with increase in insolation.

viii) The results show that the optimum channel depth

of AH-1 is 0.02 m at which all efficiencies have

the highest values for entire range of mass flow

rate and insolation investigated. Also

increase/decrease in channel depth beyond 0.02

m results in decrease in performance.

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