performance evaluation of an inclined multi-pass solar air heater with in-built thermal storage on...

Journal of Food Engineering 65 (2004) 497–509

www.elsevier.com/locate/jfoodeng

Performance evaluation of an inclined multi-pass solar air heaterwith in-built thermal storage on deep-bed drying application

Dilip Jain *, Rajeev Kumar Jain

Central Institute of Post Harvest Engineering and Technology, PAU Campus, Ludhiana 141 004, India

Received 15 July 2003; accepted 4 February 2004

Abstract

This paper presents a transient analytical model for an inclined multi-pass solar air heater with in-built thermal storage and

attached with the deep-bed dryer. The performance of a solar air heater was evaluated for drying the paddy crop in a deep bed by

using an appropriate deep-bed drying model. A parametric study was done for a day of the month of October for the climatic

condition of Delhi (India). The effect of change in the tilt angle, length and breadth of a collector and mass flow rate on the

temperature of grain have been studied. The rate of moisture evaporation and humidity of the drying air have been analyzed with

the drying time for different depth of the grain bed. It has been observed that the bed moisture content decreases with the time of the

day. The humidity of the air and the drying rate increases with the increase in the depth of drying bed.

� 2004 Elsevier Ltd. All rights reserved.

Keywords: Solar air heater; Deep-bed drying; Solar crop drying; Thermal modeling

1. Introduction

Crop drying under the natural sun is as old as cul-

tivation practices initiated by humans. Sun drying is

still common practice in many tropical and subtropical

countries (Jain & Tiwari, 2003; Szulmayer, 1971). Theproblems associated with the natural sun drying are;

over drying, insufficient drying, discoloration by the

UV radiation and contamination by the foreign mate-

rials, insects and microorganisms (Esper & M€uhlbauer,1998). Various cabinet dryers have been developed to

overcome these problems and to provide better quality

of the products (Ekechukwu & Norton, 1999). The

applications of solar cabinet dryers are limited to sun-shine hours and drying capacity. The thin layer solar

drying has been studied by several researchers (Basunia

& Abe, 2001; Yaldiz, Ertekin, & Uzun, 2001; Yaldiz &

Ertekin, 2001) and established the mathematical mod-

els. Jain and Tiwari (2003, 2004) studied the depen-

dence of convective heat transfer coefficient on rate of

moisture removal and developed a mathematical model

to predict the crop temperature and rate of moisture

*Corresponding author. Tel.: +91-161-2808155.

E-mail address: [email protected] (D. Jain).

0260-8774/$ - see front matter � 2004 Elsevier Ltd. All rights reserved.

doi:10.1016/j.jfoodeng.2004.02.013

evaporation during the natural sun drying and green-

house drying.

However, various indirect solar crop dryers of the

larger capacity have been developed to give the bet-

ter quality of the product over the cabinet dryers

(Ekechukwu & Norton, 1999). These are mainly cou-pled with the solar air heater or use the indirect solar

energy. A solar air heater provides the hot air with a

large variation in the temperature to the dryer only

during sunshine hours. Whereas, drying of many agri-

cultural products (e.g. cereals and pulses) are per-

formed at the steady and moderate temperature and

continuously for few days. In such a case, the thermal

storage is required with a solar air heater for continu-ous drying. A thermal storage unit integrated with the

solar air heater may be charged during the peak sun-

shine hours and utilized (discharged) during off sun-

shine hours for supplying the hot air to the dryer. The

performance of solar air heaters has been simulated,

designed, tested and suggested by many researchers for

crop drying purposes (Aboul-Enein, El-Sebaii, Rama-

dan, & El-Gohary, 2000; Close, 1963; Fath, 1995;Whiller, 1964; Yadav & Tiwari, 1986; Yadav, Kumar,

Sharan, & Srivastava, 1995).

Aboul-Enein et al. (2000) conducted the parametric

study of the inclined solar air heater with thermal storage

mail to: [email protected]

Nomenclature

a constant

A area, m2

b breadth of collector plate, m

b0 constant

C specific heat at constant pressure, J kg�1 K�1

d duct width, m

hc convective heat transfer coefficient,

Wm�2 K�1

hr radiative heat transfer coefficient, Wm�2 K�1

hv volumetric heat transfer coefficient,

Jm�3 s�1 K�1

H humidity of air, decimal

Ieff hourly average effective solar radiation½It þ q0I 0t ðAr=ApÞ�, Wm�2

It hourly average solar radiation on horizontal

surface, Wm�2

I 0t hourly average solar radiation on north wall,

Wm�2

K conductivity, Wm�1 K�1

Kd drying constant, s�1

L length of collector plate, mLg latent heat of vaporization of moisture from

grain, J kg�1

l thickness, m

M moisture content of grain, kgwater/kg of dry

matter

Mg mass of the grain in the bed, kg

Me equivalent moisture content, kgwater/kg of

dry matterMev hourly moisture evaporation, kg h�1

ms mass of storage material, kg_ma mass flow rate, kg s�1

Nu Nusselt number

Ra Rayleigh number

T temperature, K

DT temperature difference, K

t time, sUb bottom loss coefficient, Wm�2 K�1

v wind velocity, m s�1

x length of coordinate in direction of flow,

m

Y depth of drying bed, m

Greeks

a absorptivity

af diffusivity of air, m2 s�1

b tilt angle of collector, degree

b0 expansion factor, K�1

c relative humidity of air, decimal

e emissivity

tf kinematic viscosity of air, m2 s�1

q0 reflectivity of reflector

q density, kgm�3

go overall thermal efficiency, %

r Stefan–Boltzmann constant, Wm�2 K�4

s transmittivity

Subscripts

a air

b bottom insulation of collector

ba bottom of insulation to air

eff effective

f fluid (air)

f1 air stream-I

f1g2 air in stream-I to second glass cover

f2 air stream-IIf3 air stream-III

g grain

g1 first glass cover

g1a first glass cover to air

g1f1 first glass cover to air in stream-I

g1sky first glass cover to sky

g2 second glass cover

g2g1 second glass cover to first glass coverg2f2 second glass cover to air in stream-II

p absorber plate

pf2 absorber plate to air in stream-II

pg2 absorber plate to second glass cover

ps absorber plate to storage material

r reflector

s storage material

sf3 storage material to air in stream-IIIsky sky

v vapour

w water

498 D. Jain, R.K. Jain / Journal of Food Engineering 65 (2004) 497–509

for solar drying applications. They studied the effect of

the various storage materials like sand, granite and

water with a tilted solar collector on the outlet air

temperature and inferred that 0.12 m thickness of

granite at 30� tilt angle of solar collector gave the

maximum increase in outlet air temperature from

ambient air during night hours. Goyal and Tiwari (1999)

have done a simulated study on the effect of the thermalstorage on the deep-bed drying. They had considered

water as a storage medium for the horizontal multi-pass

solar air heater.

Since the performance of an inclined solar air heater

is better over the horizontal one. Therefore, there is a

need to evaluate performance of the tilted multi-pass

solar air heater with the thermal storage on the deep-bed

drying applications. Thus, the present simulation is to

optimize the parameters of the tilted multi-pass solar airheater for deep-bed drying.

D. Jain, R.K. Jain / Journal of Food Engineering 65 (2004) 497–509 499

2. Description of drying system

A schematic diagram of a proposed solar air heater

with the grain dryer is shown in Fig. 1(a). It consists of

the double glass cover, an absorber plate and a reflector

on the wall of the dryer. Granite grits are considered for

storage material and placed under the absorber plate

(Aboul-Enein et al., 2000). The solar air heater is ori-

ented to face south and tilted at b� angle from thehorizontal plane. The air to be heated flows between

the glass covers and absorber plate, where it gains the

thermal energy from the absorber plate. Hot air coming

from the absorber plate and flowing below the storage

material releases the thermal energy to the storage

material during sunshine hours, and gains the thermal

energy from the storage material during off sunshine

hours. Thus the variation in the outlet air temperatureof the air heater is minimized. The outlet air from solar

air heater is used for the grain drying.

Air in

First cover (g1)

Second cover (g2)

aTTf2

hcg1ahcg1f1

hhrg2g1

hrpg2

hcpf2

hcsf3

hrg1

Absorber plate (p)

S

Insu

It

hcps

Reflect

β°

b.dx=ar

b

x=0 x

ma

x+

(a)

(b)

Fig. 1. (a) Inclined multi-pass air heater with in-built thermal storage attached

of collector plate.

3. Thermal analysis

The solar radiation transmits from the glass covers

and is absorbed by the absorber plate. The air flows in

between the glass covers, above the absorber plate and

below the storage material, where it is heated along the

path. The energy balance equations on the various

components of the system are written with the following

assumptions:

ii(i) the heat capacities of the air, glass cover, absorber

plate and insulation are negligible,

i(ii) there is no temperature gradient along the thickness

of glass cover,

(iii) storage material has an average temperature (Ts) ata time (t), (this assumption may be achieved with

the small thickness of storage material),(iv) there is no stratification exists perpendicular to the

air flow in ducts,

Tf1

Tf3

Tg

Tf

hcf1g2

cg2f2

sky

Ub

torage (s)

lation

Grain dryer

or

tρ' I'

I't

Ts

ea of elemental cross section

dx x=L

T f1+dT f1T f1

with deep-bed drying system, (b) element thickness dx along the length


i(v) the system is perfectly insulated and there is no airleakage,

(vi) the volume shrinkage of the grain is negligible dur-

ing drying.

3.1. Energy balance equation on double-glazed multi-pass

flat plate collector (Fig. 1a)

(a) For the first glass cover

ag1IeffAg1 þ hrg2g1ðTg2 � Tg1ÞAg1

¼ hcg1f1ðTg1 � Tf1ÞAg1 þ hcg1aðTg1 � TaÞAg1

þ hrg1skyðTg1 � TskyÞAg1 ð1Þ

where Tsky ¼ Ta � 6 (Whiller, 1967).

(b) For the second glass cover

sg2ag2IeffAg2 þ hrpg2ðTp � Tg2ÞAg2 þ hcf1g2ðTf1 � Tg2ÞAg2

¼ hrg2g1ðTg2 � Tg1ÞAg2 þ hcg2f2ðTg2 � Tf2ÞAg2 ð2Þ

(c) For the absorber plate

sg1sg2apIeffAp

¼ hrpg2ðTp � Tg2ÞAp þ hcpf2ðTp � Tf2ÞAp

þ hcpsðTp � TsÞAp ð3Þ

(d) For air stream-I (Fig. 1b)

hcg1f1ðTg1 � Tf1Þbdx

¼ _maCa

dTf1dx

dxþ hcf1g2ðTf1 � Tg2Þbdx ð4Þ

(e) For air stream-II

hcg2f2ðTg2 � Tf2Þbdxþ hcpf2ðTp � Tf2Þbdx

¼ _maCa

dTf2dx

dx ð5Þ

(f) For air stream-III

hcsf3ðTs � Tf3Þbdx

¼ _maCa

dTf3dx

dxþ UbðTf3 � TaÞbdx ð6Þ

(g) For the storage material

hcpsðTp � TsÞAp ¼ msCs

dTsdt

þ Aphcsf3ðTs � Tf3Þ ð7Þ

3.2. Modeling of deep-bed drying (Brooker, Bakker-

Arkema, & Hall, 1992)

The differential equations of the grain drying model

are based on the law of heat and mass transfer. The setof four equations govern the drying process.

(a) Mass balance equation between grain and air is

given as

_ma

oHoY

¼ �qg

oMot

ð8Þ

(b) Energy balance equation between air and grain is

written as

_maðCa þ CvHÞ oTfoY

¼ qgCvðTf � TgÞoMot

� qgðCg þ CfMÞ oTgot

þ qgLg

oMotð9Þ

(c) Heat transfer equation between air and grain is

given by

qgðCg þ CfMÞ oTgot

¼ hvðTf � TgÞ þ qgLg

oMot

ð10Þ

where hv ¼ 8:69 104 _m1:3a (Wang, Rumsey, & Singh,

1978).(d) The rate of moisture content at a given depth Y of

the drying bed can be written as the drying equation

oMot

¼ �KdðM �MeÞ ð11Þ

where

Kd ¼ a expð�b0=TgÞ ð12Þ

and

Me ¼ 0:01lnð�cÞ

2:31 10�5ðTg þ 55:815Þ

� �ð1=2:99Þð13Þ

(Brooker et al., 1992).

For rough rice in the range of 308–333 K; a ¼ 13:88s�1, b0 ¼ 3818:2 K (Verma, Bucklin, Eadan, & Wratten,

1985).

3.3. System drying efficiency

The system drying efficiency can be well understood

by the overall thermal efficiency of the drying. The

overall thermal efficiency of solar drying system can bedefined as the ratio of heat energy utilized in the

vaporization of the moisture to that of solar radiation

collected by the solar air heater. It has been evaluated by

the following expression (Tiwari, 2002, p. 247)

go ¼Lg

Pt¼24

t¼1 Mev

3600Ap

Pt¼24

t¼1 It 100: ð14Þ

4. Input parameters

The mathematical model is solved for Delhi (lati-

tude 28�350 N, longitude 77�170 E and altitude 216 m

from mean sea level) climatic conditions during

2 4 6 8 10 12 14 16 18 20 22 240

200

400

600

800

1000

1200

1400

Time in h

Sola

r ra

diat

ion

in W

m-2

of

plat

e ar

ea

Solar radiation on horizontal surfaceSolar radiation on inclined (30o)surfaceSolar radiation on inclined plate with reflector

Tem

pera

ture

in o C

10

15

20

25

30

35

40

45

50

Ambient temperature

6-7 hours

Fig. 2. Diurnal variation of average solar radiation and ambient air temperature during month of October.


October (day of year, n ¼ 288), since this is a har-

vesting time for the paddy crop in the northern India.

Hourly average solar intensity and ambient air tem-perature used in solving the model are given in Fig. 2.

On the abscissa of Fig. 2, hourly average time is given,

which started from the average of 6 and 7 h as 1 h

(corresponding to 0 of y-axis). Similarly, every hour

on x-axis represents an average value of time. There-

fore, the maximum solar radiation lies between 12 and

13 h is represented at 7 h from the starting point. The

maximum ambient temperature lags by 2 h of maxi-mum solar intensity and lies between 15 and 16 h (10

h on x-axis). Similarly, from Figs. 3–9 on x-axis data

are the response of the average of two consecutive

hourly data.

2 4 6 8 10 120

10

20

30

40

50

60

70

80

90

100

Time

Tem

per

atur

e in

o C

6-7 hours

Fig. 3. Hourly variation of temperature at the various stages of solar

Solar intensity on the inclined surface was computed

by using the method given by Lui and Jordan (1962). The

solar intensity available on inclined (b ¼ 30�) collec-tor with and without reflector are also shown in Fig. 2.

The various input parameters are given in Table 1. The

Matlab-5.3 software has been used to solve the mathe-

matical model.

5. Results and discussion

5.1. Performance of solar air heater

A computer program was prepared to solve the en-

ergy balance equations (1)–(7) on solar air heater and to

14 16 18 20 22 24 in h

Ta

Tf1

Tf2

Tf3

Tp

Ts

collector for L ¼ 4 m, b ¼ 1 m, b ¼ 30� and _ma ¼ 0:028 kg s�1.

2 4 6 8 10 12 14 16 18 20 22 240

10

20

30

40

50

60

70

80

90

100

Time in h

Tem

per

atur

e in

o C

Tg with horizontal collector and storage

Tg with inclined collector and storage

Tg

with inclined collector with reflector and storage

6-7 hours

Fig. 4. Hourly variation of grain temperature at the different position of solar collector for L ¼ 4 m, b ¼ 1 m, b ¼ 30�, _ma ¼ 0:028 kg s�1 and

Y ¼ 0:2 m.

2 4 6 8 10 12 14 16 18 20 22 240

10

20

30

40

50

60

70

80

90

100

Time in h

Tem

per

atur

e in

o C

Tg at β

β

β

β

β

=0o

Tg at =15o

Tg at =30o

Tg at =45o

Tg at =60o

6-7 hours

Fig. 5. Hourly variation of grain temperature at the different angle of solar collector for L ¼ 4 m, b ¼ 1 m, _ma ¼ 0:028 kg s�1 and Y ¼ 0:2 m.


find out the temperatures of the air in stream-I (Tf1),stream-II (Tf2) and stream-III (Tf3), absorber plate (Tp)and storage material (Ts). The results are obtained for

the solar intensity and ambient air temperature of the

month of October for the climatic condition of Delhi.

The design parameters of the collector are; L ¼ 4 m,

b ¼ 1 m, b ¼ 30� and _ma ¼ 2:8 10�2 kg s�1 (Table 2).

Fig. 3 shows the hourly temperatures of the air in

different streams, absorber plate and storage material.The ambient air temperature is also shown in Fig. 3 to

observe in the rise of temperature by solar air heater.

The working principle of the solar air heater can beexplained from the results obtained in Fig. 3. During

sunshine hours, the ambient air at temperature Taentering into the solar air heater (stream-I) is being

heated due to the convective and radiative heat trans-

fers from first and second glass cover and attain the

temperature Tf1. Air of stream-I, then entered into the

stream-II and the temperature is further increased to

Tf2. Therefore, Tf2 is higher than the Tf1. The tempera-ture of the absorber plate (Tp) is highest during day

hours since plate absorbs the solar radiation as black

2 4 6 8 10 12 14 16 18 20 22 240

10

20

30

40

50

60

70

80

90

100

Time in h

Tem

per

atur

e in

o C

Tg at 2 m length

Tg at 4 m length

Tg at 6 m length

Tg at 8 m length

Tg at 10 m length

6-7 hours

2 3 4 5 6 7 8 9 10

30

40

50

60

70

80

90

Length of solar collector in m

Tem

pera

ture

in

o C

Tg at 12-13 hours

Tg at 17-18 hours

Tg at 0-1 hours

(a)

(b)

Fig. 6. (a) Hourly variation of grain temperature at the various length of solar collector for b ¼ 1 m, b ¼ 30�, _ma ¼ 0:028 kg s�1 and Y ¼ 0:2 m,

(b) effect of length of solar collector on average grain temperature for b ¼ 1 m, b ¼ 30�, _ma ¼ 0:028 kg s�1 and Y ¼ 0:2 m.


body. The high temperature of the absorber plate and

high convective and radiative heat transfer from theplate is responsible for the increase of Tf2. The air of

stream-II at temperature Tf2 passing underneath the

storage material heats up the storage material and the

air temperature comes down to Tf3 which is lower than

the Tf2. Simultaneously, the temperature of the storage

material also increases due to conduction and convec-

tion of heat from the absorber plate. During the sun-

shine hours, the system is utilized to charge (heat-up)the storage bed and also supply the moderate hot air

(Tf3 ranged from 20 to 60 �C) for the crop drying

application. The whole system then works reverse after

the sunset. The hot storage bed supplies the heat

(convective and radiative) to the air of stream-I,stream-II and stream-III. As a result of this, the Tf1, Tf2and Tp are almost equal and higher than the ambient

air temperature and Tf3 is little (2 �C) less than Ts butmore than Tf1 and Tf2. It is due to the fact that during

off-sunshine hours the storage material is hotter than

the incoming air. The trend of temperature Tf3 in Fig. 3

is similar with the results given by Aboul-Enein et al.

(2000) for the granite as the storage materials. Thus,the present design of solar air heater can supply the air

with smaller difference in temperature (22 �C) betweenmaximum and minimum at the end of heater.

2 4 6 8 10 12 14 16 18 20 22 240

10

20

30

40

50

60

70

80

90

100

Time in h

Tem

per

atur

e in

o C

Tg at 0.5 m breadth

Tg at 1.0 m breadth

Tg at 1.5 m breadth

Tg at 2.0 m breadth

Tg at 2.5 m breadth

6-7 hours

0.5 1 1.5 2 2.5

30

40

50

60

70

80

90

Breadth of solar collector in m

Tem

per

atur

e in

o C

Tg

at 12-13 hours

Tg

at 17-18 hours

Tg at 0-1 hours

(a)

(b)

Fig. 7. (a) Hourly variation of grain temperature at the varying breadth of solar collector for L ¼ 4 m, b ¼ 30�, _ma ¼ 0:028 kg s�1 and Y ¼ 0:2 m,

(b) effect of breadth of solar collector on average grain temperature for L ¼ 4 m, b ¼ 30�, _ma ¼ 0:028 kg s�1 and Y ¼ 0:2 m.


5.2. Effect of various parameters of solar air heater on

grain temperature

The computer program was prepared to solve

Eqs. (8)–(11) to find out the grain temperature, moisture

content of grain, rate of drying and humidity of the

drying air, where the initial drying air temperature (Tf ) isthe outlet temperature of the solar air heater. The effect

of inclination of collector plate with storage and reflec-

tor on the grain temperature (Tg) is presented in Fig. 4.

Grain temperature increases with the inclined collector

(b ¼ 30�) over the horizontal and further increases by

using with reflector. This is explained due to more solar

intensity absorbed by the collector on the inclined col-

lector and with reflector. Fig. 5 exclusively shows the

effect of different tilt angle on the grain temperature. It is

evident that Tg increases with increase in the tilt angle

from 0� to 30�. There is not much rise in the Tg beyond30� of inclination of collector. Hence, it proves the

thumb rule for optimum inclination of the solar aircollector, which states that the optimum inclination of

the solar air collector for receiving the solar radiation is

equal to latitude angle ±15� (Tiwari, 2002, p. 142).The effect of length of the collector (L) on the grain

temperature is presented in Fig. 6a and b. Increase in the

length of collector from 2 to 4 m increases the grain

2 4 6 8 10 12 14 16 18 20 22 240

10

20

30

40

50

60

70

80

90

100

Time in h

Tem

per

atur

e in

o C

Tg

at 0.014 kg s-1 mass flow rate

Tg


Tg


Tg


Tg


6-7 hours

Fig. 8. Hourly variation of grain temperature at the varying mass flow rate of solar collector for L ¼ 4 m, b ¼ 1 m, b ¼ 30� and Y ¼ 0:2 m.

2 4 6 8 10 12 14 16 18 20 22 240.1

0.12

0.14

0.16

0.18

0.2

0.22

0.24

0.26

0.28

Time in h

Mo

istu

re c

ont

ent

in k

g w

ater

/kg

dry

mat

ter

6-7 hours

Fig. 9. Variation of moisture content of grain with drying time for L ¼ 4 m, b ¼ 1 m, b ¼ 30�, _ma ¼ 0:028 kg s�1 and Y ¼ 0:2 m.


temperature significantly (up to 15 �C). There is small

increase in the Tg with increasing the length of collector

from 4 to 6 m. Whereas, there is no effect on the Tgbeyond the 6 m of collector length. Similar trend of the

Tg was obtained by increasing the breadth of collector

from 0.5 to 1 and 1 to 1.5 m. There is no effect on the Tgbeyond the 1.5 m breadth of collector (Fig. 7a and b).The increase in length and breadth of the collector in-

creases the absorbing area and storage capacity, which

results in increasing the Tg up to a certain level and

provide the optimum length and breadth of the collec-

tor.

Fig. 8 shows the effect of mass flow rate on the

temperature of grain. There is drastic drop in grain

temperature with increase in mass flow rate from 0.014

to 0.042 kg s�1. Whereas, increasing the mass flow rate

beyond the 0.042 kg s�1, there is a little drop in graintemperature. However, the higher mass flow rate will

lead to supply the air temperature close to the ambient

conditions. Therefore, the mass flow rate should be

Table 2

Range of design parameters used for optimization

Parameters Values

b 0.5, 1.0, 1.5, 2.0, 2.5 m

d 0.1 m

L 2, 4, 6, 8, 10 m

lb, lp, ls 0.05, 0.002, 0.1 m

_ma 0.014, 0.028, 0.042, 0.056, 0.07 kg s�1

b 0�, 15�, 30�, 45�, 60�

Table 1

Input operating parameters used for numerical computation

Parameters Values

Ca, Cv 1004.8, 1883 J kg�1 K�1

Cg, Cs 1300, 794 J kg�1 K�1

Kb, Kp 0.043, 137 Wm�1 K�1

Lg 2.26· 106 J kg�1

v 1 m s�1

ag1, ag2, ap 0.1, 0.1, 0.9

eg1, eg2, ep 0.8, 0.8, 0.95

c 0.5

sg1, sg2 0.9, 0.8

qa, qg, qs 1.177, 600, 2700 kgm�3

q0 0.6

r 5.67· 10�8 Wm�2 K�4


lower for getting higher temperature of grain and vice-versa.

5.3. Performance of deep-bed dryer

The performance of deep-bed dryer is presented in

terms of hourly moisture content of grain, rate of drying

and humidity of the drying air in the drying bed. Hourly

change in the moisture content with drying time is

shown in Fig. 9. The paddy crop at the initial moisture

content of 0.28 kgwater/kg of dry matter has been

considered for the drying. The moisture content reduceslinearly from 0.28 to 0.13 kgwater/kg of dry matter in

12 h of drying time. There is very slow reduction in the

moisture from 0.13 to 0.11 kgwater/kg of dry matter in

rest of the 12 h of drying. This is obvious, since the low

moisture is the bound moisture in the crop, which

evaporates at the slow rate. The effect on moisture

0.1 0.15 00

0.005

0.01

0.015

Moisture content in k

Dry

ing

rate

in k

g w

ater

/kg

dry

mat

ter

h-1

Fig. 10. Variation of drying rate with change in moisture content for

content on drying rate (kgwater/kg of dry matter h�1) is

shown in Fig. 10. The drying rate increases from 0.75 to

1.5 kgwater/kg of dry matter h�1 with the reduction in

moisture content from 0.28 to 0.20 kgwater/kg of dry

matter. The increasing in the rate of drying is due to the

fast evaporation of free moisture. Thereafter, there is

linear drop in drying rate with the reduction in moisture

content; this is due to slow evaporation of boundmoisture from the crop. The trend of drying rate ob-

tained from the model is in the concurrence with the

results presented by Bala (1983).

The drying rate in the deep-bed in term of kg of

moisture evaporated per hour per unit area of grain bed

at different depth of bed is presented in Fig. 11. It shows

the higher rate on drying (kg h�1 m�2) with larger depth

of bed. This is due to the fact that more moisture isavailable to evaporate with the larger volume of drying

bed. The result of this, the humidity of air increases in

the drying bed with the increase in depth of bed as

shown in Fig. 12. The overall thermal efficiency of the

complete system is presented in Fig. 13. The efficiency

increases with the increase in mass of the grain available

in the drying bed.

.2 0.25 0.3

g water/kg dry matter

L ¼ 4 m, b ¼ 1 m, b ¼ 30�, _ma ¼ 0:028 kg s�1 and Y ¼ 0:2 m.

2 4 6 8 10 12 14 16 18 20 22 240

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Time in h

Dry

ing

rate

in k

g w

ater

h-1

m-2

of

grai

n b

ed

Drying rate at 0.05 m depth of bedDrying rate at 0.10 m depth of bedDrying rate at 0.15 m depth of bedDrying rate at 0.20 m depth of bed

6-7 hours

Fig. 11. Hourly variation of drying rate with different depth of grain bed for L ¼ 4 m, b ¼ 1 m, b ¼ 30�, _ma ¼ 0:028 kg s�1 and Y ¼ 0:2 m.

2 4 6 8 10 12 14 16 18 20 22 240

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

Time in h

Hum

idity

in%

Humidity at 0.05 m depth of bed Humidity at 0.10 m depth of bedHumidity at 0.15 m depth of bedHumidity at 0.20 m depth of bed

6-7 hours

Fig. 12. Hourly variation in humidity with different depth of grain bed for L ¼ 4 m, b ¼ 1 m, b ¼ 30� and _ma ¼ 0:028 kg s�1.


6. Conclusions

The performance evaluation of a tilted multi-pass

solar air heater with in-built thermal storage has been

carried out for deep-bed drying applications. The grain

temperature increases with the increase of collector

length, breadth and tilt angle up to typical value of these

parameters. The thermal energy storage also affect

during the off-sunshine hours is very pertinent for cropdrying applications. The proposed mathematical model

is useful for evaluating the thermal performance of a flat

plate solar air heater for the grain drying applications. Itis also useful to predict the moisture content, grain

temperature, humidity of drying air and drying rate in

the grain bed.

Appendix A

A.1 The convective heat transfer coefficients from the

plate to glass, parallel to each other and inclined

at an angle b to the horizontal has been expressed as

10 15 20 25 30 35 40 45 50 55 600

5

10

15

20

25

30

35

40

45

50

Mass of the grain in kg

Ove

rall

the

rmal

eff

icie

ncy

in %

o = 0.6727 x Mg ; R2 = 1η

Fig. 13. Overall thermal efficiency of the system with mass of the grain for L ¼ 4 m, b ¼ 1 m, b ¼ 30� and _ma ¼ 0:028 kg s�1.


hc ¼NuKf

dðA:1Þ

where Nusselt number (Nu) can be obtained by usingexpression given by Hollands, Unny, and Konicek

(1976) for air as medium between the plate and cover

Nu ¼ 1þ 1:44 1

�� 1708

Ra cos b

�þ1

"� 1708ðsin 1:8bÞ1:6

Ra cos b

#

þ Ra cos b5830

� �1=3"

� 1

#þ

ðA:2Þ

for 0 < Ra6 105 and 06 b6 60�.The notation [ ]þ is used to denote that only positive

value to the term is to be considered else it is zero for

negative value, where Ra ¼ gb0DTd3

tfaf.

A.2 The wind heat transfer coefficient from the cover to

ambient (Watmuff, Charters, & Proctor, 1977)

hcg1a ¼ 2:8þ 3:0v ðfor 06 vP 7 m s�1Þ: ðA:3Þ

A.3 The radiative heat transfer coefficients are calcu-

lated as (Duffie & Beckman, 1991)

hrpg2 ¼ eeffrðT 2p þ T 2

g2ÞðTp þ Tg2Þ ðA:4Þ

where

eeff ¼1

ep

�þ 1

eg2� 1

��1

:

A.4 Bottom loss coefficient

Ub ¼lbKb

�þ 1

hcba

��1

: ðA:5Þ

A.5 Thermal properties of moist air (Tiwari, 2002, p.

506)

Cf ¼ 999:2þ 0:1434Tf þ 1:101 10�4T 2f

� 6:7581 10�8T 3f ðA:6Þ

Kf ¼ 0:0244þ 0:6773 10�4Tf ðA:7Þ

af ¼ 7:7255 10�10T 1:83f ðA:8Þ

tf ¼ ð0:1284þ 0:00105TfÞ 10�4: ðA:9Þ

References

Aboul-Enein, S., El-Sebaii, A. A., Ramadan, M. R. I., & El-Gohary,

H. G. (2000). Parametric study of a solar air heater with and

without thermal storage for solar drying applications. Renewable

Energy, 21, 505–522.

Bala, B. K. (1983). Deep bed drying of malt. Ph.D. Thesis, University

of Newcastle Upon Tyne cited in Bala, B. K. (1997). In Drying and

storage of cereal grains (p. 121). New Delhi: Oxford and IBH

Publishing Co. Pvt. Ltd.

Basunia, M. A., & Abe, T. (2001). Thin layer solar drying character-

istics of rough rice under natural convection. Journal of Food

Engineering, 147, 295–301.

Brooker, D. B., Bakker-Arkema, F. W., & Hall, C. W. (1992). Drying

and storage of grain and oil seeds. New York: AVI Book.

Close, D. J. (1963). Solar air heaters for low and moderate temperature

application. Solar Energy, 7(3), 114–117.

Duffie, J. A., & Beckman, W. A. (1991). Solar engineering and thermal

process (2nd ed.). New York: John Wiley and Sons.

Ekechukwu, O. V., & Norton, B. (1999). Review of solar-energy drying

systems II: An overview of solar drying technology. Energy

Conversion and Management, 40, 615–655.

Esper, A., & M€uhlbauer, W. (1998). Solar drying––an effective means

of food production. Renewable Energy, 15, 95–100.


Fath, H. E. S. (1995). Thermal performance of a simple design solar air

heater with built-in-thermal energy storage system. Energy Con-

version and Management, 36(10), 989–997.

Goyal, R. K., & Tiwari, G. N. (1999). Effect of thermal storage on the

performance of a deep bed drying. Ambient Energy, 20(3), 125–136.

Hollands, K. G. T., Unny, T. E., & Konicek, L. (1976). Free

convection heat transfer across inclined air layers. Journal of Heat

Transfer, 98, 1819.

Jain, D., & Tiwari, G. N. (2003). Thermal aspect of open sun drying of

various crops. Energy, 28, 37–54.

Jain, D., & Tiwari, G. N. (2004). Effect of greenhouse on crop drying

under natural and forced convection I: Evaluation of convective

mass transfer coefficient. Energy Conversion and Management, 45,

765–783.

Lui, B. Y. H., & Jordan, R. C. (1962). Daily insolation on surfaces

tilted towards equator. ASHRAE Journal, 3(10), 53.

Szulmayer, W. (1971). From sun drying to solar dehydration: I––

Methods and equipment.Food Technology in Australia, 23, 440–443.

Tiwari, G. N. (2002). Solar energy fundamentals, design, modelling and

applications. Narosa Publishing House.

Verma, L. R., Bucklin, R. A., Eadan, J. B., & Wratten, F. T. (1985).

Effect of drying air parameters on rice drying models. Transactions

of the ASAE, 28, 296–301.

Wang, C. Y., Rumsey, T. R., & Singh, R. P. (1978). Convective heat

transfer of the rough rice. ASAE paper No. 78-30001.

Watmuff, J. H., Charters, W. W. S., & Proctor, D. (1977). Solar and

wind induced external coefficients for solar collectors. Comples, 2,

56.

Whiller, A. (1964). Black painted solar air heaters of conventional

designs. Solar Energy, 8(1), 31–37.

Whiller, A. (1967). Design factors influencing solar collectors, low

temperature engineering application of solar energy. New York:

American Society of Heating, Refrigerating and Airconditioning

Engineers, Inc.

Yadav, Y. P., Kumar, A., Sharan, L. B., & Srivastava, V. B. (1995).

Parametric study of a suspended flat plate solar air heater. Energy

Conversion and Management, 36(5), 25035.

Yadav, Y. P., & Tiwari, G. N. (1986). Transient and analytical

solution of suspended flat plate solar air heater. Energy Conversion

and Management, 26, 265.

Yaldiz, O., & Ertekin, C. (2001). Thin layer solar drying of some

vegetables. Drying Technology, 19(3), 583–596.

Yaldiz, O., Ertekin, C., & Uzun, H. I. (2001). Mathematical

modeling of thin layer solar drying of sultana grapes. Energy, 26,

457–465.

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