Design of the Solar Dryer with Thermal Energy Storage
3.2 Estimation of Energy and Air Flow Requirements
The quantity of the energy and air flow requirements depends on the quantity of the moisture to be removed from the agricultural product under the specified conditions. These parameters can be determined by the energy balance equation as well as from the principle of the Psychrometry. The quantity of the moisture (ππ£) to be removed during drying is given by Eq.
(3.1) (Ayensu and Asiedu - Bondzie, 1986).
ο¨ ο©
ο¨
p100iο©
fv
f
m M M
m M
ο½ ο
ο (3.1)
where (ππ) is the mass of the product, ππ is the initial moisture content on wet basis (w.b.), and ππ is the final moisture content (w.b.), both in percentage.
The moisture content of any product on wet basis and dry basis in percentage can be obtained by Eqs. (3.2) and (3.3), respectively (Keey,1992).
ip drp 100
wb
ip
m m
M m
ο½ ο ο΄ (3.2)
ip drp 100
db
drp
m m
M m
ο½ ο ο΄ (3.3)
where πππ is the initial mass of the product, and ππππ is the dry mass of the product.
The relation between the wet basis and dry basis moisture contents is expressed as follows
100
db wb
db
M M
ο½ M
ο« (3.4)
The quantity of the energy required to evaporate ππ£ kg of moisture can be determined by
61
v v fg
Q ο½m h (3.5)
The latent heat of evaporation of water (βππ) can be determined employing Eq. (3.6) and it is to be increased by a factor of 10 β 20% because of the bound moisture (Forson et al., 2007).
ο¨ ο©
ο¨ ο©
0.38
1.38
ln 5
10
cr p
cr
fg v cr bp
cr bp
T T h R T T P
T T
ο¦ οΆ ο
ο½ ο§ο¨ ο·οΈ ο (3.6)
where is the π π£ gas constant for water vapour, πππ and πππ are the critical temperature and pressure of water at the atmospheric condition, respectively and πππ is the boiling point of water at the atmospheric condition.
The average temperature of the product (ππ) can be determined as (Forson et al., 2007).
Tp ο½0.25 3
ο¨
Tid ο«Tambο©
(3.7)where πππ is the drying air temperature, and ππππ is the ambient temperature.
The quantity of air required for the drying operation can be determined from the psychrometric chart as well as from the energy balance equation if the equilibrium moisture content is known for a given drying air condition (Sharma et al., 1986). If the ambient air is heated from a state (A) to a state (B) as shown in Fig. 3.2, the dry bulb temperature of the air increases, and the relative humidity of air decreases. When the drying air at the temperature of πππ and the relative humidity of π βππ passes through the drying materials, the relative and specific humidities of the air increase until the equilibrium state (C) is reached. The moisture content of the product at that state is known as the equilibrium moisture content. If π€π is the specific humidity of air at the beginning of the drying process, and π€π is the specific humidity air corresponding to the equilibrium condition. The total mass of drying air (πππ) is calculated with Eq. (3.8).
v da
f i
m m
w w
ο½ ο (3.8)
If πππ is the dry bulb temperature of the air corresponding to the equilibrium state C, then the total amount of drying air (πππ) required for evaporating of ππ£ kg of moisture can be determined from the energy balance equation Eq. (3.9).
ο¨ ο©
v da pa id od
Q ο½m C T οT (3.9)
where πΆππ is the specific heat of humid air, and it is expressed as follows. Eq. 3.9 allows to calculate (ππ£) required, once πππ is known.
1.005 1.88
Cpa ο½ ο« w (3.10)
where π€ denotes the specific humidity of air.
A
B C
Wi
Wf
Tamb Tod Tid
AB = Sensible heating process; BC = Adiabatic drying process
Fig. 3.2 Sensible heating and theoretical drying processes in the psychrometric chart.
3.2.1 Drying of chilli
The hybrid dryer is expected to be used for drying some of the high-value agricultural products of the North - Eastern region of India. The initial design of the dryer is made for drying chilli.
The primary information necessary for estimating the energy and air flow requirements are the total mass of the product, the initial and final moisture contents of the product, and the total drying time. The initial moisture content of chilli varies between 87.5% (w.b.) and 88.9%
(w.b.). The final moisture content or safe storage moisture content varies from 4.8% (w.b) to 9
63
% (w.b.) (Hossain and Bala, 2002). The drying time depends on the drying air temperature, mass flow rate, velocity, and the relative humidity. The size, shape, and the inner structure of the product also affect the drying time. However, these factors are not considered during sizing of the components of the drying system. The components are sized completely based on the simple energy and air flow requirements.
The following assumptions are made for estimating the energy and air flow requirements.
ο· The average initial moisture content of the chilli is 88% (w.b.).
ο· The desired final moisture content is 9% (w.b.).
ο· The outlet air temperature of the solar air heater varies throughout the day due to variation in the solar radiation. However, an average value of the drying air temperature is assumed which is equal to 50 ο―C.
ο· The average ambient temperature and the relative humidity of the place where the dryer is to be located are assumed to be 25 ο―C and 75%, respectively.
When the ambient air at 25 ο―C and 75% relative humidity is heated to 50 ο―C, the relative humidity is reduced to 17% at the constant specific humidity of 0.01509 kg of water vapour per kg of dry air (from psychrometric chart) as shown in Fig. 3.2. The specific heat of the humid air is 1.03 kJ/kg-K. The amount of the moisture to be removed from 10 kg of chilli while reducing the initial moisture content of 88% (w.b.) to the final moisture content of 9% (w.b.) is 8.7 kg. The average temperature of the product is 43.8 ο―C. Substituting the value of πππ = 647.5 K, πππ = 221.2 bar, πππ€ = 373 K, and π π€ = 461 J/kg-K in Eq. (3.6) and increasing by a factor of 1.15, the latent heat of evaporation is found to be 2.7 MJ/kg which is almost equal to the typical value 2.72 MJ (Ayensu and Asiedu - Bondzie, 1986). The amount of the heat required for the evaporation of 8.7 kg of water is 23.6 MJ.
The equilibrium relative humidity of the red chilli on the dry basis can be suitably predicted with the modified Oswin desorption isotherm model (Kaleemullah and Kailappan, 2004). The modified Oswin model is expressed as follows.
ο» ο½
1
( ) / 1
e C
id e
Rh
A BT M
ο½ ο©ο« ο« ο« οΉο»
(3.11)
where A, B, and C are the dimensionless coefficients, π βπ is the relative humidity in decimal, ππ is the equilibrium moisture content (d.b.), and Tid is the drying air temperature in ΒΊC.
19.299 Aο½
0.19449 Bο½ ο
1.517 Cο½
If the equilibrium moisture content is 10% (d.b.), and the drying air temperature is 50 ΒΊC, then the relative humidity of the drying air at the equilibrium condition is found to be 51.6%. The specific humidity and the dry bulb temperature corresponding to the relative humidity of 51.6%
are 0.0205 kg of vapour/kg of dry air and 37 ο―C, respectively. Substituting the value π€π = 0.01509 of water vapour per kg of dry air and π€π = 0.0205 of water vapour per kg of dry air in Eq. (3.8), the total mass of air required to remove 8.7 kg of moisture from the chilli is found to be 1608 kg.
Table 3.1
Summary of the basic design calculations.
Parameters Value
Type of product Chilli
Initial moisture content 88% (w.b.)
Desired final moisture content 9% (w.b.)
Initial mass of the product 10 kg
Expected drying time 42 h
Average drying air temperature 50 ΒΊC
Ambient air temperature and relative humidity 25 ΒΊC and 75%
Mass of water to be removed 8.7 kg
Total energy requirement 23.6 MJ
Total mass flow of air 1763 kg
Mass flow rate of air 0.012 kg/s
The total mass of air can also be determined from the energy balance equation as given below.
ο¨ ο©
v fg da pa id od
m h ο½m C T οT (3.12)
Applying Eq. (3.12) for πππ = 37 ΒΊC and πππ = 50 ΒΊC the total mass of air is found to be 1763 kg which is almost similar to the total mass of the air estimated using the psychrometric chart.
65
The drying time of the chilli dried in different types of solar dryer varied from 32 h to 55 h (Leon and Kumar, 2008; Banout et al, 2011; Akintunde, 2011; Fudholi et al. 2014a). The size of the other components of the drying system depends on the mass flow rate of air. The air flow rate also affects the energy requirement. The energy requirement increases with increase in the air flow rate and decreases with increase in the drying air temperature (Sarsavadia, 2007).
The higher is the mass flow rate, the larger is the size of the component. Therefore, assuming an average value of the drying time of 42 h and the total mass flow of the air of 1763 kg, the mass flow rate of air is found to be 42 kg/h. The summary of the basic design calculations is given in Table. 3.1.