Received: 30 October 2020
Accepted: 16 December 2020
DOI: 10.1111/jfpe.13643
ORIGINAL ARTICLE
Mathematical modeling and computational fluid dynamics
simulation of cabinet type solar dryer: Optimal temperature
control
Vishal D. Chaudhari1,2
| Govind N. Kulkarni3 |
Chandrashekhar M. Sewatkar1,4
1
Department of Mechanical Engineering,
College of Engineering, Pune, S.P. Pune
University, Pune, India
Abstract
The mathematical model for determination of auxiliary energy required to maintain
2
Department of Mechanical Engineering,
Cusrow Wadia Institute of Technology, Pune,
India
3
Department of Mechanical Engineering,
Symbiosis Institute of Technology, Lavale,
Symbiosis International (Deemed University),
Pune, India
4
set air temperature in the drying chamber is proposed for cabinet type solar dryer.
The model is developed considering the heat exchanges across the dryer control volume with solar radiation intensity and set temperature as input. The sole purpose is
to minimize the auxiliaries. The computational fluid dynamics (CFD) technique is used
to simulate the air flow inside the drying chamber for different operating conditions.
Department of Mechanical Engineering,
Government College of Engineering &
Research, Avasari, Pune, S.P. Pune University,
Pune, India
The simulations results for the temperature are very close to the results from mathe-
Correspondence
Vishal D. Chaudhari, Department of
Mechanical Engineering, College of
Engineering, Pune, S.P. Pune University, Pune,
India.
Email: vishaldchaudhari@gmail.com
97.3 kWh per day. When applied to full calendar year, the optimum temperature is
matical model. The dryer configuration discussed in illustrative example found to
have minimum auxiliary consumption at 45 C with total auxiliary expense of
found to be function of ambient temperature and solar radiation intensity. The
results obtained from mathematical model are found to be in well agreement with
simulation results. The simulation results provide a region with 1.2 m to 1.6 m on Xordinate, 0.8 m to 1.0 m on Y-ordinate and 0.7 m to 1.2 m and 3.7 m to 4.3 m on Zordinate where average temperature can be sensed. It helps in modulating the auxiliary input/s in integration with solar heat.
1
|
I N T RO DU CT I O N
flow is reported in indirect mode solar dryers (El-Sebaii &
Shalab, 2013; Sharma, Chen, & Lan, 2009). The solar dryers using nat-
Drying is an effective way of product preservation by reducing the
ural convection mode of air flow are referred as passive dryers. The
moisture content in it. One of the prominent energy consumers, drying
drying air temperature in such dryers remains a function of environ-
finds applications in many industries, namely, food processing, agricul-
mental conditions and load on the system. The better product quality
ture, pharmaceutical, paper and pulp, textile, and so forth. A traditional
and reduced drying time is observed is passive dryers (Sharma
and popular way of drying is open sun drying. It suffers from limitations
et al., 2009; Sharma, Sharma, & Garg, 1991). The non-uniformity of
of spoilage, insect infestation and very less control over moisture
the temperature distribution in such dryers does not assure continu-
removal (Ratti & Mujumdar, 1997). The solar dryers are designed and
ous drying of the product (El-Sebaii, Aboul-Enein, Ramadan, & El-
built primarily to overcome limitations of open sun drying.
Gohary, 2002; Prasad, Vijay, Tiwari, & Sorayan, 2006). Active solar
In direct mode solar dryers, the products are exposed to solar
dryers employ mechanical means like fans for air flow. The regulated
radiation. Though effective, it may result in vitamin loss, decoloration,
flow of air ensures better contact with product and improved quality
and quality deterioration (Ekechukwu & Norton, 1999; Gbaha,
in active dryers. The temperature and flow rate of the air can be con-
Andoha, Sarakaa, Kouab, & Toure, 2007; Lawand, 1966). In indirect
trolled in a better way in active dryers as against passive dryers
mode dryers, the air is heated in solar collectors and transported to
(Benhamoua,
the drying space. The better control over drying temperature and air
Belhamri, 2003; Sreekumar, Manikantan, & Vijayakumar, 2008).
J Food Process Eng. 2021;44:e13643.
https://doi.org/10.1111/jfpe.13643
wileyonlinelibrary.com/journal/jfpe
Fazouane,
&
Benyoucef,
2014;
Bennamoun
© 2021 Wiley Periodicals LLC.
&
1 of 12
2 of 12
CHAUDHARI ET AL.
Solar dryers are often used efficiently during daytime when solar
electric supply to the heaters and exhaust fans can be modulated
radiation is available in appreciable amount. This restrains the ability
using a control panel. The dryer insulation is made of glass wool. The
of solar dryers to process the products continuously with reliability.
glass wool is provided with sheets of aluminum composite to
Hence, solar dryers are to be backed up with auxiliary energy supply
strengthen and prevent heat loss to the surrounding.
The dryer is placed at a fixed location and oriented to receive
to maintain uniform conditions in the dryer.
The quality of the dried product relies on the temperature of the
maximum amount of solar heat through aperture glass glazing. The
drying medium. The greater drying temperature may harm the nutri-
dryer space temperature rises with solar heat gain, in turn increasing
tional quality of the product while lower drying temperature may
the product temperature. The drying temperature can be set
cause longer drying periods (Goyal & Tiwari, 1999; Leon, Kumar, &
depending on the product to be dried. This will be the desired dryer
Bhattacharya, 2002; Pin et al., 2009; Saleh & Badran, 2009). More-
space temperature.
over, different products require different drying air temperatures to
The water in the product evaporates and is driven out in the
be maintained inside the dryer (Chen, Hernandez, & Huang, 2005).
atmosphere. Fresh ambient air entering from the front openings
The challenge lies in the development of the dryer that blend the use
blends with hot air inside the dryer space and becomes hot and
of solar input with auxiliary heating to give desired temperature
humid. The exhaust fans drive out this hot and humid air through top
required for the drying.
openings. When solar radiation intensity is not sufficient to attain the
A mathematical model to acquire desired drying air temperature
desired drying temperature, the electric heaters can be turned on to
considering solar incident flux and auxiliary heat as input energy sup-
balance the demand of energy. If the solar radiation intensity available
plied is proposed in this work. A fan is incorporated to maintain the
is in excess of the requirement, the dryer space temperature rises
temperature. The results of the mathematical model are verified
above the desired value. The exhaust fans then accelerates the mixing
through computational fluid dynamics (CFD) simulations.
of ambient air with the hot air in the dryer space. The operation will
proceed till dryer space reaches the desired temperature. The auxiliary
power consumption constitutes that from auxiliary heater and exhaust
2
|
T H E C A B I N E T T Y P E S O LA R D R Y E R
fan. The auxiliary consumption will be minimum when the solar heat is
utilized to its maximum. To minimize the consumption of auxiliaries is
The schematic of the proposed model for industrial solar dryer is a
the objective of this work.
shown in Figure 1. The dryer has pentagonal cross section with metallic cabinet. The width of the dryer (W) is shown by inclined dimension
of the pentagon while length of the dryer (L) is in the direction of nor-
3
|
THE MATHEMATICAL MODEL
mal to the plane of the paper. The schematic in Figure 1 shows the
cross-sectional view of the dryer. The solar radiation is incident on
The energy balance for the dryer space is shown in Figure 2. The
the aperture W × L. The internal void of the cabinet can be termed as
energy interactions across the dryer space control volume affect the
the dryer space. The dryer space is composed of the air within the
internal energy of the dryer space. The dryer space receives the
control volume, internal surfaces of the walls, trays, tray frames, prod-
energy from solar radiation and/or auxiliary heaters. Part of this
uct to be dried, exhaust fans, and auxiliary electric heaters. To have
energy is used to dry the product, some part is carried away by the air
uniform heating of the dryer space, the electric heaters are sized suit-
leaving while remaining part is lost through top as well as side
ably and installed at the bottom of the dryer. To attain maximum
surfaces.
absorption of the solar heat, the aperture is made of double glass glazing. Also, the insulation is provided to all sides of the dryer. The
Energy balance of the control volume can be expressed as
follows:
X
FIGURE 1
Schematic of the cabinet type industrial solar dryer
FIGURE 2
mi cpi
∂T
∂t
= QS −QLT −QLS −Qair
Energy balance across the dryer
ð1Þ
3 of 12
CHAUDHARI ET AL.
In the Equation (1), the change in the internal energy of the dryer
_ air Cp,air ðT f −T amb Þ
QS −Ut Aa ðT f − T ambient Þ− US AS ðT f −T amb Þ− m
_ air Cp,air ðT i −T amb Þ
QS −Ut Ag ðT i −T amb Þ−US AS ðT i − T amb Þ− m
Ut Aa + US AS + m
P _ air Cp,air Δt
−
mi cpi
=e
space is shown on left hand side while right hand side describes
energy interactions across the control surface. Here, mi denotes the
mass of a single internal constituent of the dryer. The various internal
ð8Þ
constituents of the dryer are inner wall, trays, and tray frames, product to be dried and air occupying the dryer space. The specific heat of
The total heat to be supplied (QS) to maintain the desired dryer
the corresponding internal constituent is indicated as Cpi. Total heat
space temperature T, can be estimated using Equation (8) for known
capacity of the dryer space can be evaluated by knowing masses and
values of top loss coefficient Ut, side heat loss coefficient Us and air
specific heats of the internal constituents. For simplicity purpose, the
_ air . In Equation (8), parametric values at the initial instance
flow rate m
heat capacities of electric heaters and fans are omitted. The tempera-
are indicated by the subscript i and at the final instance by subscript f.
ture of the dryer space is shown by symbol T. All the internal constituents are considered to be in thermal equilibrium with each other and
at temperature T. Time step Δt is considered for the mathematical
analysis of dryer space.
The temperature of the dryer space at the end of a certain time
step Δt can be obtained by simplifying Equation (8).
_ air Cp,air ðT i −T amb Þ
T f = − C1 QS −Ut Ag ðT i − T amb Þ −US AS ðT i −T amb Þ− m
_ air Cp,air T amb g= Ut Aa + US AS + m
_ air Cp,air
−QS − Ut Ag + US AS + m
Dryer space receives heat from solar radiation (Qsun) as well as
the auxiliary heating (QAux). Total heat supplied to the dryer is den-
ð9Þ
oted as Qs. The heat loss from glazing surface and side walls is repre-
sented as (QLT) and (QLs), respectively. The energy supplied to the
−
where, C1 = e
dryer constitutes solar incident flux and auxiliary heat.
P
_ air Cp,air
Ut Aa + US AS + m
mi cpi
Δt
There may be the situations, when the heat supplied by solar radiQs = QSun + QAux
ð2Þ
ation is more than the heat required in the dryer. To tackle such situations, a blower can be fitted to the system. Mass flow rate of the air
Depending on the location parameters and environmental condi-
QSolar = IB rB ðταÞB + ID rD ðταÞD + ρG IR r R ðταÞR Ag
to be provided by the blower can be estimated by considering energy
balance across the dryer. The difference between heat supplied to the
tions, the solar incident flux is calculated as:
dryer space and heat utilized and lost from the surfaces, will be the
ð3Þ
heat carried out by the air leaving the dryer space. Thus, mass flow
rate of the blower is given as:
The solar radiation intensity, the tilt factor and average
transmittance-absorptance product are represented as I, r and (τα),
_ blower =
m
respectively while the subscript B, D, and R stands for beam, diffused
ðQS −QSun −QLT −QLS Þ
+ Minimum air circulation
Cp,air ðT i −T Þ
ð10Þ
and reflected radiation; Ag is the area of aperture.
The heat loss from top glazing and side walls are estimated by the
following equation.
When a pressure difference of hw m of water column is
maintained across the blowers, then the energy consumption of the
blowers can be calculated as:
QLT = Ut Aa ðT −T amb Þ
ð4Þ
_ blower g hw Δt
Qfan = m
QLS = US AS ðT − T amb Þ
ð11Þ
ð5Þ
The dryer is supplied with auxiliary energy in the form of heat
The extent of heat loss depends on the temperature of the air in
the dryer (T). The heat carried away by air leaving the dryer
QAux and blower power consumption QFan. The aim of the study is to
minimize the consumption of auxiliary power.
space (Qair) can be calculated as
Minimize : Auxiliaries = QAux + QFan
_ air Cp,air ðT −T amb Þ
Qair = m
4
Merging Equation (3) and (4) in Equation (1),
X
mi cpi
∂T
∂t
ð12Þ
ð6Þ
_ air Cp,air ðT −T amb Þ
= QS −Ut Aa ðT −T amb Þ− US AS ðT −T amb Þ− m
ð7Þ
|
SIMULATION APPROACH
CFD is an effective tool to analyze flow and heat transfer under various operating conditions. This technique is used successfully for
predicting distribution of flow properties as well as to study different
geometries of the dryer in industrial applications and by researchers
Solution of the differential Equation (7) may be obtained analytically over a time step Δt.
(Amanlou & Zomorodian, 2010; Mirade, 2003). In this study, the temperature distribution inside the drying chamber of the solar dryer is
4 of 12
CHAUDHARI ET AL.
∂
∂
∂
∂k
+ Sh
ðρEÞ +
½v i ðρE + pÞ =
keff
∂t
∂xi
∂xj
∂xj
investigated using CFD approach. The temperature distribution is further utilized to locate the region of average temperature of air in the
ð18Þ
dryer space.
In the above equation, along with usual notations μ represents
dynamic viscosity (kgm−1 s−1), μt is turbulent viscosity (kgm−1 s−1), σ k
4.1
|
and σ ε are turbulent Prandtl numbers for k and ε respectively, Gk and
Governing equation
Gb are generation of turbulent kinetic energy due to the mean velocity
Heat and mass transfer in the dryer space is carried out by solving
gradients and buoyancy, YM is contribution of the fluctuating dilata-
three-dimensional governing equation (mass, momentum and energy
tion in compressible turbulence to the overall dissipation rate,
equation) along with initial and boundary conditions under transient
S represents source terms and C1ε, C2ε, and C3ε are the constants used
and turbulent flow assumptions. The governing partial differential
in turbulent model.
equation to be solved is as given below:
Due to capability of CFD modeling to solve non-linear equation
Continuity equation
using numerical methods, it is comprehensively used to predict the
temperature and velocity in the drying chamber. The values of the
δρ
Þ = 0
+ r:ðρu
δt
ð13Þ
properties obtained are the time –averaged values for the time step
considered during simulation.
Momentum equation
4.2
Þ
δðρu
Þ = −rP + r:ðτeff Þ + ρgβ T 0 − T
+ r:ðρuu
δt
|
Simulation model
ð14Þ
Three dimensional model of the dryer is developed in geometry modeler of ANSYS-17.2. The computational domain consists of openings
located at the bottom of the dryer while air leaves the dryer space
Energy equation
X
δðρEÞ
ðρE + PÞÞ = r: λeff rT −
Þ
+ r:ðu
Hj Jj + ðτeff :u
δt
j
from the top openings. Thus, air flow going out is assisted by variation
!
ð15Þ
in density. Solar flux incident is provided to the top inclined plane of
the dryer body while bottom plate is given auxiliary heat or else it is
insulated. All other surfaces of the dryer are provided with insulating
material properties.
where ρ is density (kgm−3), u is mean velocity (ms−1), P is pressure
The meshing of the model is performed using FLUENT meshing
(Nm−2), τeff is effective stress tensor, β is thermal expansion coefficient, T 0 is reference temperature and T is mean temperature (K), E is
tool. Different grid densities are tried and fine setting is preferred with
specific energy of fluid ((J kg−1), Hj is enthalpy of species (J kg−1), Jj is
and tetrahedral cell. The total number of nodes and elements are
diffusion flux of species (kgm−2 s−1) and λeff is effective thermal con-
1,567,388 and 1,523,448, respectively. The average orthogonal qual-
ductivity (Wm−1 K−1).
ity and skewness for mesh considered is 0.9982 and 0.00734,
The preliminary simulations are performed to determine the
minimum cell size of 1 mm. Elements are combination of hexahedral
respectively.
nature of flow inside the drying chamber. The results obtained are
used to calculate the Rayleigh number. It indicated that the air flow
inside the drying chamber is turbulent. Therefore, turbulence model
4.3
|
Initial and boundary conditions
need to be employed during simulation. Among the many turbulence
models embedded in CFD, the k–ε turbulence model has proven to be
Initial and boundary conditions are set up to solve governing equation.
an accurate model and it is implemented successfully by many
The initial condition of air in the dryer space is set up with reference
researchers
&
to the final condition of previous time step in mathematical model.
Ghiaus, 2006). It is a semi-empirical model which is based on transport
Respective environmental conditions are specified during each simula-
equation for the turbulent kinetic energy (k) and its dissipation rate (ε)
tion. The solar incident flux value is given as input flux to inclined wall.
as in Equation (16) and (17). The standard k–ε model was used with
The hourly values of solar incident flux are obtained from standard
standard wall functions in this study.
available data and are distributed over considered time step.
(Amanlou
∂
∂
∂
ðρkÞ +
ðρkui Þ =
∂t
∂xi
∂xj
∂
∂ ðρεui Þ ∂
ðρεÞ +
=
∂t
∂xj
∂xi
&
Zomorodian,
2010;
Margaris
μ ∂k
+ Gk + Gb −ρE −Y M − SK
μ+ t
σ k ∂xj
The wall surfaces are given a thickness of 0.075 m with external
ð16Þ
heat transfer coefficient of 5 W/m2K. The wall properties are set as
mentioned in Table 1 for simulation. For naturally inducting flow, the
μ ∂ε
ε
ε2
μ+ t
+ C1ε ðGk + C3ε Gb Þ− C2ε ρ + Sε
k
ρε ∂xj
k
ð17Þ
inlet openings are set at zero gauge pressure. The specified mass flow
rate of air is mentioned at outlet openings as per the mathematical
model.
5 of 12
CHAUDHARI ET AL.
TABLE 1
Data for the illustrative example
Dryer aperture W × L
4m×6m
Slope of the aperture
21
Mass of dryer internal
constituents
933 kg
Specific heat of the dryer
internal constituents
477 kJ kg−1 K−1
Inner wall
Stainless steel, 1 mm thickness
Wall insulation
Glass wool 75 mm thick, density
48 kgm−3 thermal conductivity—
0.04 Wm−1 K−1
Outer wall
Aluminum composite sheet 3 mm
thick
Thermal conductivity—0.3
Wm−1 K−1
Location
Pune (18.53 north, 73.85 east),
India
Day
15th March
Minimum air circulation rate
0.16 kg s−1
Pressure difference across the
exhaust fans, m of water
column
0.35
5
FIGURE 3
Variation of solar radiation intensity over a day
FIGURE 4
Variation of ambient temperature over a day
RESULTS AND DISCUSSION
|
A solar dryer of aperture 4 × 6 m is considered to illustrate the proposed mathematical model. The parameters of the dryer are shown in
Table 1. The mathematical model is solved for a time horizon of 24 hr
with 10 min time step. The solar radiation data of hourly mean values
is considered for a typical day (March 15). A strict maintenance of
temperature in the dryer space ensures optimization of time, economy, and product quality. Drying processes of different products are
specified at prescribed temperatures in various investigations (Ching,
Sachin, & Sze, 2012).
The mathematical model is solved to obtain dryer space tempera-
The variation of dryer space temperature with line of constant
ture. The dryer space temperature varies with the solar radiation
temperature at 55 C is shown in Figure 5. Three regions A, B, and C
intensity and ambient temperature. The solar radiation intensity and
can be identified in Figure 5. Regions A and B appear below the set
ambient temperature varies with the time. These variations are
temperature line. During this period (1 a.m. to 9.30 a.m. and 5 p.m. to
depicted through Figures 3 and 4, respectively for March 15, at Pune,
1 a.m.) auxiliary heating is needed to maintain the set temperature.
India. The required temperature of the air inside the dryer space is
The region C is above the set temperature line of 55 C and it signifies
referred as set temperature. The energy consumed by the auxiliaries
the need of heat removal by enhanced air circulation from 9.30 hr to
can be estimated using the mathematical model for a particular set
17 hr (or 9.30 a.m. to 5 p.m.).
temperature. Auxiliaries can be modulated to obtain the set value of
dryer space temperature.
5.2 | Dryer space temperature with solar heat and
auxiliary energy supply
5.1
|
Dryer space temperature with solar heat only
The proposed configuration of dryer can be operated at any set tem-
The variation of dryer space temperature with time, considering the
perature. The mathematical model is solved using MS-EXCEL pro-
solar heat as the only energy supplied is shown in Figure 5. As
gramming. The set temperature of the air can be varied in the
expected, the temperature follows the same variation as solar
mathematical model. According to set temperature the auxiliary
radiation.
power consumption will change. It is noticed that for a set
6 of 12
CHAUDHARI ET AL.
F I G U R E 5 Variation of dryer
space temperature with a set
temperature of 55 C
F I G U R E 6 Variation of dryer
space temperature with optimum set
temperature of 45 C
temperature of 55 C, the total auxiliary energy consumption is esti-
energy consumption in kWh per day as ordinate. First characteristic
mated to be 113.1 kWh per day. The energy by auxiliary heater will
depicts the variation of auxiliary heat with set temperature. The con-
be 97.7 kWh while the fan energy consumption of 15.4 kWh over a
sumption of energy by auxiliary heater increases with set value line-
day. Changing the set value of temperature will change the auxiliary
arly while exhaust fan consumption decreases nonlinearly. The effect
energy requirement. The objective is to minimize the auxiliary energy
of increase in set temperature on total auxiliary energy consumption
requirement.
is depicted by third characteristic as shown in Figure 7. This character-
For the month of March, the auxiliary power consumption is cal-
istic indicates that total auxiliary energy will be minimum with
culated for different set temperature values using mathematical
97.3 kWh per day at a set temperature of 45 C. If the dryer is oper-
model. It is observed that, with increase in set temperature, the total
ated at 45 C, solar energy utilization will be maximum and auxiliary
auxiliary energy reduces and reaches a minimum at 45 C and it further
energy consumption will be minimum.
increases with increase in set temperature. The variation of dryer
The initial decrease of total auxiliary energy consumption may be
space temperature for set temperature of 45 C is shown in Figure 6.
attributed to a reduced auxiliary heat requirement at lower values of
In region A and B, it is required to provide auxiliary heat while in
set temperatures. At lower values of set temperatures, blower energy
region C blower to be turned on. Figure 7 also shows three character-
predominates in the total energy consumption. Blower energy con-
istics with set value of dryer space temperature as abscissa and
sumption is not as acute as electric heater consumption. Thus the
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CHAUDHARI ET AL.
F I G U R E 7 Energy consumption at
various set temperatures, total
auxiliary energy will be minimum at set
temperature of 45 C
F I G U R E 8 Variation of dryer
space temperature if dryer is operated
in day time with set temperature
of 50 C
cumulative effect is reduction in total power requirement with
increase in set temperature up to 45 C. Increase in set temperature
5.3 | Optimum temperature of dryer space round
the year
beyond 45 C enhances the contribution of electric heater. This further increases the total energy consumption beyond 45 C.
The mathematical model is applied for the complete year considering
The preceding analysis shows dryer operation for 24 hr which
the average value of solar radiation for the months. The auxiliary
means heater and blower will maintain the temperature in the dryer
energy requirement is thus found out for different set temperatures
for 24 hr.
and different solar radiation intensities and from the data, the optimum
When the drying process is combined with the available solar
temperature for each month is obtained. The maximum optimum tem-
heat, it is beneficial to operate a solar appliance in day time. The oper-
perature of 47.5 C is attained during the month of April and minimum
ation of one such solar dryer to be maintained at a set temperature of
optimum temperature 33.5 C attained in month of August. The opti-
50 C is shown in Figure 8. The dryer operates during the day time
mum temperatures acquired are plotted against the months as shown
from 6 a.m. to 7 p.m. for 13 hr. The optimum value of set temperature
in Figure 9. The optimum temperature hovers around 40 C except the
increases to 50 C with a total auxiliary consumption of 39.4 kWh per
month of August and September when lower ambient temperature and
day. This underlines more effective utilization of solar heat as com-
also lower solar radiation is experienced. Solar radiation intensity influ-
pared to 24-hr operation. Thus, it is beneficial to operate this dryer in
ences the optimum set temperature. The higher the solar radiation
daytime.
intensity the higher will be the value of optimum set temperature. So, it
8 of 12
CHAUDHARI ET AL.
F I G U R E 9 Variation of optimum
temperature, solar radiation and
ambient temperature during the year
F I G U R E 1 0 Temperature
contour obtained by simulation
on vertical plane for a set
temperature of 45 C
reveals that the optimum temperature not only a function of solar radi-
simulations, no load condition of the dryer is contemplated. The aver-
ation but is also depends on ambient temperature. The variation of
age temperature of air in the dryer space is noted at the end of the
optimum temperature (Topt) with ambient temperature (Tamb) and global
each simulation.
The simulations for set temperature of 45 C are reviewed. To
radiation intensity (Qsolar) can be predicted by the relation:
understand the extent of temperature distribution, the vertical planes
T opt = 366:15− ð0:267 x T amb Þ + ð0:0659 x Qsolar Þ
ð19Þ
(isosurfaces) are generated in the dryer model and constant temperature contours are plotted. The variation of temperature in a vertical
plane located at 1.5 m away from the side wall at 12.30 p.m., is shown
in Figure 10. High temperatures of air are observed near the wall sur-
5.4 | Dryer space temperature from simulation
approach
faces compared to core region. This may owe to the emissivity of the
inner wall surfaces. Also, stagnancy of air flow near the wall boundaries may reduce the heat flow in these regions which further
The CFD simulations are performed using ANSYS FLUENT 17.2 soft-
increases the air temperature. Similar temperature contours are real-
ware to investigate temperature distribution profile in the dryer space.
ized on parallel vertical planes.
The simulations are carried out on the solar dryer configuration con-
The temperature contours are also plotted on planes parallel to
sidered in mathematical analysis. The simulations are performed for
the bottom plate of the dryer. The temperature distribution for a
different set temperatures. The input solar incident flux values and
plane at 50 cm above the bottom plate is shown in Figure 11. The
corresponding outlet velocities are varied for each time step. During
temperature near the wall surface is higher; in the core region the
9 of 12
CHAUDHARI ET AL.
FIGURE 11
Temperature contour obtained by simulation on horizontal plane for a set temperature of 45 C
F I G U R E 1 2 Temperature contour obtained by simulation on vertical planes for a set temperature of 45 C at clock times (a) 9.30, (b) 11.30,
(c) 13.30, and (d) 15.30
10 of 12
CHAUDHARI ET AL.
F I G U R E 1 3 Deviation of air
temperature obtained during
simulation from set temperature in
mathematical model
FIGURE 14
Location of average temperature region in dryer space
variation of temperature is comparatively less and is near to the aver-
The temperature distribution on vertical and horizontal planes
age temperature. It is observed that the air temperature is close to the
implies that the product to be dried should be placed away from the
average temperature (±1 C) for about 70% of the region.
wall boundary surfaces. This will avoid the burning of the product due
Similar temperature plots are obtained for other clock times as
to high temperatures encountered. Also, proper location of tray/s can
presented in Figure 12. Comparison of theses temperature plots
be obtained so that all the products will be exposed to reasonably
shows slightly higher temperatures near the boundary, during time
same temperature.
periods (12–14 O'clock) when solar radiation available is more.
Except the regions very close to the boundary wall, temperature is
found close to the average temperature of the air that is, 318 K.
The recirculation patterns of the air are also noticed and these pat-
5.5 |
space
Location for average temperature in dryer
terns may assist to keep the temperature around the average
temperature.
In commercial applications, it is desired to maintain temperature in the
The deviation of the air temperature obtained using simulations
dryer near to drying temperature of the product. To maintain constant
from the set temperature considered in mathematical model is
temperature in the dryer, the use of auxiliaries like heater and blower
shown in Figure 13 for different clock times throughout the day.
is recommended. The energy supply to the auxiliaries is required to be
The maximum deviation of about 2.5 C is observed while minimum
modulated as it is different for different set (desired) temperature.
deviation is about 0.4 C. The average deviation of about 2% is
This necessitates locating the point/s in the dryer space where the
noted between the simulation and mathematical results for temper-
probability of getting average temperature is highest. The simulations
ature profile. Thus, mathematical model is verified by simulation
results obtained are used to get locations where average temperature
model.
is obtained. Such points are acquired from simulation for various time
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CHAUDHARI ET AL.
steps. The common locations are sorted out and a region/s is found
where the average temperature can be observed. The region lies
about 1.2 m to 1.6 m on X-ordinate, 0.8 m to 1.0 m on Y-ordinate and
0.7 m to 1.2 m and 3.7 m to 4.3 m on Z-ordinate. These regions are
shown in Figure 14. The temperatures sensed in these regions provide
reasonable accuracy to modulate the auxiliaries and get required temperature of air in the dryer space.
6
|
C O N CL U S I O N
The proposed mathematical model is an improvised design of cabinet
type solar dryer suitable for industrial applications. Due to inclusion of
auxiliaries, it is possible to maintain a constant temperature inside the
dryer which increases the reliability of the drying process. The model
ensures effective utilization of solar heat by minimizing the auxiliary
energy.
The model is operated at different set temperatures and it is
found that the auxiliary power consumption is minimum at 45 C. At
45 C, the total energy consumption amount to be 97.3 kWh per day.
If the dryer is operated at 45 C solar energy utilization will be maximum and auxiliary energy consumption will be minimum. If the set
temperature increases beyond 45 C, the total auxiliary consumption
per day increases. The mathematical model applied to yearly solar
radiation data shows that maximum optimum temperature of 47.5 C
is experienced in month of April while in August the minimum optimum temperature 33.5 C is attained. This underlines the more effective utilization of solar heat in combination with auxiliary heat.
The results of mathematical model are verified using simulation
model. The simulations carried out at different clock time show that
the average temperature variation is less than 2%. The results unveils
that product should be located away from the wall boundary as air
temperature experienced are more near the boundary. The simulation
results help to predict the location of average temperature. The average temperature sensed at this location can be used to modulate the
auxiliaries.
CONF LICT OF IN TE RE ST
The authors declare no conflicts of interest.
AUTHOR CONTRIBUTIONS
Vishal Chaudhari: Conceptualization; data curation; formal analysis;
investigation; methodology; software; writing-original draft. Govind
Kulkarni: Project administration; supervision; validation. Chandrashekhar Sewatkar: Project administration; supervision; validation.
ORCID
Vishal D. Chaudhari
https://orcid.org/0000-0001-6717-7431
RE FE R ENC E S
Amanlou, Y., & Zomorodian, A. (2010). Applying CFD for designing a new
fruit cabinet dryer. Journal of Food Engineering, 101(1), 8–15. https://
doi.org/10.1016/j.jfoodeng.2010.06.001
Benhamoua, A., Fazouane, F., & Benyoucef, B. (2014). Simulation of solar
dryer performances with forced convection experimentally proved.
Physics Procedia, 55, 96–105. https://doi.org/10.1016/j.phpro.2014.
07.015
Bennamoun, L., & Belhamri, A. (2003). Design and simulation of a
solar dryer for agriculture products. Journal of Food Engineering,
59(2–3),
259–266.
https://doi.org/10.1016/S0260-8774(02)
00466-1
Chen, H. H., Hernandez, C. E., & Huang, T. C. (2005). A study of the drying
effect on lemon slices using a closed-type solar dryer. Solar Energy, 78
(1), 97–103. https://doi.org/10.1016/j.solener.2004.06.011
Ching, L. H., Sachin, V. J., & Sze, P. O. (2012). Solar drying: Fundamentals,
applications and innovations. Singapore. ISBN: 978-981-07-3336-0.
Ekechukwu, O. V., & Norton, B. (1999). Review of solar-energy drying systems II: An overview of solar drying technology. Energy Conversion &
Management, 40(6), 615–655. https://doi.org/10.1016/S0196-8904
(98)00093-4
El-Sebaii, A. A., Aboul-Enein, S., Ramadan, M. R. I., & El-Gohary, H. G.
(2002). Experimental investigation of an indirect type natural convection solar dryer. Energy Conversion & Management, 43(16), 2251–2266.
https://doi.org/10.1016/S0196-8904(01)00152-2
El-Sebaii, A. A., & Shalab, S. M. (2013). Experimental investigation of an
indirect-mode forced convection solar dryer for drying thymus and
mint. Energy Conversion & Management, 74, 109–116. https://doi.org/
10.1016/j.enconman.2013.05.006
Gbaha, P., Andoha, H. Y., Sarakaa, J. K., Kouab, B. K., & Toure, S. (2007).
Experimental investigation of a solar dryer with natural convective
heat flow. Renewable Energy, 32(11), 1817–1829. https://doi.org/10.
1016/j.renene.2006.10.011
Goyal, R. K., & Tiwari, G. N. (1999). Performance of a reverse flat plate
absorber cabinet dryer: A new concept. Energy Conversion & Management, 40(4), 385–392. https://doi.org/10.1016/S0196-8904(98)
00123-X
Lawand, T. A. (1966). A solar cabinet dryer. Solar Energy, 10(4), 158–164.
https://doi.org/10.1016/0038-092X(66)90002-8
Leon, M. A., Kumar, S., & Bhattacharya, S. C. (2002). A comprehensive procedure for performance evaluation of solar food dryers. Renewable and
Sustainable Energy Reviews, 6(4), 367–393. https://doi.org/10.1016/
S1364-0321(02)00005-9
Margaris, D. P., & Ghiaus, A. G. (2006). Dried product quality improvement by air flow manipulation in tray dryers. Journal of Food Engineering, 75(4), 542–550. https://doi.org/10.1016/j.jfoodeng.2005.
04.037
Mirade, P. (2003). Prediction of the air velocity field in modern meat dryers
using unsteady computational fluid dynamics (CFD) models. Journal of
Food Engineering, 60(1), 41–48. https://doi.org/10.1016/S0260-8774
(03)00009-8
Pin, K. Y., Chuah, T. G., Abdull Rashih, A., Law, C. L., Rasadah, M. A., &
Choong, T. S. Y. (2009). Drying of betel leaves (Piper betle L.):
Qualityand drying kinetics. Drying Technology, 27(1), 149–155. https://
doi.org/10.1080/07373930802566077
Prasad, J., Vijay, V. K., Tiwari, G. N., & Sorayan, V. P. S. (2006). Study on
performance evaluation of hybrid drier for turmeric (Curcuma longa L.)
drying at village scale. Journal of Food Engineering, 75(4), 497–502.
https://doi.org/10.1016/j.jfoodeng.2005.04.061
Ratti, C., & Mujumdar, A. S. (1997). Solar drying of foods: Modelling and
numerical simulation. Solar Energy, 60(3–4), 151–157. https://doi.org/
10.1016/S0038-092X(97)00002-9
Saleh, A., & Badran, I. (2009). Modeling and experimental studies on a
domestic solar dryer. Renewable Energy, 34(10), 2239–2245. https://
doi.org/10.1016/j.renene.2009.03.001
Sharma, A., Chen, C. R., & Lan, N. V. (2009). Solar-energy drying systems: A review. Renewable and Sustainable Energy
Reviews, 13(6–7), 1185–1210. https://doi.org/10.1016/j.rser.
2008.08.015
12 of 12
Sharma, V. K., Sharma, S., & Garg, H. P. (1991). Mathematical modelling
and experimental evaluation of a natural convection type solar cabinet
dryer. Energy Conversion & Management, 31(1), 65–73. https://doi.org/
10.1016/0196-8904(91)90106-S
Sreekumar, A., Manikantan, P. E., & Vijayakumar, K. P. (2008). Performance
of indirect solar cabinet dryer. Energy Conversion & Management, 49(6),
1388–1395. https://doi.org/10.1016/j.enconman.2008.01.005
CHAUDHARI ET AL.
How to cite this article: Chaudhari VD, Kulkarni GN,
Sewatkar CM. Mathematical modeling and computational fluid
dynamics simulation of cabinet type solar dryer: Optimal
temperature control. J Food Process Eng. 2021;44:e13643.
https://doi.org/10.1111/jfpe.13643