Mathematical modelling and verification of open sun drying of cotton seeds

Abstract

Researchers have carried out the kinetics of various agro products for open sun drying, but research articles still need to address such analysis for cotton seeds. Open sun drying of cotton seeds has been experimentally investigated and presented in this paper. Shorting of cotton seeds was carried out to collect appropriate samples in current research work. Cotton seeds were found to have a nearly ovoid shape with an average radius of 2 to 2.5 mm. The initial moisture content of cotton seeds was estimated to be 14.65% wet-basis using the hot air oven method. During drying, the reduction in the mass of cotton seeds was measured at every one-hour time interval. From this data, it was observed that drying occurred with a falling rate period. Drying data were fitted with 10 mathematical models available in the literature. Multi-regression analysis in Excel-solver equation was performed to obtain values of constants and coefficients of these models. Coefficient of determination (R2), reduced chi-square (χ2) and root mean square error were taken as criteria for the selection of the best drying model. The diffusion approach and models by Verma et al. were chosen as the most suitable drying models for open sun drying of cotton seeds. Effective diffusivity was estimated and found within the range suggested in the literature.

Full text

†, https://orcid.org/0000-0002-3787-9712
‡, https://orcid.org/0000-0002-0351-9559
International Journal of Low-Carbon Technologies 2023, 18, 887–895
© The Author(s) 2023. Published by Oxford University Press.
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/), which
permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.
https://doi.org/10.1093/ijlct/ctad075 Advance Access publication 18 August 2023 887
Mathematical modelling and verication of
open sun drying of cotton seeds
..............................................................................................................................................................
Vijay Patel1,2,K. B. Judal2,*,Hitesh Panchal3,†,Naveen Kumar Gupta4,
Musaddak Maher Abdul Zahra5and Mohd Asif Shah6,7,8,9,‡
1Mechanical Engineering Department, Gujarat Technological University, Ahmedabad,
382424, India;2Mechanical Engineering Department, Government Engineering College,
Palanpur, 385001, India;3Mechanical Engineering Department, Government Engineering
College, Patan, 384265, India;4Department of Mechanical Engineering, GLA University,
Mahtura 281406, India; 5Computer Techniques Engineering Department, Al-Mustaqbal
University College, Hillah 51001, Iraq & Electrical Engineering Department, College of
Engineering, University of Babylon, Hillah, Babil, Iraq;6Department of Economics, College
of Business and Economics, Kabridahar University, Kabridahar, Po Box 250, Ethiopia;
7School of Business, Woxsen University, Kamkole, Sadasivpet, Hyderabad, Telangana,
502345, India; 8Division of Research and Development, Lovely Professional University,
Phagwara, Punjab, 144001, India;9School of Engineering and Technology, Sharda
University, Greater Noida 201310, India
.............................................................................................................................................
Abstract
Researchers have carried out the kinetics of various agro products for open sun drying, but research articles
still need to address such analysis for cotton seeds. Open sun drying of cotton seeds has been experimentally
investigated and presented in this paper. Shorting of cotton seeds was carried out to collect appropriate
samples in current research work. Cotton seeds were found to have a nearly ovoid shape with an average
radius of 2 to 2.5 mm. The initial moisture content of cotton seeds was estimated to be 14.65% wet-basis using
the hot air oven method. During drying, the reduction in the mass of cotton seeds was measured at ever y one-
hour time interval. From this data, it was observed that drying occurred with a falling rate period. Drying
data were tted with 10 mathematical models available in the literature. Multi-regression analysis in Excel-
solver equation was performed to obtain values of constants and coecients of these models. Coecient
of determination (R2),reducedchi-square(χ2) and root mean square error were taken as criteria for the
selection of the best drying model. The diusion approach and models by Verma et al.werechosenasthe
most suitable drying models for open sun drying of cotton seeds. Eective diusivity was estimated and
found within the range suggested in the literature.
Keywords:drying kinetics; open sun drying; eective diusivity; drying rate; moisture ratio
*Corresponding author:
judalkb@gmail.com Received 25 November 2022; revised 5 June 2023
.................................................................................................................................................................................
1INTRODUCTION
In India, 54.6% of the total population is involved in agriculture
or allied sectors like animal husbandry, processing of agricultural
products, export of various agricultural products, etc. [1]. India
had 126.07 lakh hectares of cultivation area for cotton crops in
the year 2019, which was the highest in the world. Nearly 45 to
55 million people were farming, trading and processing this crop
[2]. The total area of plantation and production of cotton in India
for the year 2017–18 was 124.29 lakh hectares and 34.89 million
tons, respectively [1]. Cotton has applications in ginning mills, oil
industries, cattle feed, pigments, etc. Cotton seeds are processed
to extract cotton oil and produce cotton seed cake. Cotton seeds
Downloaded from https://academic.oup.com/ijlct/article/doi/10.1093/ijlct/ctad075/7245784 by guest on 21 August 2023

V. P a t e l et al.
Figure 1. Open sun drying of cotton seeds in industries: (a) Sidhdhi Industries, Visnagar (b) Devine Bro. Cotton Ind., Palanpur.
comprise 12%–14% of oil and 80%–85% cotton seed cake [3]. Cot-
ton oil has several health benets because it contains 65%–70%
unsaturated fatty acid and 26%–35% saturated fatty acid. [4].
Processing raw cotton requires uniform drying of cotton seeds
to produce cotton oil and cotton seed cake. At present, cotton
seeds processing industries utilize sun drying for this purpose.
Figure 1 represents such practices followed by two industries.
Drying of products reduces water content and increases its life
by retarding microbe activity. It markedly reduces the weight and
volume of products, minimizing the cost of packing, handling,
storage and transportation. Open sun drying is an ancient way of
dryingandpreservingagroproducts.Eventoday,manydevelop-
ing countries, especially tropical and subtropical, utilize it to dry
[5]. Solar energy is the best renewable energy source as it is inex-
haustible, abundant, non-pollutant, cheap and environmentally
friendly [6].
Drying events are accurately explained by thin-layer drying
equations insensitive to external variables. Thin layer drying
equations can produce drying time estimates and generalizations
of drying curves. With the assistance of mathematical modelling
ofthedryingprocess,itisfeasibletomakeapredictionof
the moisture content (MC) of the product [7]. It requires only
knowledge of initial drying conditions.
Several studies are presented for the drying kinetics behaviour
of various herbs, vegetables, fruits and agro products like parsley,
mint, basil [5], rough rice [6], apricot, grapes, peaches, g, plum
[7], apricot [8], potato slices [9], red pepper [10], carrot [11],
eggplant [12], Citrus aurantium leaves [13], black turmeric [14],
grapes [15], Moroccan horehound leaves [16], beef [17]andstevia
leaves [18]. In literature, drying kinetics analysis of cotton seeds
for open sun drying is scarce. The main objectives of this study
are as follows:
•Study of open sun drying of cotton seeds and computation of
its drying kinetics.
•Matching of experimental and predicted values of moisture
ratio using curve tting technique.
•Selection of appropriate drying model to represent open sun
drying of cotton seeds.
•Calculation of eective diusivity of cotton seeds.
2EXPERIMENTAL PROCEDURE
Experimentsondryingintheopensunwerecarriedoutduring
the month of January 2021. Experiments were conducted on the
rst oor of Mechanical Engineering Department of the Govt.
Engineering College, Palanpur, India, for better exposure to direct
sunlight. Fresh cotton seeds were collected from a local cotton
oil mill during experimentation days. During collection, care was
taken to obtain cotton seeds in their natural condition. Spoiled
seeds were removed to have good samples. The average radius
of cotton seeds is 2 to 2.5 mm, and the average length is 8 to
10 mm with an ovoid shape. Two samples were prepared to have
200 gm mass each: the rst was used to estimate the initial MC
by hot air oven method. Cotton seeds were distributed evenly
in stainless steel dish and were placed in the oven at 105◦Cfor
nearly 11:30 hours to achieve an equilibrium moisture level [19].
Reduction in sample mass was measured at every one-hour inter-
val of time. Readings were taken until the dierence between two
consecutive measurements was not less than ±0.1 g. It indicates
that mass reduction of the sample is not possible as the sample has
reached its equilibrium MC [20].
The second sample of cotton seed was uniformly distributed
on a plastic sheet and was exposed to direct sun rays. Drying
experiments were performed from 10:00 am to 5:00 pm under
the open sun for three days. The reduction in the mass of cotton
seeds was measured at every one-hour interval. Dry samples were
stored overnight in an airtight plastic bag to avoid reabsorption
of moisture from the air. The same dried cotton seed sample was
again exposed to direct sun rays for drying the next day. The
drying process was terminated when there was no discernible
decrease in the sample’s mass. Figure 2 shows a block diagram
of drying in the open sun. Initial mass measurement, hot air
oven drying and arrangement of measuring instruments used
during the experiment are represented in Figure 3.Electronic
weighing machine was kept in the room to avoid inaccuracy in
measurement due to wind eect.
2.1. Instrumentation and measurement
Retardation in water content of the product was a critical variable
in this study, as estimation of MC, drying rate and moisture
888 International Journal of Low-Carbon Technologies 2023, 18, 887–895
Downloaded from https://academic.oup.com/ijlct/article/doi/10.1093/ijlct/ctad075/7245784 by guest on 21 August 2023

Mathematical modelling and verication of open sun drying of cotton seeds
Tab l e 1 . Instruments used in experiments with range and accuracy
Sr. no. Measuring instrument Var i a ble m e asu r e d Symbol Unit Range Accuracy
1Electronic weighting machine Mass of cotton seed m g 0–300 ±0.01 g
2Solar power meter Intensity measurement IW/m20–1999 ±10 W/m2
3Digital anemometer Wind ve locity Vm/s 0–45 ±3% +0.1rdg
4Thermo-hygrometer Air temperature ToC−50– 70 ±1%
5Thermo-hygrometer Air RH RH %10–99 ±3%
Figure 2. Block diagram of cotton seed drying in the open sun.
ratio were dependent on it. It was also employed for plotting
the drying curve. So it was measured with the electronic weight-
ing machine (measurement range, 0–300 g; accuracy, ±0.01 g).
Solar radiation intensity was measured using a solar power meter
(model, TM-207; maximum reading limit, 1999 W/m2; accuracy,
±10 W/m2). Wind velocity measurement was done with a digital
anemometer (EUROLAB; model, AM4201; range, 0–45 m/s with
±3% +0.1 rdg accuracy). Thermo-hygrometer was utilized for
measurement of air temperature and relative air humidity (HTC
INST.; model, 288-CTH/288-ATH; temperature range, −50◦C–
70oCwith±1% accuracy; relative humidity range, 10%–99%
with ±3% RH (50%–80%) accuracy). A detail of range, accuracy
and variable measured using measuring instruments is given in
Tabl e 1 .
2.2. Experimental uncertainty
Uncertainty in experimental measurements can arise due to fac-
tors like instrument selection, surrounding conditions, obser-
vation, connection, the mindset of observer, test planning and
reading [14,21]. In this experimental study, measurement was
carried out for mass loss, solar radiation intensity, air temperature,
humidity and wind velocity. Uncertainties in the measurement
of these independent variables bring uncertainty in the estimated
value of dependent variable.
The physical quantity P is some function of independent phys-
ical quantities q1,q
2,q
3...qn.LetδP is the uncertainty in P and
δq1,δq2,δq3.....δqnbe uncertainty in measured (independent)
variables, then they are correlated using Eq. (2,22].
P=Pq1,q2·········qn(1)
δP=∂P
∂q1
δq1+2
+∂P
∂q2
δq2+2
+········· +∂P
∂qn
δqn21
2
(2)
Tab l e 2 . Uncertainties of critical independent–dependent variables inu-
encing drying kinetics
Var i a ble Unit Uncertainty
MC %±0.045
Moisture ratio %±0.3277
Drying rate %±0.149
Uncertainties values that occurred in the measurement of crit-
ical dependent variables used for drying kinetics are listed in
Tabl e 2 . Uncertainty calculations are shown in Appendix.
3DRYING ANALYSIS
3.1. Drying kinetics
Initial, nal and instantaneous MCs of the product were calcu-
lated on a wet basis with the help of the following equations
[23]:
Initial M.C Mi=(mi−moven)
mi
(3)
Final M.C Mf=(ms−moven)
mi
(4)
Instantaneous M.C Mt=(mi−moven)
mi
(5)
MC of the product is represented in non-dimensional form by
moisture ratio. It is calculated with Eq. (6), provided that relative
humidity has maintained constant during drying experiments. As
in open sun drying, relative humidity varies continuously due
to variations in air temperature and solar radiation intensity, so
under such a situation, the moisture ratio is obtained using Eq.
(7)[24,25];
Moisture ratio MR =(Mt−Me)
(Mi−Me)(6)
Moisture ratio MR =Mt
Mi
(7)
Drying rate of a product is dened as [9] follows:
DR =Mt−Mt+Δt
Δt(8)
International Journal of Low-Carbon Technologies 2023, 18, 887–895 889
Downloaded from https://academic.oup.com/ijlct/article/doi/10.1093/ijlct/ctad075/7245784 by guest on 21 August 2023

V. P a t e l et al.
Figure 3. (a) Initial mass measurement of cotton seeds; (b) hot air drying in the oven; and (c) Measuring instruments utilized.
Tab l e 3 . Thin layer drying models used to described open sun drying of cotton seeds
Sr. no. Model name Model equation Reference
1Newton MR = exp(−kt) [27]
2Page MR = exp(−ktn)[28]
3Modied page MR = exp(−(kt)n)[29]
4Two t er m MR = a exp(−kot) +b exp(−k1t) [30]
5Twotermexponential MR = a exp(−kt) +(1-a) exp(−kat) [9]
6Diusion approach MR = a exp(−kt) +(1-a) exp(−kbt) [28]
7Henderson and Pabis MR = a exp(−kt) [31]
8Logarithmic MR = a exp(−kt) +c[32]
9Verm a et al.MR = a exp(−kt) +(1-a) exp(−gt) [33]
10 Middili and Kuck MR = a exp(−ktn)+bt [9]
Thin layer drying models in the literature were used to inves-
tigate how cotton seeds dry. Eleven commonly used thin-layer
drying equations were compared to nd the optimal model for
open sun drying of cotton seeds [5,19]. Tab l e 3 has a listing of
many models used in current research work. Tab le 4 shows the
results of non-linear regression analysis to the open sun drying of
cotton seeds.
3.2. Statistical analysis
Calculated and anticipated moisture ratios were displayed against
drying time (DT). Non-linear regression study in Excel-solver
equation determined the optimal thin layer drying model. Coef-
cient of determination (R2), reduced chi-square (χ2)androot
mean square error (RMSE) were considered as criteria for the
selection. A drying model with a higher value of R2and lower
values of χ2, RMSE, were chosen as the best suitable model [9,26].
Calculations of R2,χ2and RMSE were done using Eqs (9)–(11)
[14,19]:
R2=1−
N

i=1MRexp,i−MRpr,i2
N

i=1MRavg,pr −MRexp,i2
(9)
χ2=
N

i=1MRexp,i−MRpr,i2
N−n(10)
RMSE =



1
N
N

i=1MRexp,i−MRpr,i2(11)
3.3. Estimation of eective diusivity
For the drying process occurring with a falling rate period, diu-
sion is the main phenomenon controlling the drying rate. Eec-
tive diusivity value for a given drying process represents the
eectiveness of drying. A higher value of it means a faster dry-
ing process [34]. Fick’s law can be utilized to estimate eective
diusivity [16].
dM
dt =Dd2M
dr2(12)
The solution of the above equation can be obtained by assuming
uniform moisture distribution initially with external resistance to
movement of moisture is negligible compared to internal resis-
tance. It is also assumed that the moisture concentration on the
outer surface remains the same. The analytical solution of Eq. (13)
forlongslabgeometryisgivenby[
5]thefollowing:
MR =Mt−Me
Mo−Me
=8
Π2
∞

n=0
1
(2n+1)2exp −(2n+1)2Π2De t
4l2(13)
ForverylongDT,theaboveequationcanbeexpressedas
follows:
ln(MR)=ln 8
Π2−Π2De t
4l2(14)
890 International Journal of Low-Carbon Technologies 2023, 18, 887–895
Downloaded from https://academic.oup.com/ijlct/article/doi/10.1093/ijlct/ctad075/7245784 by guest on 21 August 2023

Mathematical modelling and verication of open sun drying of cotton seeds
Tab l e 4 . Result of non-linear regression analysis to described open sun drying of cotton seeds
Sr. no Model Coecient and
constant
R2χ2RMSE
1Newton Model k= 0.06561 0.44995393 0.01176587 0.10847060
2Page Model k= 0.28388,
n= 0.39793
0.98572866 0.00062768 0.02441925
3Modied Page Model k= 0.04224,
n= 0.39793
0.98953528 0.00031039 0.01719333
4Two t er m a = 0.39252,
Ko = 0.04184
b = 0.39252,
K1 = 0.04184
0.92868968 0.00462366 0.06467849
5Diusion approach a = 0.38483,
K = 0.65710
b = 0.03393
0.99266147 0.00016801 0.01232906
6Henderson and Pabis a = 0.78504,
K = 0.04184
0.79805776 0.00439247 0.06467849
7Logarithmic a = 0.52176,
K = 0.27679
c = 0.43229
0.96547037 0.00079051 0.02740414
8two term exponential a = 0.14452,
K = 0.36635
0.66750781 0.00734172 0.08361885
9Ver m a e t al. a = 0.61515,
K = 0.02229
g = 0.65704
0.99266147 0.00016801 0.01232906
10 Middili and Kuck a = 1.00249,
K = 0.0384
b = 0.29371,
n = 0.57932
0.99047270 0.00023023 0.01404787
Bold face represent that diusion approach and Verma et al. models give the highest value of R2and lowes t values of χ2and RMSE. Therefore, the diusion approach and
Verma et al. models are selected as the most suitable models for expressingsun dr ying of cotton seeds.
The eective diusivity was estimated from the slope of plot ln
[(2/8)∗MR] versus DT. Slop of this curve can be expressed as Eq.
(15):
slop =Π2De
4l2(15)
4RESULT AND DISCUSSION
During open sun drying experiments, atmospheric conditions
like air temperature, relative air humidity and solar radiation
intensity uctuated from 20.6 to 35.4◦C, 10% to 35% and 190 to
818 W/m2,respectively.Figure 4 represents uctuations of solar
radiation intensity, air temperature and air relative humidity for
14, 15, 16 January 2021. It is clear from the gure that the intensity
of solar radiation and air temperature has increased from morning
time to maximum in the aernoon, then dropped to its lowest val-
ues. On 16 January 2021, experiments were conducted up to 2 pm
as cotton seeds achieved equilibrium conditions, due to which
further reduction in mass was not possible. Completely reverse
behaviourcanbeseenfortheairrelativehumidity.Theinitial
MC of cotton seeds was estimated to be 14.65% wet-basis. Drying
was performed until no signicant variation in mass reduction
was observed. The nal MC was found to be 6.37% wet-basis on
Figure 4. Solar radiation intensity, air temperature and air relative humidity
variation with time.
the third day of drying. The total reduction in MC observed was
8.28% wet basis.
4.1. Drying curves
Figure 5 illustrateshowtheMCofcottonseedsshisinresponse
to changes in DT. It is observed that reduction in MC from 14.65%
International Journal of Low-Carbon Technologies 2023, 18, 887–895 891
Downloaded from https://academic.oup.com/ijlct/article/doi/10.1093/ijlct/ctad075/7245784 by guest on 21 August 2023

V. P a t e l et al.
Figure 5. MC variation with DT.
to 6.37% wet-basis took 20 hours, excluding the night period.
It is seen that MC reduces continuously with DT. The entirety
of the drying process took place during the time that the falling
rate was in eect. It suggests no steady-state drying period during
which cotton seeds can be dried. Under such conditions, the
drying rate is controlled by the diusion of moisture from the
interior part of the product towards the surface. These ndings
are consistent with prior research on a wide range of agro products
[10,13]. A total of 45.35% retardation in MC was obtained in the
rst 7 hours, while the remaining means 54.64% retardation in
MC took 13 hours. It occurred due to the evaporation of surface
moisture in the initial hours from the outer part of cotton seeds,
which required comparatively less energy than that required to
evaporate interior moisture.
AplotofdryingrateversusDTisrepresentedinFigure 6.
SimilarnatureasthatofMCversusDTisobservedinthiscurve
also. Fluctuations in the drying rate are caused due to alterations
in solar radiation intensity, wind speed and air temperature. It
is also concluded that the drying rate reduces with DT, but at a
certain point in the graph, it raises due to higher solar radiation
intensity and its eect on air temperature [19,21]. Aer 5 hours of
drying, the drying rate became very low as high energy is required
to extract interior MC. At certain points in the curve, the drying
rate turns out to be very low due to the lesser intensity of solar
radiation.
4.2. Mathematical modelling of drying curves
Forselectingasuitablethindryinglayermodel,itisrequired
to represent experimental data in the non-dimensional form by
estimating the moisture ratio. A plot of experimental moisture
ratio versus DT is shown in Figure 7.EstimatedvaluesofMR
obtained from thin drying layer models selected for non-linear
regression analyses were tted with this plot as shown in Figure 8.
Figure 6. Dryingrate(gmofwater/gmofwetmatter∗hours) variation with DT.
Figure 7. Experimental moisture ratio versus DT.
Result of non-linear regression analysis is given in Tab l e 3 .The
model was selected based on a higher value of R2and lower values
of χ2, RMSE. The result concluded that the diusion approach
and models by Verma et al. gave the highest value of R2and
lowest values of χ2and RMSE. The values were R2= 0.99266147,
χ2= 0.00016801 and RMSE = 0.01232906. Therefore, the diu-
sion approach and models by Verma et al.wereselectedasthe
most suitable models for expressing sun drying of cotton seeds.
A comparison of experimental values of MR and predicted
values of MR using the most suitable models is represented in
Figure 9. Predicted values of MR are represented by a straight
line.ItisseenthatexperimentalvaluesofMRarelyingveryclose
to it, which authenticates the suitability of the selected model
892 International Journal of Low-Carbon Technologies 2023, 18, 887–895
Downloaded from https://academic.oup.com/ijlct/article/doi/10.1093/ijlct/ctad075/7245784 by guest on 21 August 2023

Mathematical modelling and verication of open sun drying of cotton seeds
Figure 8. Experimental and estimated MR versus DT.
Figure 9. Comparis on of experimental values of MR and predicted values of MR.
[19,21]. The diusion approach and models by Verma et al.can
be expressed in Eq. (16)andEq.(17):
MR =0.38483∗exp −0.65710∗t
+(1−0.38483)∗exp −0.65710∗0.03393∗t(16)
MR =0.61515∗exp −0.02229∗t
+(1−0.61515)∗exp −0.65710∗t(17)
4.3. Eective diusivity
The slope of Eq. (14)isameasureofeectivediusivity.Itis
obtainedfromaplotofln[(2/8)∗MR] versus DT, as shown in
Figure 10. For open sun drying of the cotton seeds value of eec-
Figure 10. Plot of ln [(2/8)∗MR] versus DT.
tive diusivity is found 1.991 ×10−11m2s−1. This eective diusiv-
ity value ranges from 10−9to 10−11m2s−1for food materials [35].
5CONCLUSION
In this current research work, open sun drying of cotton seeds was
investigated. Drying took 20 hours to reduce MC from 14.65% to
6.37% wet basis. It was occurred with falling rate period having
absence of constant rate period. Experimental results of MR were
tted with predicted values of MR for selection of most appro-
priate drying model for sun drying of cotton seeds. Among the
selected models, diusion approach and the models by Verma
et al. have given better t with experimental data. These models
gavethehighestvalueofR
2= 0.99266147 and the lowest values
of χ2= 0.00016801 and RMSE = 0.01232906. Value of eective
diusivity was estimated as 1.991 ×10−11m2s−1.
AUTHOR CONTRIBUTIONS
Vijay Patel, K. B. Judal (Writing—original dra, Experimenta-
tion), Hitesh Panchal, Naveen Kumar Gupta (Conceptulization,
Methodology), Musaddak Maher Abdul Zahra and Mohd. Asif
Shah (Formal analysis, Data curation)
DATA AVAILABILITY STATEMENT
Data will be available to send email to corresponding author with
reasonable request.
REFERENCES
[1] GoI. 2019. Annual Report 2018–19. Department of Agriculture, Coop-
eration & Farmers Welfare, Ministry of Agriculture & Farmers Welfare,
Government of India, 1–224.
International Journal of Low-Carbon Technologies 2023, 18, 887–895 893
Downloaded from https://academic.oup.com/ijlct/article/doi/10.1093/ijlct/ctad075/7245784 by guest on 21 August 2023

V. P a t e l et al.
[2] Zone N, Zone C, Pradesh M et al. Cotton sector 1. Ministry of Textile,
Government of India, 2018.
[3] Seed C, Cake O, Meal C. Nsight 15, D ecember2014.National Bulk Handling
Corporation Private Limited, Mumbai, India, 1–5.
[4] Shahrajabian MH, Sun W, Cheng Q. Review article considering white gold,
cotton, for its ber, Seed oil, traditional and modern health benets. JBiol
Environ Sci 2020;14:25–39.
[5] Kuma r M, Sahd ev RK, Tiwar i S et al. Manchanda experimental free
convection thin layer groundnut greenhouse drying Agric. Eng Int CIGR J
2019;21:203–11.
[6] Kuma r M, Sahd ev RK, Tiwar i S et al. Thermal performance and
kinetic analysis of vermicelli drying inside a greenhouse for sus-
tainable development. Sustain Energy Technol Assess, Article 2021;44:
101082.
[7] Pandiaraj S, Tamilvanan Ayyasamy M, Hasanuzzaman GA et al. An
experimental investigation on a locally fabricated dryer integrated
with a novel solar air heater for the drying of potato slices. Energy
Sources, Part A Recov Util Environ Eects 2022;44:9811–26. https://doi.o
rg/10.1080/15567036.2022.2143967.
[8] Pehlivan D. Modelling of drying kinetics of single apricot. J Food Eng
2003;58:23–32.
[9] AkpinarE.Singlelayerdryingbehaviourofpotatoslicesinaconvec-
tive cyclone dryer and mathematical modeling. Energy Convers Manag
2003;44:1689–705.
[10] Akpinar EK, Bicer Y, Yildiz C. Thin layer drying of red pepper. J Food Eng
2003;59:99–104.
[11] Doymaz I. Convective air drying characteristics ofthin layer carrots. J Food
Eng 2004;61:359–64.
[12] Ertekin C, Yaldiz O. Drying of eggplant and selection of a suitable thin
layer drying model. J Food Eng 2004;63:349–59.
[13] Mohamed LA, Kouhila M, Jamali A et al. Single layer solar drying
behaviour of citrus aurantium leaves under forced convection. Energy
Convers Manag 2005;46:1473–83.
[14] Lakshmi DVN, Muthukumar P, Layek A et al. Drying kinetics and quality
analysis of black turm eric (Curcuma caesia) drying in a mixed mode forced
convection solar dryer integrated with thermal energy storage. Renew
Energy 2018;120:23–34.
[15] Hamdi I, Kooli S, Elkhadraoui A et al. Experimental study and numer-
ical modeling for drying grapes under solar greenhouse. Renew Energy
2018;127:936–46.
[16] Bahammou Y, Tagnamas Z, Lamharrar A et al. Thin-layer solar dry-
ing characteristics of Moroccan horehound leaves (Marrubium vul-
gare L.) under natural and forced convection solar drying. Sol Energy
2019;188:958–69.
[17] MewaEA,OkothMW,KunyangaCNet al. Experimental evaluation of
beef drying kinetics in a solar tunnel dryer. Renew Energy 2019;139:
235–41.
[18] Castillo Téllez M, Pilatowsky Figueroa I, Castillo Téllez B et al. Solar
drying of stevia (Rebaudiana Bertoni) leaves using direct and indirect
technologies. Sol Energy 2018;159:898–907.
[19] Rabha DK, Muthukumar P, Somayaji C. Experimental investigation of
thin layer drying kinetics of ghost chilli pepper (Capsicum Chinense
Jacq.) dried in a forced convection solar tunnel dryer. Renew Energy
2017;105:583–9.
[20] ErickCésarLV,AnaLiliaCM,OctavioGVet al. Thermal performance of
a passive, mixed-type solar dryer for tomato slices (Solanum lycopersicum).
Renew Energy 2020;147:845–55.
[21] Akpinar EK. Drying of mint leaves in a solar dryer and under
open sun: modelling, performance analyses. Energy Convers Manag
2010;51:2407–18.
[22] Holman JP. Experimental Methods for Engineers. Singapore: McGraw-Hill,
1994.
[23] Ayua E, Mugalavai V, Simon J et al. Comparison of a mixed modes solar
dryer to a direct mode solar dryer for African indigenous vegetable and
chili processing. J Food Process Preserv 2017;41:1–7.
[24] Midilli A. Mathematical modeling of thin layer drying of pistachio by using
solar energy. Energy Convers Manag 2003;44:1111–22.
[25] Gunhan T, Demir V, Hancioglu E et al. Mathematical modelling of drying
of bay leaves. Energy Convers Manag 2005;46:1667–79.
[26] Rabha DK, Muthukumar P, Somayaji C. Energy and exergy analyses of
the solar drying processes of ghost chilli pepper and ginger. Renew Energy
2017;105:764–73.
[27] Ayensu A. Dehydration od food crops using a solar dryer with convective
heat ow. Sol Energy 1997;59:121–6.
[28] Diamante LM, Munro PA, North P et al. Mathematical modeling of the
thin layer solar drying of sweet potato slices. Sol Energy 1993;51:271–6.
[29] Panchariya PC, Popovic D, Sharma AL. Thin-layer modeling of black tea
drying process. J Food Eng 2002;52:349–57.
[30] Yaldiz O, Ertekin C, Uzun HI. Mathematical modeling of thin layer solar
drying of sultana grapes. Energy 2001;26:457–65.
[31] Yaldız O, Ertekin C. Thin layer solar drying of some vegetables. Dry Techn
2001;19:583–97.
[32] Chandra PK, Singh RP. Applied Numerical Methods for Food and Agricul-
tural Engineers. CRC Press, Boca Raton, 1993. 163–7.
[33] Verma L, Bucklin R, Endan J et al. Eects of drying air parameters on rice
drying models. Tra ns A SA E 1985;28:296–301.
[34] Andharia JK, Bhattacharya P, Maiti S et al. Development and performance
analysis of a mixed mode solar thermal dryer for drying of natural rubber
sheets in the north-eastern part of India. Sol Energy 2020;208:1091–102.
[35] Doymaz I. Sun drying of gs: an experimental study. J Food Eng
2005;71:403–7.
Uncertainty Calculation:
[1] Uncertainty in the measurement of MC:
M=mi−moven
mi
=1−moven
mi
ΔM
Δmi
=moven
mi2=170.7
(200)2=0.0043
ΔM
Δmoven
=1
mi2=1
(200)=0.005
ΔM=ΔM
Δmi
×δmi2
+ΔM
Δmoven
×δmoven21
2
ΔM=(0.0043 ×0.01)2+(0.005 ×0.01)21
2
ΔM=6.59 ×10−5
ΔM
M=6.59×10−5
0.1465 ×100
ΔM
M=0.045%
[2] Uncertainty in the measurement of moisture ratio:
MR =mt
mi
ΔMR
Δmt
=1
mi
=1
0.1465 =6.8259
ΔMR
Δmi
=mt
mi2=0.0581
(0.1465)2=2.71
ΔMR =ΔMR
Δmt
×δmt2
+ΔMR
Δmi
×δmi21
2
894 International Journal of Low-Carbon Technologies 2023, 18, 887–895
Downloaded from https://academic.oup.com/ijlct/article/doi/10.1093/ijlct/ctad075/7245784 by guest on 21 August 2023

Mathematical modelling and verication of open sun drying of cotton seeds
ΔMR =6.8259 ×6.59 ×10−52+2.71 ×6.59 ×10−521
2
ΔMR =0.0013
ΔMR
MR =0.0013
0.3966 ×100 =0.3277%
[3] Uncertainty in the measurement of drying rate:
DR =mt−mt+Δt
Δt=Δmt
Δt
ΔDR
Δmt
=1
Δt=1
ΔDR =ΔDR
Δmt×δmt21
2
== 1×6.59 ×10−521
2
=6.59 ×10−5
ΔDR
DR =6.59×10−5
0.00442 ×100 =0.149%
International Journal of Low-Carbon Technologies 2023, 18, 887–895 895
Downloaded from https://academic.oup.com/ijlct/article/doi/10.1093/ijlct/ctad075/7245784 by guest on 21 August 2023