Analysis of the Heat Transfer Coefficient, Thermal Effusivity and Mathematical Modelling of Drying Kinetics of a Partitioned Single Pass Low-Cost Solar Drying of Cocoyam Chips with Economic Assessments

Abstract

This study examines the heat and mass transfer coefficient, thermal effusivity, and other thermal properties of solar-dried cocoyam chips, as well as the drying kinetics. The research also assessed the economics of the solar dryer. For these reasons, a solar dryer with a partitioned collector was developed that creates a double airflow travel distance to delay the airflow inside the collector. The partitioning of the collector delays the airflow and helps to create more turbulence for the airflow with increased energy. The solar dryer was locally developed at the Michael Okpara University of Agriculture and tested during the humid crop harvesting period of September for the worst-case scenario. The obtained drying curves and kinetics for cocoyam drying are subjected to the vagaries of weather conditions. The drying rate showed declining sinusoidal characteristics and took about 25 h to attain equilibrium. Analysis of the airflow velocity showed gravitation between laminar and turbulent flow, ranging from 171.69 to 5152.77. Specific heat capacity, thermal conductivity, and effusivity declined with moisture content while the thermal diffusivity increased. However, the values of thermal effusivity ranged from 12.2 to 47.94 W·s^1/2·m⁻²·K⁻¹, which is within the range of values for insulators. The heat and mass transfer coefficient varied as a function of the airflow velocity. Fitting the drying curve into semi-empirical models showed that the two-term model was the best-fitted model for the experimental data from drying cocoyam. Using the solar dryer in Nigeria can save $188.63–$1886.13 in running costs with a payback period of 0.059–0.59 years (21.54–215.35 days) at a rate of 10–100% of usage.

1. Introduction

The preservation of food is an important component of food safety and security as it aids to add value to the product and maintain stability in the nutritional contents of the product. The Food and Agriculture Organization (FAO) estimated that about 811 million people globally lack food or are underfed in 2021 [1]. The need to improve the quality of agricultural products has always been a major challenge experienced in agricultural processing across different parts of the world [2]. This challenge can be addressed through technological development in processing equipment. This is important to prevent post-harvest losses of agricultural produce owing to primitive methods of post-harvest handling and storage. The drying of agricultural products happens to be the first unit operation in the preservation and storage of most agricultural products to enhance their shelf-life [3]. Drying removes the moisture from the product to a stable level where microbes that cause deterioration might not thrive. Globally, energy consumption for drying purposes is very high, contributing to about 15% of the global energy consumption in developed countries [4]. Energy sourced from fossil fuel dominates this proportion and contributes to the massive generation of greenhouse gases. This is dangerous as they harm the environment and destroy the ozone layer [5]. This mode of drying can be substituted with solar drying, which is environmentally friendly. Solar energy is universally acceptable and widely in use as it is a source of renewable energy and offers large capacity variability and potential [6]. Thus, solar drying utilizes energy from the sun in the form of heat and light. However, sun-drying, which is the earliest method of drying farm produce, still dominates the mode of drying agricultural products in developing countries. The process runs at the risk of spoilage due to adverse climatic conditions, e.g., rain, wind, mist, and dust, loss of produce to birds, insects, and rodents, dependency on good weather conditions, and slow drying rate with the danger of mould growth, thereby causing deterioration and decomposition of the produce [7]. The process also requires a large land area, significant time, and it is labour intensive. This puts solar dryers at an advantage over sun drying because they can overcome the challenges listed above if properly designed. Solar dryers are specialized dryers that capture the solar radiation with an enclosed collector and control the drying process in the drying chamber at a temperature greater than the ambient temperature and at a lower relative humidity [8]. Solar dryers have shown the capacity to meet the drying requirements of crops, animal products etc., within a shorter time frame and with lower energy utilization. In addition, they take up less space and are regarded as one of the healthiest methods for preserving the quality of dry products. Thus, the nutritional quality of the dried products is preserved [9].

Several designs of the solar dryer are in existence in the literature [10,11,12,13,14,15], but the consensus is that the performance of each dryer is environment-specific and depends on the meteorological data of that area. However, the presentation of new designs with new ideas encourages the modification of the previous design, which can be adopted in any environment. Variation of fluid path distance is currently of interest as this can help to increase the fluid duration in the collector to gain higher temperatures [16,17]. Another challenge faced in advancing the adoption of the solar dryer by manufacturers in Africa or most developing nations is convincing the farmers of the cost-effectiveness of using the solar dryer in comparison with other existing artificial dryers. Although many solar dryers are available, cost indicators that can help in decision making are lacking [18]. Often, the performances are presented but the cost index that gives the user an idea of when to recoup his investments is lacking. The idea behind this research, therefore, is to double the airflow travel distance using a lower collector length. The goal is to delay the airflow inside the collector to allow for more time for heat exchange between the collector and the air to increase the temperature and allow the air to shade more moisture before entering the drying chamber. Partitioning the collector helps to create more turbulence for the air with increased energy. The reason for this is that the operating environment for the solar dryer is highly humid, which means greater moisture in the inlet air. Shading some of this moisture will increase the moisture carrying capacity of the inlet air to the drying chamber. This is because, in such an environment, a small rise in the ambient temperature will support the quick drying of products.

The thermo-physical properties of agricultural products are required in the design, fabrication, and optimization of their processing equipment [19]. The drying kinetics and thermal properties, such as the specific heat, thermal conductivity, thermal diffusivity, effective moisture diffusivity, heat and mass transfer coefficients, etc., are needed to understand the mechanism of heat and mass transfer and to quantitatively determine the energy exchange between media. These properties are influenced by the mode of drying, initial moisture content, type of crop, environmental conditions, initial treatment given, etc. [20]. Therefore, a generalized determination of these parameters for all agricultural products is not possible but must instead be product-specific. Again, of interest in solar dryer design is the problem of rewetting the product during the off-sunshine period. This occurs when the product has lost its heat and absorbs moisture instead of giving off moisture. The rate at which the heat from a product is lost to the surrounding air is the thermal effusivity or delay factor (conductive capacity or inertia) [21]. The higher the value of conductive capacity (thermal effusivity), the quicker the surface temperatures will easily equilibrate thermodynamically with the product ambient temperature. Therefore, thermal effusivity has been explained as the rate at which the thermal energy of the product radiates from the product [21]. Thermal effusivity is inversely correlated to thermal impedance. Often, in the thermal analysis of agricultural products in solar drying, this very important property has been overlooked by most researchers. Currently, reference literature on thermal effusivity is not available [22]. However, the understanding of this property might aid solar dryer designers in managing the issue of rewetting that aids microbial growth on the dried products.

Cocoyam corm is rich in vitamins and minerals and is a common food for the elderly and invalids [23]. Nevertheless, it is a highly perishable corm that requires further processing to increase the shelf-life. It is mostly processed into chips for export or dried and converted into flour [24]. Although a large number of people engage in the production and processing of this product, basic process parameters that can aid in the industrial or medium scale processing of this product are lacking. With the recent interest in advocacy for environmentally friendly energy applications in drying, the future of drying this product will include the use of solar dryers. Therefore, it is necessary to study the thermal properties and drying kinetics of this product in solar drying, especially its thermal effusivity, which is not available for any corm in the literature. Additionally, evaluating a new solar dryer design as presented will expand the available literature and increase the design choice available to be implemented in a different environment. Thus, the specific objectives of this study were (1) to investigate the performance of a portioned single pass collector solar dryer for drying cocoyam with the air driven by a wind-powered suction fan, (2) to study the effect of using the dryer on the thermal properties and heat and mass transfer co-efficient of cocoyam slices, (3) to study the drying kinetics and mathematical modelling of the cocoyam, and (4) to present the economic feasibility of using the solar dryer.

2. Material and Methods

2.1. Description of Solar Dryer Used

The single partitioned, single-pass, active, low-cost solar dryers were fabricated at the Michael Okpara University of Agriculture, Umudike. All the material employed in the fabrication was locally sourced and the cost of fabrication is presented in

Table 1. Material specification.

Units	Specifications	Source
Solar collector	Hard wood (2 × 2 inch), tilted 15 °N, 0.6 m × 0.6 m × 0. 59 m	Custom design
Absorber	Black painted aluminum sheet, 0.6 × 0.6 m × 0.001 m	Custom design
Glazing	Transparent glass, 0.57 m × 0.6 m, 0.004 m	Perspex
Drying Chamber	Plywood (lined with black painted aluminum inside), 0.6 × 0.6 × 1 m, 45° tapering at 0.3 m height at 0.7 m from the base	Custom design
Drying trays	Hardwood (2 × 2 inches) skeleton, plastic wire mesh, 0.57 m × 0.57 m, 4 trays at 0.15 m gap	Custom design
Chimney	Hollow galvanized steel, pipe; ϕ 0.12 m and 0.3 m high	Custom design
Wind generator and fan	ϕ 0.05 m hollow pipe, 0.15 m−0.10 m, 3 curved aluminum arms, 0.156 m axial fan blade, frictionless bearings	Custom design

while the cost of materials is presented in

Table 2. Costs of materials for the solar dryers.

S/N	Materials	Specification	Quantity	Cost ()
1	Planks	2 inches × 2 inches	8 pieces	2700
2	Glass	4mm thick (57 cm × 60 cm)	1sheets	2250
3	Screw	2 inches	1 pack	900
4	Board	4 feet × 8 feet	2	8000
5	Nail	3inches and 1 inch	1.5 pounds weight	1200
6	Door hinge	Medium size	2 pieces	400
7	Paint	Black oil paint	4 litters	4500
8	Painting brush	Big size	1 piece	350
9	Aluminum sheet	3.5 inches × 8 inches, black	1 sheet	4000
10	Top bond gum	Medium size	1 can	1000
11	Baton	Flat size	2 pieces	300
12	Net	Green colour	1.5 yards	1050
13	Suction fan blade	Steel type	1 piece	350
14	Steel pipe	Cylindrical, 4 mm thick	1 piece, 35 cm long	800
15	Bearing	6mm diameter ring	2 pieces	500
	Variable Cost
16	Labour			18,000
17	Transportation			3000
18	Miscellaneous			2000
19	Total Cost			50,950 ($122.714 as of 3 May 2022)

. The dryers consist of a solar air collector section, drying chamber, and chimney. The solar collector (0.6 × 0.6 × 0.59 m) and drying chamber (0.6 × 0.6 × 1 m) are of simple cabinet type, as shown in Figure 1. Both the collector and the drying chamber were supported on a four leg-standing at a height of 0.36 m above the ground. The solar collector was partially partitioned horizontally in the middle, leaving an opening equal to that of the air inlet towards the end wall for air passage into the second chamber before entering the drying chamber, as shown in Figure 1. The two chambers of the collector were loaded with black painted granite stones (0.04 m minimum length at the longest side) with horizontal sharp edges. The granite stones were carefully laid in short ridges inside the collector chambers such that the sharp long edges faced vertically upwards and together create fin-like edges at the top. The solar collector was fitted to the drying chamber at an angle of 15°. The chimney was constructed with a galvanized cylindrical metal pipe of 0.12 m diameter and height of 0.30 m which was fixed centrally on the top of the drying chamber. The wind generator shaft made of hollow pipe was fitted through the middle of the chimney with the help of two frictionless bearings. The down tip of the shaft was attached to the suction fan fitted at the top end of the drying chamber. The fan is controlled by the wind generator with the help of the wind. With this, the design is completely renewable with no grid-based electricity associated with the design. Four removable trays with nets and a skeleton made from 2 × 2-inch wood were placed on the tray racks fitted by the sides of the drying chamber at a vertical gap of 0.15 m from each other to hold the dried products. The collector was glazed with a transparent glass sheet of 4 mm thickness, fixed at the top of the solar collector. The two chambers of the solar collector and the drying chamber were covered with a black painted aluminum sheet to absorb and retain heat inside the solar dryer.

Novelty of Design

The dryer consists of two major design futures, which include (1) the horizontal partial partitioning of the collector, (2) laying the granite stones to form fin-like long ridges at the top, and (3) the incorporation of a wind-powered suction fan. The partitioning and the pattern of laying the granites force the inlet air to traverse a longer distance and surface area within the collector before exiting into the drying chamber. Partitioning helps to create more turbulence for the air with increased energy. Through these designs, the inlet air coming in at high relative humidity will shade some of its moisture to increase its moisture carrying capacity before it enters the drying chamber. Additionally, the integration of wind-powered fans to circulate the drying air, instead of a grid electricity-powered fan, reduces the running cost of the dryer to almost zero. With this design, interest in the dryer will increase, especially in those agricultural crop-producing areas where the electricity penetration density is almost zero.

2.2. Drying Procedure and Instrumentation

Tubers of cocoyam were purchased from a local farm in Abia State, southeastern Nigeria. These cocoyam tubers were thoroughly washed to ensure the removal of sand and other foreign dirt. The cocoyam tubers were later peeled and sliced manually to a thickness of 5 mm each and uniform quadrant shape. Approximately 125 g of the slices were placed on each of the four drying trays inside the drying chamber, as shown in Figure 1. The experiment was carried out at Umudike, southeastern Nigeria (Latitude 050°29′ N and longitude 070°33′ E). Typical metrological data for this location are presented in

Table 3. A typical Umudike Monthly Meteorological data in 2012 (Lat.05°29′, Long.07°33′, Alt.122 m) [5].

Months	Rainfall (mm)		Temperature (°C)		Evaporation (mm)	Relative Humidity (%)		Sunshine (h)
	amount	day	max	min	----	-----	-------	---
Jan	0.0	0	32	23	0.22	72	45	6.4
Feb	88.2	7	35	22	0.46	73	50	6.3
Mar	57.0	3	35	23	0.50	77	53	3.9
April	142.0	17	33	24	0.82	76	59	6.1
May	233.7	16	32	24	4.70	84	70	5.0
Jun	213.0	14	31	23	9.25	87	77	3.2
July	362.0	24	30	23	10.55	86	75	3.4
Aug	161.8	19	30	24	6.10	88	78	2.2
Sept	349.0	25	30	24	8.80	59	75	2.9
Oct	244.6	16	31	24	4.80	86	78	2.9
Nov	58.5	6	33	25	0.31	97	70	4.1
Dec	0.0	0	32	21	0.20	75	49	4.9

below.

The positions of the trays were constantly interchanged during the drying periods to ensure uniformity in drying. The performance parameter was monitored hourly. This includes the ambient temperature and relative humidity, solar radiation intensity, wind speed, the weight of cocoyam, collector and drying chamber temperature and relative humidity. Measurements inside the collector and drying chamber were performed at three points and the average was used for analysis. The test was carried out from 9:00 a.m. to 5:00 p.m. daily until constant weight was attained. The specifications and sensitivities of the instruments used are shown in

Table 4. Specifications and sensitivities of measuring instruments.

Instruments	Specifications	Sensitivity
Temperature	Thermocouple (TM-902C, −50 °C to 750 °C), type K thermocouple-China)	±0.1 °C
Solar Radiation	Pynarometer (Lutron SPM-1116SD)	$\pm 0.1 \mathrm{W}/{\mathrm{m}}^2$
Air Velocity	Anemometer (CR2032, 3 Volts Lithium Cell)	±0.1 m/s
Relative Humidity	Humidity/Baro/Tempt Data recorder (Lutron MHB-382-Taiwan)	±0.1
Mass	Electronic Weighing Scale (KERRO SF-400-China)	1000 g × 1 g; 353 oz × 0.1 oz

. Data analyses were carried out using Excel.

2.3. Experimental Uncertainties

The primary data measured were solar radiations, relative humidity, temperatures, air velocities, and weight loss. The data were used to determine the experimental uncertainties for the secondary data, including moisture contents, moisture ratio, and drying rate, using Equation (1) [25].

$$U_R={\left[{\left(\frac{\partial R}{x_1}\right)w_1}^2+{\left(\frac{\partial R}{x_2}\right)w_1}^2+\dots +{\left(\frac{\partial R}{x_2}\right)w_n}^2\right]}^{1/2}$$

(1)

where w₁, w₂, and w_n are the uncertainties in the independent variables x₁, x₂, and x_n. For moisture content, moisture ratio, and drying rate, the determined uncertainties were ±0.015, ±0.031, and ±0.021.

2.4. Performance Evaluation

The hourly moisture content of the dried cocoyam was determined as follows [26].

$$m_t=\frac{w_t-w_d}{w_i}$$

(2)

where w_t is the hourly weight of the cocoyam, w_i is the initial weight of the cocoyam (kg), and w_d is the dry weight of the cocoyam (kg).

The hourly solar drying, which is the hourly mass of moisture evaporated from the cocoyam, was determined with Equation (3) [27].

$$DR=\frac{w_i-w_d}{t}$$

(3)

where $w_i$ = mass of sample before drying (kg), $w_d$ = mass of sample after drying (kg), $t$ = drying period (h).

The solar collector efficiency is given as

$${ᶯ}_C=\frac{Q_u}{Ic \times Ʈ \times A_{C }}\times 100$$

(4)

where $A_C$ is the collector area (m²), $I_C$ is the insolation on collector surface (W/m²), Ʈ is the transmittance, and Q_u is the rate of energy utilized (W) for the solar dryer, given as

$$Q_u=A_c{F}_R\left[I_cƮ-U_O\left(T_c-T_a\right)\right]$$

(5)

where F_R is the heat recovery factor, T is the temperature (°C), Ʈ is transmittance, and U_o is the overall heat loss coefficient.

The solar drying efficiency is given as [28].

$${ᶯ}_d=\frac{M_{w}Lv}{Q_u}\times 100$$

(6)

where $M_w$ is the weight of water evaporated from the cocoyam (kg), $Lv$ is the latent heat of evaporation of water (kJ/kg), and $t$ is the drying period (h).

2.5. Mathematical Modelling of the Drying Curve

The dimensionless moisture ratios were obtained with Equation (7).

$$MR =\frac{M_t –{ M}_e}{M_i-{ M}_e}$$

(7)

where M_t is the moisture content of the cocoyam at time t and M_e is the equilibrium moisture content, which is obtained with three consecutive moisture content measurements [29].

Curve fitting was conducted using seven semi-theoretical and empirical models available in the literature and shown in

Table 5. Drying kinetic models.

Model Name	Model	Reference
Lewis	$MR=\mathit{exp}\left(-kt\right)$	[29]
Henderson and Pabis’s	$\mathit{MR}={\mathit{ae}}^{-\mathit{kt}}$	[29]
Logarithmic model	$\mathit{MR}={\mathit{ae}}^{-\mathit{kt}}+c$	[29]
Wang and Singh	$\mathit{MR} =1+\mathit{at}+{\mathit{bt}}^2$	[29]
Two term	$MR=a\mathit{exp}\left(-k_{o}t\right)+\mathit{bexp}\left(-k_{1}t\right)$	[29]
Vermer et al.	$MR=a\mathit{exp}\left(-kt\right)+\left(1-a\right)\mathit{exp}\left(-\mathit{gt}\right)$	[29]
Two Term Exponential	$MR=a\mathit{exp}\left(-kt\right)+\left(1-a\right)\mathit{exp}\left(-\mathit{kat}\right)$	[29]

[2]. The root mean square error and coefficient of determination presented in Equations (8)–(10) were used to assess the goodness (model verification) of fittings and the best model selected. Model fitting and analysis were performed with Curve Expert graphing and analysis software.

$$R^2=1-\frac{{{\displaystyle \sum }}_{i=1}^N{\left(M{R}_{pre,i}-M{R}_{exp,i}\right)}^2}{{{\displaystyle \sum }}_{i=1}^N{\left({\overline{MR}}_{pre}-M{R}_{exp,i}\right)}^2}$$

(8)

$${\chi }^2=\frac{{{\displaystyle \sum }}_{i=1}^N{\left(M{R}_{pre,i}-M{R}_{exp,i}\right)}^2}{N-n}$$

(9)

$$RMSE={\left[\frac{1}{N}{\displaystyle \sum }_{i=1}^N{\left(M{R}_{pre,i}-M{R}_{exp,i}\right)}^2\right]}^{\frac{1}{2}}$$

(10)

2.6. Thermal Analysis

2.6.1. Effective Moisture Diffusivity

The solar drying effective moisture diffusivity (D_e) of the cocoyam was determined by plotting −ln (MR) against time [23]. The effective diffusivity was deduced from the slope K using Equation (11).

$$K=\frac{{\pi }^2{D}_e}{L^2}$$

(11)

2.6.2. Heat and Mass Transfer Coefficient

The hourly variation of the heat and mass transfer coefficient for the drying of cocoyam using the dryer was deduced with the Equation (12) [19].

$$\frac{h_c}{h_m{\rho }_a{\alpha }_a}=Le$$

(12)

The Lewis number is written as follows:

$$Le=\frac{\phi }{D_m}$$

(13)

where $\phi$ is the thermal diffusivity given as follows

$$\phi =\frac{k}{{\rho }_a{C}_p}$$

(14)

The diffusivity coefficient (D_m) is calculated from an Arrhenius equation as follows

$$D_e=D_{m}exp\left(-\frac{E_a}{RT}\right)$$

(15)

The effective moisture diffusivity (D_e) was calculated from the experiment while the activation energy (3.704 kJ/mol) was taken from [23] for cocoyam (taro). T is the temperature of the drying air assumed as the temperature of the drying chamber; R is the gas constant (8.31446 J/mol⋅K).

The coefficient of mass transfer, h_m (m/s), was deduced from the empirical relationship [30].

$$h_m=\left(\frac{D_m}{d}\right)\left(2.0+0.522R{e}^{0.5}S{C}^{0.33}\right)$$

(16)

$$SC=\frac{\eta }{\rho d}$$

(17)

$$R_e=\frac{\rho d\mu }{\eta }$$

(18)

where d is the particle diameter (m), $\rho$ is the density of the fluid (kg/m³); $\eta$ is the dynamic viscosity of fluid (kg/ms), and $\mu$ is the fluid velocity (m/s), which varied due to variation of the wind.

2.6.3. Variation in Thermal Properties of Cocoyam

The hourly specific heat capacity (C_p) and the thermal conductivity (k) variation of the cocoyam slices were determined using the equation presented by [23] for a solar drying of food products with thermal storage as a function of hourly moisture changes as follows

$$C_P=1256.26\left(\frac{X}{X_0}+0.818\right)$$

(19)

$$k=0.05+0.06\frac{X}{X_o}$$

(20)

The thermal effusivity was determined as a function of thermal conductivity and specific heat capacity [21].

$$\varrho =\sqrt{k{\rho }_a{C}_p}$$

(21)

2.7. Cost Analysis of the Solar Dryers

2.7.1. Cost Saving

The cost-saving potential of the dryer is calculated by comparing the energy consumed with that of grid-based electricity. The daily total energy utilization (E_c) by the dryers is calculated in terms of the rate of the energy consumed and the total time the dryer is in operation [31] given in the equation.

$$E_c=Q_u . t$$

(22)

where Q_u is the energy utilized (kW), t is time for drying per day

$$t=\frac{m}{D_c}{t}_T$$

(23)

where $t_T$ is the total time (h/batch) the dryer is in operation daily, m is the mass of product dried per day, and D_c is the dryer capacity (kg/day).

Considering that the dryer is used for a minimum of 20 working days in a month [31] for the 12 month period in a year, the total yearly energy consumption for drying is given in Equation (20)

$$E_{year}=E_c . w . 12$$

(24)

where w (20 days) is the number of days the dryer is in operation per month. Therefore, the amount of saving in a year based on percentage utilization when compared with the electricity price per KWh of electric energy is given by

$$A{M}_{yr}=P_u . E_{year} . E_p$$

(25)

where P_u is the percentage utilization, which ranges from 0.1 to 1.0, and E_p is the current price of a kWh of energy per country. Using Nigeria as a case study, the current electric energy cost per kWh as of May 2022 is taken as 0.057$ per unit of household energy consumption [32].

2.7.2. Payback Period

The payback period (PBP), which is the amount of time to recover the initial investment, is calculated according to [33] as follows

$$\mathrm{PBP}=\frac{C_c-C_s}{S_1}$$

(26)

where C_c is the initial capital cost of the dryer, presented in Table 2, S₁ is the average annual savings of the dryer, and C_s is the salvage value taken as 10% of the initial cost for the dryer [34].

2.8. CO₂ Emission Reduction Analysis

The CO₂ mitigation potential of the solar dryer was analysed by comparing the energy utilization of the solar dryer with an equivalent dryer that uses diesel to power the drying process. Ndukwu et al. [14] gave the energy in kWh utilized by a diesel-powered solar dryer as:

$$U_{Ed}=v_d{k}_d{\eta }_d$$

(27)

where v_d is the volume of diesel (L), k_d is the heating value of diesel (kWh/L), and η_d is the diesel efficiency (%). To determine the volume of diesel that will be burnt to produce the equivalent amount of energy produced by the solar dryer to dry the cocoyam, Equation (27) is equated with Equation (5) as follows

$$Q_u=v_d{k}_d{\eta }_d$$

(28)

Therefore, the volume of diesel utilized is deduced as follows

$$v_d=\frac{Q_u}{k_d{\eta }_d}$$

(29)

The mass of CO₂ produced by a litre of diesel is given by Ndukwu et al. [14] as follows

$$m_{{CO}_2}=v_d{k}_f$$

(30)

The values of k_f, k_d, and η_d were presented by Ndukwu et al. [14] as 2.63 kg/L, 10.08 kWh/L, and 30%, respectively.

3. Results and Discussion

3.1. Dryer Performance

The solar dryer was tested under the worst-case environmental conditions of the rainy season (2–4 September 2021). Though this time is the peak of the harvesting season for tuber crops in this area, it is characterized by high humidity and low solar radiation, as presented in Figure 2. Open sun drying is so difficult during this time and a little temperature gain above the ambient means a lot to farmers in drying their crops. The goal of evaluating the solar dryer during this period is to have the minimum performance of the solar dryer which will improve during the dry season or harmattan period with lower humidity and higher solar radiation. During the test period, the maximum solar radiation was 521.7 W/m² with an average value of 303.6 W/m². The average value of solar radiation obtained is lower than the 368.38 W/m²/day reported by Ndukwu et al. [18] for this area. Higher solar radiation occurred from 11.00 a.m. to 3.00 p.m. local time while 9.00 a.m. to 11.00 a.m. had lower solar radiation. Low solar radiation can be used as a warm-up period as no meaningful drying can be achieved during this period [35]. Figure 2 shows that higher solar radiation is synonymous with higher temperature and lower relative humidity. However, the temperature of the area ranged from 19.4 to 42.1 °C and the relative humidity ranged from 51.6 to 88.1%. During these drying periods, the average collector and drying chamber temperatures were 33.41 and 32.53, while the relative humidity was 66.92% and 67.5% respectively. The highest temperature difference between the ambient and the collector was 7 °C, while it was 5.5 °C for the drying chamber. However, the minimum relative humidity for the collector and the drying chamber was 50.6% and 52.3%, respectively.

The determined variation of the air velocity for the solar dryer for the three-day drying periods is shown in Figure 3. The air velocity varied between 0.063 and 1.9 m/s with an average value of 0.42 m/s for the three days. It was observed that the airflow velocity affected the relative humidity of the collector and the drying chamber. Comparing Figure 3 and Figure 4 shows that the relative humidity of the collector and drying chamber decreased as the airflow velocity decreased, and also increased with the airflow velocity. The reason for this might be that, at high airflow velocity, greater airflow volume with higher moisture will be available per time compared to lower airflow velocity. However, due to the partitioning, this air is delayed a little bit to receive more heat, which leads to an increase in temperature observed at a high relative humidity on the first day between 12.00 p.m. and 2.00 p.m. local time. This period can be regarded as a warm up period for the solar dryer as it was not observed again.

AA summary of the average operational performance of the solar dryer is presented in

Table 6. Summary of the drying performance of the two developed solar dryers.

Parameters	Unite	Values
Average solar collector temperature	(°C)	34.1
Average solar drying chamber temperature	(°C)	33.1
Average relative humidity of the solar collector	(%)	66.9
Average relative humidity of the drying chamber	(%)	67.4
Average solar radiation	(W/m2)	303.27
Average ambient temperature	(°C)	31.10
Average flow rate	(kg/s)	0.12
Initial moisture content on a wet basis	(%)	82.9
Final moisture content on a wet basis	(%)	10.32
Final mass	(g)	138
Average drying rate	(kg/kg h)	0.018686
Energy consumed	(MJ)	3.970 (1.103 kWh)
Solar collector efficiency	(%)	13.47
Overall solar drying efficiency	(%)	7.59
Drying time	(h)	25
CO2 mitigated per year	tons	317.11

, illustrating that the dryer took about 25 h to dry the cocoyam slice from the moisture content of 82.9% w.b to 10.32% at an average energy consumption of 3.97 MJ. This drying time is far lower than the 30 h recorded for the open sun drying of potato chips from 60.7% to 8.4% in the month of December at the same location [14]. This showed good performance considering the period during which the experiment took place. The December period in this location is characterized by lower humidity, which favours open sun drying, unlike the September period when this experiment was conducted. This implies that if this experiment was performed in the month of December in the same location, a drying time shorter than 25 h will be obtained. Table 6 also shows the average collector efficiency to be 13.47% with a drying efficiency of 7.57%.

3.2. Drying Kinetics and Mathematical Modelling

The evolution of moisture ratio and the drying rate of the cocoyam chips are shown in Figure 5 and Figure 6. Although, the moisture ratio decreased continuously and followed the falling curve behaviour, the drying rate showed sinusoidal characteristics, which depict the non-isothermal characteristics of solar dryers [36]. The reason for this is that the temperature and humidity evolution which drives the drying process is subjected to the vagaries of weather conditions that are not static. The downward nature of the sinusoidal curve of the drying rate still showed that the diffusion mechanism dominates the moisture transfer mechanism. This is similar to the results obtained by Hawa et al. [29] for untreated Cabaya fruits. The drying rate was highest at the first 6 h of drying but decreased afterwards. This is because the rate of mass transfer is higher due to greater moisture availability, but as the drying progresses, more energy is required to break the moisture bond due to the increased internal mass resistance of the material [37]. The moisture ratios were obtained by converting the moisture content into dimensionless form. To predict the moisture behaviour, the moisture ratio was fitted into seven semi-theoretical and empirical models to select the best-fitted model to predict it, and the results are presented in

Table 7. Model constants and statistical parameters for solar drying the cocoa yam slice.

Model	Constants	R2	RMSE	χ2
Lewis	k = 0.03157	0.9569	0.0347	0.001165
Two Term	a = 0.16656 ko = 0.22505 b = 0.8701 k1 = 0.02673	0.9666	0.02923	0.00145
Two term exponential	a = 0.17564 k = 0.14164	0.96648	0.03179	0.00145
Henderson and Pabis	a = 0.98466 k = 0.03351	0.95837	0.03772	0.00171
Logarithmic	a = 11.11849 k = 0.00376 c= −10.0901	0.96172	0.0745	0.00191
Wang and Singh	a = −0.036 b = 0.000556	0.95821	0.03784	0.00172
Modified page	k = 0.03202 n = 0.88042	0.96427	0.03341	0.00152
Vermer et al.	a =1150.18 k = 0.03668 g = 0.03668	0.95421	0.03891	0.00185

. Table 6 also shows the values of the model constants, R², χ², and RMSE values for each model. The goodness of fit between the experimental and predicted moisture ratio was verified by a higher R² value and lower chi-square and RMSE [38]. However, as shown in Table 6, for all the models used, R², χ², and RMSE values ranged from 0.95421 to 0.9666, 0.001165 to 0.00191, and 0.02923 to 0.03891, respectively, with the two-term model having the best fit. The plot of the predicted moisture ratio with the two-term model and the experimental moisture ratio is shown in Figure 5.

3.3. Evolution of the Thermal Properties

Figure 7 and Figure 8 show the relationships between the specific heat capacity (C_p), thermal conductivity (K), thermal diffusivity ($\phi$), and thermal effusivity ($\varrho$) with moisture loss. The specific heat capacity and thermal conductivity were determined as a function of the moisture content. In contrast, the thermal diffusivity and effusivity were deduced as a function of the thermal conductivity and specific heat capacity. Loss of moisture resulted in the decline of the specific heat capacity, thermal conductivity, and thermal effusivity, while the thermal diffusivity increased, as shown in Figure 7 and Figure 8 below.

Specific heat capacity, thermal effusivity, and thermal conductivity are thermal properties linked with heat distribution or storage within the product drying structure. Therefore, they are a function of the available product moisture and the food composition of the product. A decrease in moisture increases the volatility of food constituents, loss of moisture, and creation of voids by breaking the intercellular links distributing heat (tortuosity factor). Consequently, these properties are decreased [39]. The values of thermal effusivity of cocoyam ranged from 12.2 to 47.94 W S^1/2 m⁻² K⁻¹. This range of values is higher than that given for agricultural soil (1.38–4.01 W S^1/2 m⁻² K⁻¹) and static air (5.0 W S^1/2 m⁻² K⁻¹) [40]. In contrast, the values are less than that of water (1600W S^1/2 m⁻² K⁻¹), green leaves (675 W S^1/2 m⁻² K⁻¹ to 750 W S^1/2 m⁻² K⁻¹), and polymers (400–1500 W S^1/2 m⁻² K⁻¹) but lie within the range given for insulators (10–400 W S^1/2 m⁻² K⁻¹). The thermal diffusivity value showed the effectiveness of heat energy transport within the cocoyam chips during drying. The value of thermal diffusivity is a function of thermal conductivity and specific heat capacity. The behaviour of the thermal diffusivity curve is an indication of the degree of the magnitude of variation of specific heat and thermal conductivity, although Jayalakshmy and Philip [21] have shown that this value can be inconsistent. The average values of the thermal conductivity, thermal effusivity, specific heat capacity, thermal diffusivity, and effective moisture diffusivity are presented in

Table 8. Average values of thermal properties.

Thermal Property	Average Value	Standard Deviation
Specific heat capacity (J/kg K)	1866.154	249.4573
Thermal conductivity (W/m K)	0.090049	0.011914
Thermal diffusivity (m/s)	3.93965 × 10−5	5.62695 × 10−8
Effective moisture diffusivity (m/s)	3.21462 × 10−10	-
Thermal effusivity (S1/2 m−2 K−1)	35.30598	7.690472
Heat transfer coefficient (W/m K)	3.85	0.67931
Mass transfer coefficient (m/s)	0.01757	0.034469
Diffusivity coefficient(m2/s)	0.000179	0.000306

. These values are given as 0.090049 W/m.K, 35.30598 S^1/2 m⁻² K⁻, 1866.154 J/kg K, 3.9396 × 10⁻⁵ m/s, and 3.21462 × 10⁻¹⁰ m/s, respectively. The obtained value of the effective moisture diffusivity for the cocoyam is within the range obtained in the literature for agricultural products [41].

All the thermal properties determined were presented as a function of the moisture ratio, as shown in

Table 9. Regression Equations for Thermal properties.

Equations	Regression Coefficients	R2	Standard Error
$C_p=\mathsf{{\rm Y}}+\omega r^{M/M_o}+\vartheta \frac{M}{M_o}$	$\mathsf{{\rm Y}}=$1026	0.99	0.0004041
	$\omega$= 1.2696
	$r=$1256
	$\vartheta$= 0.9334
$K={\left(ϵ+\chi \frac{M}{M_o}+\omega {\left(\frac{M}{M_o}\right)}^2\right)}^{-1}$	$ϵ=17.884$	0.99	0.0000608731
	$\chi =$ −12.883
	$\omega =4.0961$
$\varrho =\frac{\phi \alpha +\tau {\left(\frac{M}{M_o}\right)}^{\gamma }}{\alpha +{\left(\frac{M}{M_o}\right)}^{\gamma }}$	$\phi =7.9336$	0.99	0.000003156964
	$\alpha =6.2569\times {10}^5$
	$\tau =6.0135\times {10}^6$
	$\gamma =0.1$
$\phi =\varpi +\beta ln\left(\frac{M}{M_o}\right)$	$\varpi =0.000039327$	0.98	0.00000000830198
	$\beta =-0.000001563$

, with a coefficient of determination for non-linear fittings ranging from 0.98 to 0.99, while the standard error ranged from 8.3 × 10 ⁻⁹ to 4.01 × 10 ⁻⁴. The obtained result showed a good fit for the equations.

3.4. Variation in Heat and Mass Transfer Coefficient

The plot of the Reynolds number in Figure 9 shows that it varies from 171.7 to 5152.669, which indicates that the airflow condition gravitates between laminar and turbulent flow due to the effect of partitioning and the wind air generator. This is a result of inconsistency in wind speed as they vary due to the vagaries of weather changes. A lower Reynolds number indicates the dominance of vicious force at that moment while a higher Reynolds number is an indication of inertia force domination due to the increased speed of the flow. The non-linear relationship between the Reynolds number and the airflow velocity is presented in Equation (23). The values of the Reynolds number affect the mass and diffusivity transfer coefficient and are linearly related. For this research, the variation of the heat transfer, mass transfer, and diffusivity coefficient was computed with the Schmidt and Reynolds numbers. Additionally, the mass transfer coefficient and the Lewis number were used to compute the heat transfer coefficient for the drying of the cocoyam. Therefore, the results also mimicked the sinusoidal characteristics of the plot of the Reynolds number as shown in Figure 10 and Figure 11. However their values varied from 7.1 × 10⁻⁵ to 1.2 × 10⁻¹ m/s for mass transfer coefficient, 1.05 × 10⁻⁶ to 1.035 × 10⁻³ m/s for diffusivity coefficient, and 3.056 to 5.771 W/m °C for heat transfer coefficients with average values of 1.757 × 10⁻² m/s, 1.79 × 10⁻⁴ m/s, and 3.85 W/m °C, respectively.

$$Re=\varnothing \left(1+\lambda \frac{\left(v\right)}{\mathsf{\Gamma }}\right)\left(\frac{-1}{\lambda }\right)$$

(31)

where $\varnothing$, $\lambda$, and $\mathsf{\Gamma }$ are regression coefficients, given as 0.00859, −0.1, and −0.00000297, respectively, and v is the air velocity (m/s).

3.5. Economic Assessment

Solar drying has the advantage of cost-saving over most other dryers. The cost analysis is based on the prevailing economic conditions and monetary policy of Nigeria. For ease of the analysis, it was assumed that the solar dryers operate for 20 days monthly excluding the official weekends (Saturday, Sunday, and half a day on Fridays). However, it is also assumed that the rate of usage might vary depending on the availability of sunshine hours, which vary between 3.5 and 9 h in Nigeria [42,43]. Therefore, the percentage usage graduated from 10% to 100%. The initial cost of fabricating the dryer is presented in Table 2 with a total cost of $122.714. Considering the energy consumption presented in Table 5 and the unit cost of electricity in Nigeria, the amount of saving per rate of usage is presented in Figure 12. The computed values increased from $188.63 to $1886.13. This amount of savings is huge for a poor country like Nigeria where a lot of people are still living below the poverty line. The amount saved was used to compute the payback periods based on the percentage usage. The payback period ranged from 0.059 to 0.59 years (21.54–215.35 days). This is far lower than the payback period for tunnel dryers calculated as 13 years [44]. Therefore, assuming a life span of 10 years, the dryer will run almost cost-free throughout its entire life.

3.6. Environmental Impact Analysis

The ecological benefit of using such a dryer is the mitigation of atmospheric CO₂, unlike fossil-based dryers where the energy sources release CO₂ into the atmosphere. A comparative analysis was performed using this solar dryer and a diesel-powered dryer in terms of an equal amount of energy utilization to dry the same amount of cocoyam. The determined CO₂ reduction per year was 317.11 tonnes per year, as presented in Table 5. This is high and represents an indicator of the ecological benefits of using the solar dryer.

4. Conclusions

The performance evaluation and thermo-physical data of cocoyam chips were evaluated with a partitioned single pass solar dryer powered by the wind. Drying of the cocoyam chips took 25 h with a collector efficiency of 13.47% to attain equilibrium moisture content under a highly humid condition and average solar radiation intensity. The specific heat, thermal conductivity, thermal diffusivity, diffusivity coefficient, heat and mass transfer coefficient, and thermal effusivity were empirically determined. The specific heat capacity, thermal conductivity, and thermal effusivity declined with moisture content. In contrast, the thermal diffusivity increased. The diffusivity coefficient and heat and mass transfer coefficient varied with the airflow rate. Determination of the Reynolds number indicates that the airflow through the collector gravitates between laminar and turbulent flow due to the impact of the wind generator. The two-term model was the best-fitted model for the drying kinetics of cocoyam under variable external climatic conditions of the study area. Using the solar dryer in Nigeria can save $188.63–$1886.13 in running costs with a payback period of 0.059–0.59 years (21.54–215.35 days) at a rate of 10–100% of usage. The results obtained will be useful in the process optimization of the solar drying of cocoyam. Future simulation of the drying process considering the fluid behaviour is recommended for future study.