Drying Characteristics, Kinetic Modeling, Energy and Exergy Analyses of Water Yam (Dioscorea alata) in a Hot Air Dryer

Abstract

In this study, drying characteristics, kinetic modelling, energy and exergy analyses of a convective hot air dryer are presented for water yam. The drying experiments were carried out at temperature levels of 50, 60, and 70°C and slice thicknesses of 3, 6, and 9 mm. The effects of drying variables on the drying rate (DR), moisture diffusivity (D_eff), activation energy (E_a), energy utilization (EU), energy utilization ratio (EUR), exergy loss (EX_L), exergy efficiency (EX_eff), improvement potential (IP), and exergetic sustainability index (ESI) were investigated. The results showed that increasing air temperature increased the DR, D_eff, EU, EUR, EX_L, EX_eff, IP, and ESI, while increasing the slice thickness increased D_eff and E_a, but decreased the DR. The highest D_eff and E_a values were 4.2 × 10⁻⁸ m²/s, and 53 KJ/mol, respectively. EU and EUR varied from 10 to 150 J/s and 0.39 to 0.79, respectively. EX_L and EX_eff varied between 2 and 12.5 J/s and 58 to 75 %, respectively. Midilli’s model had the best performance in predicting the moisture ratio of water yam with coefficient of determination (R² = 0.9998), root mean square error (RMSE = 0.0049), and sum of square error (SSE = 0.0023).

1. Introduction

Tuber crops are salient drivers of food security, income creation and sustainable development in many countries, e.g., in Africa, the tropical Pacific islands, and Southeast Asia. They serve as an important source of carbohydrate, mineral, and medicinal values to the ever-growing population of the world [1,2]. Yam is a tuberous root crop, including over 600 species, of which Dioscorea alata, Dioscorea cayenensis, and Dioscorea rotundata has the highest economic importance [3].

Water yam (Dioscorea alata) is one of the edible specie of yam; it is white in colour and originated from tropical Asian countries. It is characterized with low sugar content, high water content (70–73%), high yield, high multiplication index, and better storability in relation to other yam species. The nutritional composition of water yam includes: carbohydrate (about 22%), protein (6–8%), ash (4–5%), fat (about 1%), rich in essential minerals, and B Vitamins [3,4]. Due to the high moisture content of water yam, it is therefore necessary to convert it into a form that can be storable [5]. Low water activity retards the development of microorganism which causes food spoilage [6,7].

Drying is a technological tool for food preservation and a thermodynamic process of heat and mass transfer. It involves the simultaneous transfer of heat to food for evaporation of water and the transport of water vapor formed away from the food [8]. Drying causes moisture reduction which increases shelf life, weight and volume reduction, reduction in packaging cost, ease of storage and transportation [9,10,11]. Hot air drying has been predominantly used in most agro-industries. Some of its advantages include low production and operation costs, efficient surface water removal, good physicochemical, nutritional and functional properties [8,12].

Drying is a relatively slow process, it is therefore necessary to model the drying process to prevent product degradation, reduce drying time, equipment stress, energy utilization, and product yield improvement so as to strengthen industrial design and production [11,13]. Theoretical, empirical, and semi-empirical models have been successfully used in the literature for modelling the drying kinetic of food products. Theoretical models are derived from Fick’s second law of diffusion, and they describe the drying kinetic and the internal mechanism of mass transfer with respect to the geometry of the product while empirical and semi-empirical models are analogues of Fick’s second law and Newton’s law of cooling with little modification, they describe the statistical correlation between moisture content and drying time, though they are more convenient for practical drying systems [14].

Energy consumption is one of the engineering and technological issues of drying in the industry [15]. The high energy demand of most industrial dryers causes increase in the cost of operation, making drying process exorbitant. Energy and exergy analyses of a drying process provide information on energy savings and optimum process conditions [15]. Energy analyses quantitatively explain the energy required for a system while exergy analyses qualitatively describe the useful energy utilized by the system [16,17]. Exergy is either consumed or destroyed during the drying process (i.e., irreversible) [18]. It describes the quality of energy available in the various components of the drying systems and is important in sustainable industrial drying design systems [19,20,21]. Additionally, exergy analyses are important in evaluating energy consumption, energy conversion efficiency, impact of energy resources utilization on the environment, and the operation cost of a drying process [15,22].

Several investigations have been carried out on the energy and exergy analysis of drying different agricultural products using different dryers. Corzo et al. [23] carried out energy and exergy analyses of coroba slices in an air dryer; and established that energy utilization, exergy loss, and exergy efficiency increased with an increase in temperature and air velocity. Icier et al. [24] explored the exergetic performance of three different drying systems used on broccoli florets of which a fluid bed dryer showed the highest exergy efficiency. Akbulut and Durmus [25] evaluated the drying of mulberry slices in a forced solar dryer and observed that the energy utilization ratio and exergy loss decreased with an increase in the air mass flow rate while exergy efficiency increased. Aghbashlo et al. [20] conducted an experiment to analyse energy and exergy of fish oil microencapsulation in a spray dryer and obtained that energy and exergy efficiency increases at high drying temperatures (140 to 180 °C). Aviara et al. [15] observed that energy efficiency, exergy loss, and exergy efficiency of cassava starch in a tray dryer increased with an increasing temperature. Darvishi et al. [26] evaluated the effect of microwave power levels and sample thickness on the energy and exergy analysis of kiwi fruit slices, and established that energy and exergy efficiencies increased with increasing microwave power and with decreasing sample thickness. In addition, the energy efficiency was higher than exergy efficiency that was in agreement in an experiment carried by Surendhar et al. [27] on the energy and exergy analysis of turmeric in a microwave. Beigi et al. [17] conducted an exergy analysis of deep bed drying for rough rice in a convective dryer and noticed that the exergy loss and improvement potential increased with temperature and air velocity. The exergy efficiency and sustainability index of the drying process and the drying chamber increased with temperature but decreased with air velocity. Liu et al. [22] carried out an analysis of energy and exergy of mushroom in a hot air impingement dryer. It was observed that energy utilization and exergy loss increased with temperature, sample thickness and air velocity. Exergy efficiency increased with temperature and air velocity but decreased with sample thickness. Castro et al. [28] conducted the exergy analysis of a continuous-convective dryer of onion slice as a test crop. Their results showed that exergy loss increased with drying air temperature velocity, but exergy efficiency decreased with temperature and increased with air velocity. Argo and Ubaidillah [29] explored the energy and exergy analysis of cassava chips in a tray dryer and observed that energy utilization, exergy efficiency, and exergy loss increased with drying time. Energy utilization ratio, energy efficiency, and improvement potential decreased with drying time. Parhizi et al. [30] explored pennyroyal drying in a solar-hot air dryer. An increase in temperature and bed thickness increased the energy utilization ratio, exergy loss and exergy efficiency.

The summary of these studies revealed that exergy efficiency is usually lower than energy efficiency. Energy utilization, exergy inflow, exergy outflow, energy efficiency, exergy efficiency, exergy loss, and energy utilization ratio were all affected by the drying temperatures, air velocity, microwave power levels, solar radiation, and product thickness. Although similar trends of the effects of the drying parameters have been observed from the literature, different values of the energy and exergy evaluation were reported even when the same type of dryer was used. This signifies that the exergy requirement of every crop differs even when the same dryer is used, also the environmental relative humidity and temperature can also affect its requirement. Furthermore, it has been proven from the literature that exergy analysis is certainly important in optimization of industrial drying process. Hence, information regarding exergy requirement of agricultural crops is highly beneficial to industries. Moreover, there is no information regarding the energy and exergy analyses of water yam drying using hot air convective dryer in scientific literature. Therefore, the objective of present study was to comprehensively model the drying kinetic of water yam using theoretical, semi-empirical, and empirical models and to perform the energy and exergy analyses of the drying process at different temperatures and slice thicknesses.

2. Materials and Methods

2.1. Sample Preparation

Fresh water yam was purchased from a local market in Omu-Aran, Kwara state, Nigeria. The yam tubers were manually peeled and diced in rectangular cubes (50 mm × 25 mm) of varying thickness (3, 6, and 9 mm) using a stainless knife before the commencement of the drying experiment. The different slice thickness adopted was according to Ojediran et al. [8]. The initial moisture content of the water yam was 73.70 ± 0.21% wet basis, as determined according to AOAC [31] method in triplicate, oven drying at 105 °C for 24 h [32]. About 40 g of yam slice was used to calculate the moisture content.

2.2. Drying Experimentation

2.2.1. Dryer Description and Operation

Drying experiment was conducted with a laboratory hot air dryer (Figure 1). The drying chamber consists of perforated rectangular trays (380 mm × 400 mm × 30 mm) arranged horizontally, an enclosure containing two heating elements (1 kW each), a centrifugal fan that produced the drying air at velocity (0.7 m/s), and a vent for releasing the used air. The body of the dryer was lagged with fibre glass material (thickness of 30 mm) to reduce heat loss to the surrounding and also to properly house other functional units. The automatic data logger which consists of the following parts; an Arduino interfaced with a temperature sensor (DS18B20 temperature sensor, temperature range −55 to 125 °C, resolution 9 to 12 bit, power supply 3 to 5 V, current consumption 1 mA, accuracy ±0.5 °C), a humidity sensor (DHT11 humidity sensor, humidity range 20 to 90%, power supply 3.5 to 5.5 V, resolution 16 bit, accuracy ± 1%, current consumption 0.3 mA), and an LCD screen were measurement are recorded and observed at intervals. Once the temperature inside the drying environment gets to the set temperature the heating element is thermostatically triggered OFF, and ON when it gets lower than the set temperature. Two temperature and humidity sensors were used; one was set at the air exit point while the other was set at the drying air inlet point. These values were recorded at 10 min intervals on the LCD screen of the data logger and validated occasionally with a hygrometer (PCE-310, 0–100% relative humidity, accuracy ±3%, response time 60 s, resolution 0.1%, resistance humidity sensor) during the drying experiment. During the drying experiment, the dried air supplied constantly picks up moisture emanating from the product and discharges it through the air vent, causing weight reduction until equilibrium is reached.

2.2.2. Drying Procedure

Prior to the commencement of the drying operation, the dryer after being set to the required temperature was allowed to run for one hour for proper stabilization of the drying environment. The test procedure employed was as detailed by Aviara et al. [15] and Ojediran et al. [8]. The ambient air temperature and relative humidity varied between 27 and 32 °C and 55 and 67%, respectively during the drying period. For the experimental run, three (3) different temperatures (50, 60, and 70 °C) and slice thickness (3, 6, and 9 mm) were used, respectively. Air velocity was kept constant at (0.7 m/s). A factorial design was adopted for the combination of the variables, generating a total of nine experimental run with three replicates. Average weight loss was used for further analyses. The weight loss of the yam slice placed on the tray during drying was monitored. In the first hour, the sample was weighed at interval of 10 min, and for the next three hours it was weighed at intervals of 30 min; subsequently it was weighed at intervals of one hour until three identical readings was reached, showing the dynamic equilibrium point. The weighing balance (AND GR-200, Japan, accuracy ±0.0001 g, readability of 0.1 mg and maximum capacity 210 g) was placed very close to the dryer and weighing period of 15 s was maintained. During the course of the experiment, inlet and outlet temperature, inlet and outlet relative humidity and the ambient condition were all monitored and recorded.

2.3. Drying Kinetic

The drying kinetic for the water yam slices was computed using the following equations.

2.3.1. Moisture Content

The moisture content (MC) variation of the yam slice across the drying time was determined using Equation (1) [33]

$${\mathrm{M}}_{\mathrm{t}}=\frac{{\mathrm{W}}_{\mathrm{t}}-{\mathrm{W}}_{\mathrm{d}}}{{\mathrm{W}}_{\mathrm{d}}}$$

(1)

2.3.2. Moisture Ratio

The moisture ratio (MR) was calculated from the moisture content values as shown in Equation (2) [34,35].

$$\mathrm{MR}=\frac{{\mathrm{M}}_{\mathrm{t}}}{{\mathrm{M}}_{\mathrm{o}}}$$

(2)

2.3.3. Drying Rate

The drying rate reveals the moisture loss from the sample at unit time; it was calculated using Equation (3) [8,36].

$$\mathrm{DR}=\frac{{\mathrm{M}}_{\mathrm{t}}-{\mathrm{M}}_{\mathrm{t}+\Delta \mathrm{t}}}{\Delta \mathrm{t}}$$

(3)

2.4. Mathematical Model

The actual data of the moisture ratio against time from the drying experiment for each treatment was fitted into ten (10) mathematical models (

Table 1. Mathematical models tested for the moisture ratio of water yam.

S/N	Model Name		References
1	Page	$\mathrm{MR}=\exp \left(-{\mathrm{kt}}^{\mathrm{n}}\right)$	[38]
2	Henderson and Pabis	$\mathrm{MR}=\mathrm{aexp}\left(-\mathrm{kt}\right)$	[39]
3	Newton	$\mathrm{MR}=\exp \left(-\mathrm{kt}\right)$	[40]
4	Aghbashlo et al.	$\mathrm{MR}=\exp \left(-\frac{{\mathrm{k}}_1\mathrm{t}}{1+{\mathrm{k}}_2\mathrm{t}}\right)$	[41]
5	Logarithmic	$\mathrm{MR}=\mathrm{aexp}\left(-\mathrm{kt}\right)+\mathrm{c}$	[42]
6	Approximation of diffusion	$\mathrm{MR}=\mathrm{aexp}\left(-\mathrm{kt}\right)+\left(1-\mathrm{a}\right)\exp \left(-\mathrm{kbt}\right)$	[43]
7	Two-term	$\mathrm{MR}=\mathrm{aexp}\left(-\mathrm{gt}\right)+\mathrm{bexp}\left(-\mathrm{ht}\right)$	[44]
8	Wang and Singh	$\mathrm{MR}=1+\mathrm{at}+{\mathrm{bt}}^2$	[45]
9	Parabolic	$\mathrm{MR}=\mathrm{a}+\mathrm{bt}+{\mathrm{ct}}^2$	[46]
10	Midilli et al.	$\mathrm{MR}=\exp \left(-{\mathrm{kt}}^{\mathrm{n}}\right)+\mathrm{bt}$	[47]

) using Matlab 2017a. These models were used to examine the drying kinetic of water yam in the hot air dryer. The goodness of the fit was evaluated using coefficient of determination (R²), root mean square error (RMSE), and sum of squared errors (SSE). The best model was chosen based on the highest R² value, lowest RMSE, and SSE values [10,37]. These values were calculated using Equations (4)–(6).

$${\mathrm{R}}^2=\frac{{\displaystyle \sum }{\left({\mathrm{MR}}_{\mathrm{pre}}-{\mathrm{MR}}_{\exp }\right)}^2}{{\displaystyle \sum }{\left({\mathrm{MR}}_{\mathrm{AVpre}}-{\mathrm{MR}}_{\exp }\right)}^2}$$

(4)

$$\mathrm{RMSE}={\left(\frac{{\displaystyle \sum }{({\mathrm{MR}}_{\mathrm{pre}}-{\mathrm{MR}}_{\exp })}^2}{\mathrm{N}}\right)}^{\frac{1}{2}}$$

(5)

$$\mathrm{SSE}=\left[\frac{1}{\mathrm{N}}{\displaystyle \sum }{\left({\mathrm{MR}}_{\exp }-{\mathrm{MR}}_{\mathrm{pre}}\right)}^2\right]$$

(6)

2.5. Moisture Diffusivity

The Fick’s second law was used to describe the moisture diffusion during drying of agricultural products [14,48].

$$\frac{\partial \mathrm{M}}{\partial \mathrm{t}}={\mathrm{D}}_{\mathrm{eff}}{\nabla }^2\mathrm{M}$$

(7)

Integrating Equation (7) for rectangular slab geometry with boundary conditions; uniform initial moisture distribution, negligible external resistance, negligible shrinkage, and constant diffusivity as given by Doymaz [45] and Srikanth et al. [2] gives Equation (8).

$$\mathrm{MR}=\frac{{\mathrm{M}}_{\mathrm{t}}}{{\mathrm{M}}_{\mathrm{o}}}=\frac{8}{{\mathsf{\pi }}^2}{\displaystyle \sum }_{\mathrm{n}=0}^{\infty }\frac{1}{{\left(2\mathrm{n}+1\right)}^2}\exp \left(-\frac{{\left(2\mathrm{n}+1\right)}^2{\mathsf{\pi }}^2{\mathrm{D}}_{\mathrm{eff}}\mathrm{t}}{4{\mathrm{L}}^2}\right)$$

(8)

Linearizing Equation (8) gives Equation (9)

$$\mathrm{lnMR}=\ln \left(\frac{8}{{\mathsf{\pi }}^2}\right)-\left(\frac{{\mathsf{\pi }}^2{\mathrm{D}}_{\mathrm{eff}}\mathrm{t}}{4{\mathrm{L}}^2}\right)$$

(9)

A plot of ln(MR) against drying time [t] gave a curve with slope K and the moisture diffusivity can be calculated from Equation (10).

$$\mathrm{K}=\frac{{\mathsf{\pi }}^2{\mathrm{D}}_{\mathrm{eff}}}{4{\mathrm{L}}^2}$$

(10)

2.6. Activation Energy

Activation energy is the energy required for moisture diffusion during drying of agricultural products. The Arrhenius equation is used in describing the correlation between moisture diffusivity and activation energy [8].

$${\mathrm{D}}_{\mathrm{eff}}={\mathrm{D}}_0\exp \left(-\frac{{\mathrm{E}}_{\mathrm{a}}}{\mathrm{R}\left(\mathrm{T}+273.15\right)}\right)$$

(11)

Linearizing Arrhenius equation

$${\mathrm{lnD}}_{\mathrm{eff}}={\mathrm{lnD}}_0-\frac{{\mathrm{E}}_{\mathrm{a}}}{\mathrm{R}\left(\mathrm{T}+273.15\right)}$$

(12)

2.7. Energy Analyses

The energy analyses for the water yam drying process were calculated from the data obtained during the experiment. The flow was assumed to be steady. The first law of thermodynamics for an open system was adopted in these analyses [15,25].

Energy balance equation:

$$\mathrm{Q}-\mathrm{W}=\Delta \mathrm{U}={\displaystyle \sum }{\dot{\mathrm{M}}}_{\mathrm{A}2}\left[{\mathrm{h}}_2+\frac{{\mathrm{v}}_2{}^2}{2}\right]-{\displaystyle \sum }{\dot{\mathrm{M}}}_{\mathrm{A}1}\left[{\mathrm{h}}_1+\frac{{\mathrm{v}}_1{}^2}{2}\right]$$

(13)

Assume no mechanical work is performed, no resultant motion and equal mass flow rate at inlet at outlet during the drying process of the yam slices. Therefore, Equation (13) becomes:

$$\mathrm{Q}={\dot{\mathrm{M}}}_{\mathrm{A}}\left({\mathrm{h}}_2-{\mathrm{h}}_1\right)$$

(14)

The mass flow rate and air enthalpies in the dryer were calculated from Equations (15) and (16), respectively.

$${\dot{\mathrm{M}}}_{\mathrm{A}}={\mathsf{\rho }}_{\mathrm{A}}{\dot{\mathrm{V}}}_{\mathrm{A}}$$

(15)

$$\mathrm{h}={\mathrm{C}}_{\mathrm{pA}}{\mathrm{T}}_{\mathrm{dA}}+{\mathrm{Hh}}_{\mathrm{sat}}$$

(16)

$${\mathrm{C}}_{\mathrm{pA}}=1.003+0.00005{\mathrm{T}}_{\mathrm{dA}}$$

(17)

2.7.1. Energy Utilization

The energy utilization of the dryer for drying of the yam slices was calculated from Equation (18) [22].

$$\mathrm{EU}={\dot{\mathrm{M}}}_{\mathrm{A}}\left({\mathrm{h}}_2-{\mathrm{h}}_1\right)$$

(18)

2.7.2. Energy Utilization Ratio

Energy utilization ratio (EUR) of the drying unit was calculated using Equation (19) [15,49].

$$\mathrm{EUR}=\frac{{\dot{\mathrm{M}}}_{\mathrm{A}}\left({\mathrm{h}}_1-{\mathrm{h}}_2\right)}{{\dot{\mathrm{M}}}_{\mathrm{A}}\left({\mathrm{h}}_1-{\mathrm{h}}_{\infty }\right)}$$

(19)

2.8. Exergy Analyses

The analyses of exergy for the drying process of the yam slices in a hot air dryer was carried out using the second law of thermodynamics which states that heat cannot flow from a body at lower temperature to a body at higher temperature spontaneously except using an external factor. The second law shows that when an amount of heat energy is supplied to a system, a part of energy becomes un-transformable to useful work while the other part would be use by the system to do work. The exergy balance is described by Equation (20) for an open system [15,25,29].

$$\mathrm{EX}=\left[\mathrm{U}-{\mathrm{U}}_{\infty }\right]-{\mathrm{T}}_{\mathrm{o}}\left[\mathrm{S}-{\mathrm{S}}_{\infty }\right]+{\mathrm{P}}_{\infty }\left[\mathrm{V}-{\mathrm{V}}_{\infty }\right]+\frac{{\mathrm{v}}^2}{2}+\left[\mathrm{Z}-{\mathrm{Z}}_{\infty }\right]\mathrm{g}+\mathrm{V}\left[\mathrm{P}-{\mathrm{P}}_{\infty }\right]$$

(20)

There was no relative motion or vibration in the dryer. Therefore, the gravity and momentum components were dropped, Equation (20) reduced to Equation (21):

$$\mathrm{EX}=\left[\mathrm{U}+\mathrm{PV}\right]-\left[{\mathrm{U}}_{\infty }+{\mathrm{P}}_{\infty }{\mathrm{V}}_{\infty }\right]-{\mathrm{T}}_{\mathrm{o}}\left[\mathrm{S}-{\mathrm{S}}_{\infty }\right]$$

(21)

Replacing U+PV in Equation (22) with enthalpy (h) gives Equation (22):

$$\mathrm{EX}={\mathrm{C}}_{\mathrm{pA}}\left[\left({\mathrm{T}}_{\mathrm{dA}}-{\mathrm{T}}_{\mathrm{o}}\right)-{\mathrm{T}}_{\mathrm{o}}\ln \frac{{\mathrm{T}}_{\mathrm{dA}}}{{\mathrm{T}}_{\mathrm{o}}}\right]$$

(22)

2.8.1. Exergy Inflow, Exergy Outflow and Exergy Loss

Exergy inflow, exergy outflow, and exergy loss were calculated using Equations (23)–(25) [37].

$${\mathrm{EX}}_1={\mathrm{C}}_{\text{pA1}}\left[\left({\mathrm{T}}_{\text{dA1}}-{\mathrm{T}}_{\mathrm{o}}\right)-{\mathrm{T}}_{\mathrm{o}}\ln \frac{{\mathrm{T}}_{\text{dA1}}}{{\mathrm{T}}_{\mathrm{o}}}\right]$$

(23)

$${\mathrm{EX}}_2={\mathrm{C}}_{\text{pA2}}\left[\left({\mathrm{T}}_{\text{dA2}}-{\mathrm{T}}_{\mathrm{o}}\right)-{\mathrm{T}}_{\mathrm{o}}\ln \frac{{\mathrm{T}}_{\text{dA2}}}{{\mathrm{T}}_{\mathrm{o}}}\right]$$

(24)

$${\mathrm{EX}}_{\mathrm{L}}={\mathrm{EX}}_1-{\mathrm{EX}}_2$$

(25)

2.8.2. Exergy Efficiency

The exergy efficiency of the dryer in moisture diffusion of the yam slice was calculated using Equation (26) [16,22].

$${\mathrm{EX}}_{\mathrm{eff}}=\frac{{\mathrm{EX}}_1-{\mathrm{EX}}_{\mathrm{L}}}{{\mathrm{EX}}_1}\times 100$$

(26)

2.8.3. Improvement Potential

Exergetic improvement potential rate is also referred to the improvement potential for the dryer. Exergy improvement potential is the amount of exergy that can be reused by minimizing wasted exergy. It was calculated using Equation (27) [15,50].

$${\mathrm{I}}_{\mathrm{P}}=\left(1-\left(1-\left(\frac{{\mathrm{EX}}_{\mathrm{L}}}{{\mathrm{EX}}_1}\right)\right)\right)\times \left({\mathrm{EX}}_1-{\mathrm{EX}}_2\right)$$

(27)

2.8.4. Exergetic Sustainability Index

The exergetic sustainability index (ESI) of the drying process was evaluated using Equation (28) [17,28].

$$\mathrm{ESI}=\frac{1}{1-{\mathrm{EX}}_{\mathrm{eff}}}$$

(28)

The reference condition of the drying environment is T_o = 29.5 °C, relative humidity of 61%, and${ \mathrm{P}}_{\infty }$ of 101.3 kPa

2.9. Statistical Analyses

Microsoft Excel (version 2016) was used in analysing the experimental data, calculating the standard deviation, and plotting the graphs. MATLAB software (version R2017a) was used for fitting the drying kinetic data in the different mathematical models.

2.10. Uncertainty Analyses

Uncertainty analyses are usually performed for reliability and soundness of the experimental and predicted data obtained [14,51]. The uncertainty analysis was conducted using Equation (29).

$$\mathrm{U}={\left[{\left(\frac{\partial \mathrm{y}}{\partial {\mathrm{x}}_1}{\mathrm{u}}_1\right)}^2+{\left(\frac{\partial \mathrm{y}}{\partial {\mathrm{x}}_2}{\mathrm{u}}_2\right)}^2+{\left(\frac{\partial \mathrm{y}}{\partial {\mathrm{x}}_3}{\mathrm{u}}_3\right)}^2+\cdots +{\left(\frac{\partial \mathrm{y}}{\partial {\mathrm{x}}_{\mathrm{n}}}{\mathrm{u}}_{\mathrm{n}}\right)}^2\right]}^{\frac{1}{2}}$$

(29)

3. Results

3.1. Drying Kinetic

The variation between the MR and the time for all drying parameters (temperatures versus slice thickness) is shown in Figure 2a–c. MR was found to decrease by an increase in drying time. The decrease in moisture ratio with time was faster at higher temperatures and smaller slice thicknesses. The temperature rise increases the heat and mass transfer rate. At the minimum slice thickness, there is lower volume of water and faster moisture transport from the core of the slice for evaporation [8]. The shortest drying time was observed at the maximum temperature (70 °C) and the minimum slice thickness (3 mm) by 900 min while the longest was at the minimum temperature (50 °C) and maximum slice thickness (3 mm) by 1860 min. A similar trend on the effect of temperature and slice thickness on drying kinetic has been reported by Fang et al. [33] for the effect of temperature on Chinese yam, Onwude et al. [52] for the effect of temperature on sweet potato, and Ojediran et al. [8] for the effect of temperature and slice thickness on Dioscorea rotundata.

3.2. Drying Rate

The effect of temperature and slice thickness on the drying rate (DR) versus moisture content is presented in Figure 3a–c. Drying rate increased with an increase in moisture content. The highest DR was recorded at the initial stage of drying due to a higher amount of moisture in the yam slice. Moisture diffusion was faster at the beginning stage of drying due to the available moisture in the surface of the slice, but the moisture diffusion reduced as drying progress. As the temperature was increased, the rate of drying increased while as slice thickness was increased the drying rate was reduced. In the initial drying stage falling rate was dominant indication moisture loss is controlled by diffusion, but at the middle to the end of the drying process, a constant rate was experienced [53]. This was in agreement with the findings reported by Harish et al. [54] for elephant foot yam, Ojediran et al., [8] for Dioscorea rotundata and Ononogbo et al., [32] for yam slices.

3.3. Moisture Diffusivity

The results of the moisture diffusivity (D_eff) are reported in Figure 4. The D_eff increased as drying temperature and slice thickness increased. The highest moisture diffusivity value was 4.2 × 10⁻⁸ m²/s at the air temperature of 70 °C and the slices thickness of 9 mm while the lowest value was 2.7 × 10⁻⁹ m²/s at the air temperature of 50 °C and the slice thickness of 3 mm. The increase in D_eff at higher temperature could be a result of destruction of the cell wall and a reduction in the moisture resistance ability of the yam slice. At the lower slice thickness, moisture diffusion is easier but augments with increase in thickness of the slices [8]. The D_eff range of most food products was between 10⁻¹² and 10⁻⁸ m²/s [55]. Similar D_eff range has been reported by many researchers such as in the researches of Harish et al., [54] for elephant foot yam (10⁻⁹ to 10⁻⁸ m²/s), Fang et al. [33] for Chinese yam (10⁻⁹ m²/s)and Geng et al., [56] for carrot(10⁻¹⁰ to 10⁻⁹ m²/s).

3.4. Activation Energy

Figure 5 shows the variation inactivation energy (E_a) with slice thickness. Activation energy ranged from 32 to 53 kJ/mol. The E_a increased with slice thickness. This signifies that more energy is required for moisture diffusion at higher slice thickness. A similar finding was reported by Ojediran et al., [8] for Dioscorea rotundata slices in a hot air dryer. Fang et al. [33] reported E_a for raw Chinese yam as 41.149 kJ/mol.

3.5. Mathematical Modelling of Drying Kinetic

The results of kinetic modelling using ten thin layer drying models are presented in

Table 2. Results of statistical analysis on the modelling of moisture ratio and drying time of water yam.

Drying Conditions	Model
		1	2	3	4	5	6	7	8	9	10
50 °C + 3 mm	SSE	0.0122	0.0123	0.0123	0.0103	0.0074	0.0123	0.0122	0.7625	0.4036	0.0089
	R2	0.9964	0.9964	0.9964	0.997	0.9978	0.9964	0.9964	0.7775	0.8822	0.9974
	RMSE	0.0217	0.0217	0.0213	0.0199	0.0172	0.0221	0.0226	0.1713	0.1271	0.0189
50 °C + 6 mm	SSE	0.0070	0.0073	0.0073	0.0059	0.0058	0.0056	0.0051	0.1945	0.1255	0.0064
	R2	0.998	0.9979	0.9979	0.9983	0.9983	0.9984	0.9985	0.9436	0.9636	0.9981
	RMSE	0.0167	0.0171	0.0168	0.0153	0.0156	0.0153	0.0150	0.0882	0.0723	0.0163
50 °C + 9 mm	SSE	0.0032	0.0032	0.0032	0.0032	0.0030	0.0021	0.0032	0.0868	0.0561	0.0028
	R2	0.9991	0.9991	0.9991	0.9991	0.9992	0.9994	0.9991	0.9757	0.9843	0.9992
	RMSE	0.0110	0.0110	0.0108	0.0110	0.0110	0.0093	0.0115	0.0578	0.0474	0.0107
60 °C + 3 mm	SSE	0.0038	0.0068	0.0084	0.0037	0.0068	0.0065	0.0068	0.6086	0.3402	0.0035
	R2	0.9987	0.9976	0.9971	0.9987	0.9976	0.9977	0.9976	0.7878	0.8814	0.9988
	RMSE	0.0135	0.0180	0.0196	0.0133	0.0184	0.018	0.0189	0.1702	0.1304	0.0132
60 °C + 6 mm	SSE	0.0063	0.0062	0.0076	0.0075	0.0059	0.0050	0.0062	0.516	0.2368	0.0060
	R2	0.9978	0.9979	0.9974	0.9974	0.998	0.9983	0.9979	0.8207	0.9177	0.9979
	RMSE	0.0170	0.0168	0.0181	0.0184	0.0168	0.0155	0.0176	0.1531	0.1062	0.0169
60°C + 9 mm	SSE	0.0018	0.0018	0.0019	0.0019	0.0018	0.0019	0.0018	0.1275	0.0785	0.0018
	R2	0.9994	0.9994	0.9994	0.9994	0.9994	0.9994	0.9994	0.9594	0.975	0.9994
	RMSE	0.0090	0.0090	0.0088	0.0090	0.0091	0.0092	0.0093	0.0745	0.0597	0.0091
70 °C + 3 mm	SSE	0.0041	0.0071	0.0099	0.0059	0.0066	0.0088	0.0037	0.5434	0.3082	0.0023
	R2	0.9983	0.997	0.9958	0.9975	0.9972	0.9963	0.9984	0.7717	0.8706	0.999
	RMSE	0.0150	0.0198	0.0228	0.0181	0.0197	0.0227	0.0153	0.1738	0.1346	0.0115
70 °C + 6 mm	SSE	0.0013	0.0043	0.0064	0.0008	0.0034	0.0009	0.0010	0.1725	0.1108	0.0013
	R2	0.9995	0.9984	0.9976	0.9997	0.9987	0.9996	0.9996	0.9355	0.9586	0.9995
	RMSE	0.0082	0.0150	0.0179	0.0066	0.0137	0.0072	0.0075	0.0953	0.0785	0.0084
70 °C + 9 mm	SSE	0.0010	0.0012	0.0012	0.0007	0.0005	0.0012	0.0012	0.0898	0.0533	0.0005
	R2	0.9996	0.9996	0.9995	0.9997	0.9998	0.9995	0.9996	0.9662	0.98	0.9998
	RMSE	0.0070	0.0077	0.0076	0.0059	0.0049	0.0080	0.0080	0.067	0.0529	0.0049

and Figure 6a–c. The most performed model was based on the R², RMSE, and SSE values. Several models, e.g., Midilli et al., logarithmic, approximation of diffusion, two-term, Page, Henderson and Pabis all performed well, but Midilli et al. was selected as the best model since it out-performed the other models used more frequently. The most correlation values were maximum coefficient of determination (R² = 0.9998), minimum root mean square error (RMSE = 0.0049), and minimum sum of square errors (SSE = 0.0023) for drying water yam slices in a convective hot air dryer. Moreover, Figure 5a–c further depicts the performance of Midilli et al. in predicting the drying behaviour of the yam slices in the hot air dryer. Midilli et al. has been selected by other authors for its high prediction ability; Chikpah et al., [57] for pumpkin drying in a convective dryer with different slice thicknesses, Hadjout-Krimat et al., [58] for pea pod drying in a microwave and convective dryer and Çetin [59] for orange slice drying in a convective dryer.

3.6. Uncertainty Analyses

The results of the uncertainties are as shown in

Table 3. Uncertainties of the experimental measurements and overall uncertainties for predicted energetic and exergetic responses.

Parameters	Unit	Uncertainty (%)
Experimental measurements
Drying air temperature	°C	±0.5
Drying air relative humidity	%	±1.0
Product weight loss	g	±0.0001
Process time	s	±3.0
Drying air velocity	m/s	±0.52
Predicted drying kinetic responses
Moisture ratio	Dimensionless	±1.46
Effective diffusivity	m2/s	±2.66
Activation energy	kJ/mol	±2.89
Predicted energetic responses
Mass flow rate	kg/s	±0.63
Energy utilization	J/s	±1.43
Energy utilization ratio	Dimensionless	±3.84
Energy efficiency	%	±2.21
Predicted exergetic responses
Exergy inflow	J/s	±1.35
Exergy outflow	J/s	±1.68
Exergy loss	J/s	±2.65
Exergy efficiency	%	±2.33
Improvement potential	J/s	±2.77
Exergetic sustainability index	Dimensionless	±2.98

. It was observed that the uncertainty percentage for both the experiment measurements and the calculated or predicted values were all lower than 5%, which was within the acceptable range. These results agree with the findings observed by other researchers such as Akpinar et al. [16], Beigi et al. [17], Liu et al. [22] and Zohrabi et al. [51].

3.7. Energy Evaluation

3.7.1. Energy Utilization

The result of the energy utilization (EU) as a function of air temperature and slice thickness of the water yam is represented in Figure 7. EU varied from 10 to 150 J/s for all parameters considered. EU increased during the drying process by an increase in temperature (50 to 70 °C). This was due to high input enthalpy and fast heat and mass transfer rate [60]. This result is compatible with the results observed by Aviara et al., [15] for hot air drying of cassava starch, Beigi et al. [17] for deep bed convective drying of rough rice, Okunola et al. [61] for forced convection cabinet drying of okra, and Liu et al. [22] for hot air impingement drying of mushroom slice. Additionally, EU increased by an increase in the slice thickness (3 to 9 mm) (Figure 7). This is due to the increase in volume of the slice requiring more energy consumption for moisture transport through pores of the product [62]. A similar result was reported by Liu et al. [22] for hot air impingement drying of mushroom slices.

3.7.2. Energy Utilization Ratio

The relationships between energy utilization ratio (EUR), air temperature, and slice thickness are shown in Figure 8. EUR varied from 0.39 to 0.79 for all the temperature and slice thickness levels considered. In addition, EUR increased by an increase in the temperature levels (50 to 70 °C). This is because at high temperatures there is more transfer of heat between the walls of the dryer, thereby increasing moisture evaporation rate from the product [22]. This observation was in agreement with previous work by Aghbashlo et al. [19] for thin layer drying of potato in a continuous band dryer and Liu et al. [22] for hot air impingement drying of mushroom slice. Moreover, EUR increased by an increase in slice thickness (3 to 6 mm), but from slice thickness of 6 to 9 mm EUR decreased at 50 and 60 °C and a slightly increased at 70 °C (Figure 8). This observation was similar with the findings in the study of Liu et al. [22] for hot air impingement for drying of mushroom slices.

3.8. Energy Evaluation

3.8.1. Exergy Inflow, Exergy Outflow and Exergy Loss

The variations in exergy inflow (EX₁), exergy outflow (EX₂), and exergy loss (EX_L) with temperature and slice thickness levels of the yam slices in a convective hot air dryer are presented in Figure 9. The highest EX₁, EX₂, and EX_L were 30, 17.5, and 12.5 J/s, respectively which were recorded at 70 °C and slice thickness of 9 mm, and the lowest values were 8, 6 and 2 J/s, respectively which were achieved at 50 °C and slice thickness of 9 mm. The findings showed that EX₁, EX₂, and EX_L increased by an increase in temperature from 50 to 70 °C. This signifies that the more energy supplied by the dryer at high temperature is not fully utilized by the product during drying experiment [22]. This finding was consistent with several studies, such as the results of Akpinar et al. [16] for convective hot air drying of red pepper, Corzo et al. [23] for thin layer drying of coroba slice, Beigi et al. [17] for deep bed convective drying of rough rice, Castro et al. [28] for convective drying of onion slice, and Liu et al. [22] for hot air impingement drying of mushroom slice. In addition, EX₁, EX₂, and EX_L slightly increased for bigger slice thickness, although at 50 °C, EX₁, EX₂, and EX_L decreased slightly with sample thickness. The increase in EX_L was due to more moisture evaporation, which caused a reduction in exergy at the outlet airflow. A similar finding was reported by Liu et al. [22] for hot air impingement drying of mushroom slice.

3.8.2. Exergy Efficiency

The result of the exergy efficiency (EX_eff) is shown in Figure 10. EX_eff ranged between 58 and 75% for all drying parameters. The highest EX_eff was at 70 °C and slice thickness of 9 mm, while the lowest EX_eff was at 50 °C and same thickness. The EX_eff of the sample increased by an increase in temperature (50 to 70 °C). EX_eff in a thermodynamic system is evaluated by the exergy of the air at the outlet of the drying system. The outlet exergy either increases or reduces the EX_eff. An increase in exergy efficiency was expected due to the fact of higher exergy loss at higher temperature [23]. This finding was in agreement with ones Colak and Hepbasli [63] reported for tray drying of green olive, Aviara et al. [15] for tray drying of cassava starch, and Okunola et al. [61] for forced convection cabinet drying of okra. Additionally, EX_eff was slightly decreased by an increase in slice thickness for 50 and 60 °C temperature, whereas for 70 °C, EX_eff increased with sample thickness. The decrease in EX_eff is as a result of higher exergy loss experienced on larger sample thickness. Similar decrease in EX_eff as a function of sample thickness was reported by Liu et al. [22] for hot air impingement drying of mushroom slice at a constant temperature of 65 °C and also the study conducted by Darvishi et al. [26] for microwave drying of kiwi slice.

3.8.3. Improvement Potential

Figure 11 shows the variation in improvement potential (IP) with drying air temperature and sample slice thickness. The IP ranged from 0.7 to 5.5 J/s. The highest IP was observed at slice thickness of 9 mm and air temperature of 70 °C, while the lowest IP was at slice thickness of 9 mm and air temperature of 50 °C. IP of the hot air dryer increased by an increase in drying air temperature (50 to 70 °C). A similar trend was reported by Icier et al. [24] for tray drying of broccoli florets, Aghbashlo et al. [20] for spray drying of fish oil microencapsulation, Aviara et al. [15] for tray drying of cassava starch, and Beigi et al. [17] for deep bed convective drying of rough rice. The IP of the dryer increased by an increase in sample thickness for temperature of 60 and 70 °C, but for 50 °C, IP decreased by an increase in sample thickness.

3.8.4. Exergetic Sustainability Index

The relationship between exergetic sustainability index (ESI), drying air temperature and slice thickness are presented in Figure 12. As shown, the highest ESI was found 5.3 at 70 °C and slice thickness of 9 mm, while the lowest ESI was 2.5 at 50 °C and slice thickness of 9 mm. An increase in drying air temperature increased the ESI. Therefore, it is advised to enhance the exergy efficiency of energy intensive process so as to reduce the environmental impact. Beigi et al. [17] reported that higher temperature increases the ESI of deep bed drying of rough rice in a convective dryer. ESI decreased by an increase in slice thickness for 50 and 60 °C, but for 70 °C ESI increased with slice thickness.

4. Conclusions

In this study, the effect of air temperature and slice thickness on drying characteristics, energy, and exergy parameters using a hot air dryer was investigated for water yam. The results revealed that Midilli amongst the several mathematical models used had the best prediction of the thin layer drying kinetics for water yam with R², RMSE, and SSE values of 0.9998, 0.0049, and 0.0023, respectively. D_eff increased with drying air temperature and slice thickness, while E_a increased with slice thickness. Increasing the air temperature and decreasing the slice thickness levels increased the drying rate and reduced the drying time. Increasing the temperature increased the EU, EUR, EX₁, EX₂, EX_L, EX_eff, IP, and ESI, while increasing the slice thickness showed a fluctuating effect on the energy and exergy parameters. EU, EUR, EX_L and EX_eff varied from 10 to 150 J/s, 0.39 to 0.79, 2 to 12.5 J/s and 58 to 75%, respectively. In addition, IP and ESI were in the range of 0.7 to 5.5 J/s and 2.5 to 5.3. Energy and exergy analyses is important for eliminating system losses during drying and in optimization of the performance regarding the drying process of water yam in a convective hot air dryer. Finally, to improve the thermodynamic performance and reduce the harmful environmental effects of the process, higher hot air temperatures and thinner samples should be used.