Thin Layer Drying Modelling for Some Selected Nigerian Produce: A Review

Transcription

1 American Journal of Food Science and Nutrition Research 2016; 3(1): ISSN: X (Print); ISSN: (Online) Thin Layer Drying Modelling for Some Selected Nigerian Produce: A Review Chinweuba Dennis Chukwunonye 1, *, Nwakuba Reginald Nnaemeka 2, Okafor Victor Chijioke 1, Nwajinka Charles Obiora 3 1 Department of Agricultural and Bioresource Engineering, School of Engineering and Engineering Technology, Federal University of Technology, Owerri Imo State, Nigeria 2 Department of Agricultural and Bioresource Engineering, College of Engineering and Engineering Technology, Michael Okpara University of Agriculture, Umudike Abia State, Nigeria 3 Department of Agricultural and Bioresource Engineering, Faculty of Engineering and Engineering Technology, Nnamdi Azikiwe University Awka Anambra State, Nigeria address dennischukwunonye@gmail.com (C. D. Chinweuba) * Corresponding author To cite this article Chinweuba Dennis Chukwunonye, Nwakuba Reginald Nnaemeka, Okafor Victor Chijioke, Nwajinka Charles Obiora. Thin Layer Drying Modelling for Some Selected Nigerian Produce: A Review. American Journal of Food Science and Nutrition Research. Vol. 3, No. 1, 2016, pp Received: March 11, 2016; Accepted: April 11, 2016; Published: June 2, 2016 Abstract Drying is an important technique used to remove moisture from a product. Various drying techniques apply to different agricultural products. Each technique has its own limitation. Therefore, choosing the right drying techniques is a very important first step in the process of drying. The raw agricultural products with 80-90% moisture content are brought down to equilibrium moisture content and improving its shelf life. Present work reviewed the research works done on thin layer drying characteristics of different agricultural products grown in Nigeria under different drying process. The drying data fitted into different thin layer drying models. The performance of these models was investigated by comparing the coefficient of determination (R 2 ), sum of square errors (SSE) and root mean square error (RMSE) between the observed and predicted moisture ratio. On the basis of highest value of R2 and lowest value of sum square errors (SSE) and root mean square error (RMSE) appropriate model will be selected. The Page and Midilli et al models dominates in describing the drying behaviour of most Nigeria crops. Keywords Review, Modelling, Thin-Layer, Drying 1. Introduction Fruits and vegetables are perishable in nature and get spoiled due to improper handling, growth of spoilage microorganisms, action of naturally occurring enzymes, chemical reactions and structural changes during storage. For the prevention of crop from deterioration and for increasing its shelf life, various preservation methods are employed. A major goal of food processing is to convert perishable commodities into stable products that can be stored for extended periods thereby reducing losses and making them available at the time of scarcity and off-season use and for places which are far away from production site. Processing can change foods into new or more usable forms and make them more convenient to prepare. Several processing technologies have been employed on industrial scale to preserve food products. These include canning, refrigeration, controlled atmosphere storage, dehydration, chemical treatment and use of subatomic particles [1]. Drying is the most common way to preserve agricultural produce especially the surplus ones. It is well known that the

2 2 Chinweuba Dennis Chukwunonye et al.: Thin Layer Drying Modelling for Some Selected Nigerian Produce: A Review product quality is greatly affected by drying methods and drying process. Dried foods can be stored for long periods without deterioration. The principle reasons for this are that the micro-organisms which cause food spoilage and decay are unable to grow and multiply in the absence of sufficient water and many enzymes which promote undesired changes in the chemical composition of the food cannot function without water [1]. Drying involves simultaneous heat and mass transfer. The main objective of drying is to reduce the moisture content and to increase the shelf life [2]. Simulation modelling is the process of creating and analysing a digital prototype of a physical model to predict its performance in the real world. It helps the designers and engineers to understand whether, under whatever conditions, and in which ways a part could fail and what loads it can withstand for instance. It can also help predict fluid flow and heat transfer patterns [3]. Cutting edge technology in agriculture has brought about the handling and processing of plant and animal materials by various approaches ranging from mechanical, thermal, electrical, optical, to even sonic techniques. The ever increasing importance of agricultural products together with the complexity of modern technology for their production, processing and storage need more in depth knowledge of their engineering properties so that machines, processes and handling operations can be designed for efficiency and the optimal quality of the final end products [4]. The objective of this research work is to review some of the work done on thin layer drying modelling of some crops grown in Nigeria. Thus, the definition of accurate mathematical models is necessary to simulate the drying kinetics of biological materials. Simulation models of the drying process are used for designing new drying systems, improving the existing systems, predicting the air flow over the product, and even for controlling the process [5]. Mathematical modelling of thin layer drying is important for performance improvements of drying systems [6]. As part of a larger program of food processing directed toward village level entrepreneurs, drying breadfruit can increase food supply, improve seasonal food choice, possibly generate income, and decrease excessive dependence on imported processed foods [7]. Drying of many fruits and other agricultural products has been successfully predicted [8]. Drying influence physicochemical and quality characteristic of products, thus, modelling of drying kinetic is one tool for process control [9]. 2. Basic Principles in Drying Drying is one of the oldest methods of food preservation. It is probably the main and most expensive step in postharvest operations [10]. It is the process of removing moisture in a product up to certain threshold value by evaporation. In this way, there is decrease in the water activity of the product, reduced microbiological activity and minimizes physical and chemical changes. [11, 12]. Drying can be explained on a microscopic level as having four different processes happening simultaneously. Typically one procedure will limit the whole process although this may change during the drying process. For the simple example of hot, dry air blowing over a wet food the four processes are: a. the heat transfer from the air to the surface of the product (convection) b. The mass transfer from the surface of the product to the immediate air c. The heat transfer from the surface of the product to the internals of the product (conduction) d. Mass transfer from the internals of the product to the surface Heat Transfer The heat from the air is transferred to the solid using convective means. The heat transfer is determined by material properties and the temperature gradient. The heat from the hotter air is transferred to the cooler product which is then used as latent heat to vapourize the moisture at the surface, essentially lowering the temperature of the exiting air. Due to the heating of the surface by air convection, a temperature gradient arises within the product. This causes heat to flow from the surface to the centre area and is controlled by the thermal resistance of the product to conductive heat transfer. This is dependent on the material properties [13] Mass Transfer The vapourised moisture is carried away by the air, increasing the humidity of the air and decreasing the moisture content of the product [13]. This is again controlled by convective means. All solids exert pressure on the internal moisture. This is dependent on ambient surroundings and material properties. With the surface evaporation, a concentration gradient occurs within the product increasing the vapour pressure within the product. The moisture transfer will continue until the vapour pressure within the product equates the partial pressure of the water in the air. This condition is known as equilibrium moisture content and is specific for the particular ambient conditions [13]. The vapour pressure is caused by the manner in which water is held by a product. This could be as a solution within the solid, held in capillaries, within the cellular structures or by chemical or physical forces. This has led to a definition of materials by the way they hold water as non-hygroscopic capillary-porous, hygroscopic-porous or colloidal media [13] Drying Psychometry Psychrometry is the study of moist air [14]. It is relevant to the drying or dehydration process as water is removed from the food product and carried away by the air. To induce this water transfer, a concentration gradient is needed and this is provided by hot dry air in the case of hot air convective drying.

3 American Journal of Food Science and Nutrition Research 2016; 3(1): Most dryers are of convective heated air type. In other words, hot air is used both to supply the heat for evaporation and to carry away the evaporated moisture from the product. Exceptions to this are freeze and vacuum dryers, which are used almost exclusively for drying heat-sensitive products though they tend to be significantly more expensive than dryers operated near to atmospheric pressure. Another exception is the emerging technology of superheated steam drying [15]. During the initial stage of drying the rate of moisture loss is considered as a function of three external parameters; namely, air-velocity, drying air temperature and relative humidity in the plenum chamber. The process of drying can, therefore, be examined on a standard ASHRAE Psychrometric Chart Number-1 for normal temperature range shown in figure 1 (16, 17) Law or Partial Pressures Law is commonly utilized. This law states that the total pressure of the mixture is the sum of the individual pressures, temperature and volume are considered to be the same (the total amount) for both the air and water [14]. Thus, for a humid air mixture at atmospheric pressure the air will have a specific pressure (air vapour pressure) and the water vapour will have a specific pressure which in summation will equal atmospheric pressure. This is expressed mathematically as: (1) Where is the total pressure. The vapour pressure ( ) and air pressure ( ) can be calculated from the ideal gas law: Where the gas constant and T is is the absolute temperature. (2) (3) Where is the gas constant for water vapour Both the temperature (T) and specific volume (V) used are the total temperature and total volume. Of consideration is the air to water ratio. By definition the humidity ratio or specific humidity is [14]; (4) Where is the mass of water vapour, is the mass of dry air, is the mole fraction for water vapour and X a is the mole fraction for the dry air defined by Gibbs-Dalton Law as [14]: (5) Figure 1. ASHRAE psychrometric chart [16]. The psychrometric chart is a graphical representation of the above properties (figure 1). It is usually defined for a specific pressure, the most common being kpa (sea level atmosphere). The y-axes display specific humidity and the x-axis the dry bulb temperature. Other curves and lines on the graph depict constant relative humidity, constant specific volume, constant enthalpy and constant wet bulb temperatures [14]. The lines of constant wet bulb temperature and enthalpy coincide whilst the dew point is indicated along the 100% relative humidity line. The psychrometric chart can be used for calculating processes as well which makes it a useful and quick reference point provided two or more parameters are known Psychrometric Properties and Definitions To determine the properties of moist air, the Gibbs-Dalton The number is the ratio of water to air molar masses and is a common number in psychrometric equations. Another method to determine the amount of moisture present in air is the relative humidity. This is the ratio between how much water is in the air to how much water that air could potentially carry (in other words before saturation occurs) [14]. This is a percentage that ranges from 0-100% in comparison with specific humidity which is a ratio that is often a number less than Relative humidity is defined in moles as in equation 6! " " # 100 # 100 (6) Relative humidity is dependent on temperature and must thus always be specified with a given temperature [14]. To determine the specific heat capacity of humid air (% &' ), equation 7 is used % &' % & % & (7) [13]. Where % & ()* % & are the mean heat capacities of

4 4 Chinweuba Dennis Chukwunonye et al.: Thin Layer Drying Modelling for Some Selected Nigerian Produce: A Review the dry gas and vapour, respectively and is the temperature in degree Celsius This leads to the definition of the enthalpy of humid air +, ' - in equation 8 as, ' % &' / 0 12 (8) Where 0 12 is the latent heat of vapourisation. Enthalpy is the energy associated with the pressure required to flow and is a combination of the internal energy (energy due to kinetic and potential energies of the elements) and this flow energy. Enthalpy is measured relative to a certain set zero point which is commonly defined as the fluid at triple point temperature of 0.01 C and its own vapour pressure of Pa [13]. To calculate enthalpy the temperature needs to be known. There are two types of temperature in Psychrometry dry bulb and wet bulb temperatures. The dry bulb temperature is defined as the temperature as indicated by a temperature sensor (such as a mercury thermometer) where the bulb is exposed to the fluid without interference. This is the standard form of measuring temperature and gives an indication of sensible heat [14]. Wet bulb temperature is defined as the temperature read when bulb of the thermometer is covered by a wet wick and exposed to flowing unsaturated air (normally achieved by swinging the thermometer around like a sling) [14]. This causes the moisture in the wet wick to evaporate. It requires latent heat of evaporation from the bulb causing a drop in temperature recorded by the thermometer. The wet-bulb temperature is thus an indication of the quantity of latent heat. Wet-bulb temperature is dependent on humidity (the wick will keep evaporating until it is at the same relative humidity as the air). Thus, the difference between the wet and dry bulb temperatures can be used to read relative humidity [14]. Dew point temperature is the point at which vapour will condense because it has reached saturation for its specific partial pressure [14] Drying Techniques Drying is a complex operation involving transfer of heat and mass along with several rate processes, such as physical or chemical transformations [18]. Figure 2. Different ways of sun drying [19]. Different methods of crop drying: (a).raised platform method, (b): Direct sun radiation, (c): Drying under shade (thatch). The most common method for drying produce is open air drying which can be done in direct sunlight or under shaded conditions. Sunlight heats food effectively driving out moisture but direct sunlight and heat can destroy fragile vitamins and can cause food to lose colour [7]. The selection of drying technique largely depends on the production scale and affordability in terms of cost [20]. Thin layer drying is a layer of material exposed fully to an airstream during drying; the depth (thickness) of the layer should be uniform and should not exceed three layers of particles [21]. Different drying methods are used in the drying of fruits and vegetables. Air drying is the most common method in the drying of foodstuffs. The major drawback of air-drying is the longer drying period, low drying rates in the falling rate period, worsening of the taste, colour and nutritional content of the product, higher drying temperature, low energy efficiency and high costs which is not a desirable situation for food industry [22]. Reference [20] conducted drying experiments using airventilated oven and sun dryer to simulate the artificial and natural drying processes of cocoa beans, Reference [12] developed a microwave dryer for the purpose of determining the drying behaviour of a shrimp, Reference [8] used cabinet

5 American Journal of Food Science and Nutrition Research 2016; 3(1): laboratory type dryer to estimate the thin-layer drying characteristics of kiwifruit, Reference [9] used a convective tray dryer (IIC, Model TD-12) to investigate the effect of temperature on hot-air drying kinetics of stone apple (Aegle marmelos correa), the drying characteristics of fresh tilapia fillets was thoroughly studied by Reference [23] in a heat pump dryer which satisfied the need of large-scale fish drying in the food processing industry, The drying kinetics of garlic pre-treated by immersion in 0.5% metabisulfite solution at the drying air temperatures 55 to 85 C was determined [24]. They found that this treatment considerably improved the quality of the dried product by preventing the browning reactions. Reference [25] reported that the drying air temperature and the slice thickness were significant factors that affected the drying rates of thin garlic slices, while reference [26] determined the drying kinetics of garlic slices at various slice thicknesses ( mm), the drying air temperatures (40 to 60 C) and a constant drying air flow rate of 2.5 ms Heated Air Dryers Traditionally, a dryer is made up of five basic components: the air heater, the air mover, the air duct system, the chimney and the cabinet to hold the product. The drying chamber of a drier usually contains mesh trays on which the product is spread and is usually made of metal or sometimes wood. Hence, the heat loss to the side walls of the drying chamber causes loss of efficiency. As the hot air passes through the mesh drying takes place, and the air passes out of the dryer through the chimney. It is somehow difficult to predict what is going on in the closed cabinet as the drying progresses. This is achievable through modelling and simulation of the drying process if the parameters of the system are known. Since emphasis is more on the product, the knowledge of the changing properties that characterize drying is very critical in the process. The parameters of air, which are affected by thermal radiation, such as, pressure, velocity, relative humidity and temperature difference affect the efficiency of driers also. They can be determined or calculated using basic knowledge of heat transfer, mass transfer and fluid mechanics with experimental back-up. In drying analysis, a bed of food grains is assumed to be composed of thin layers normal to the hot air flow direction. To analyse the drying process and dryers, empirical, theoretical and semi-theoretical models are usually selected to suit that particular condition and product. However, the conditions of the grain and air change with position and time during drying when bed of grains is deep. Logarithmic, exponential and diffusion models have been applied to both thin-layer and deep bed drying simulations with measurable success Microwave Dryers Microwave energy has been widely used either as pretreatment prior to other drying process to enhance mass transfer rate, which could be attributed to the cell damage during microwave exposure [27] or in combination with other drying process, as finishing drying method for osmotic dehydration, convective or vacuum drying [28]. Microwave drying, however, results in adverse and unacceptable overall quality of product if the process is not controlled properly [28]. Non-uniform temperature and moisture distribution are few major drawbacks in microwave drying as they lead to hot spot generation [29]. Furthermore, microwave heating results in surface moisture build-up due to enhanced (pressuredriven) flow of moisture to the surface and the cold ambient air's inability to remove moisture at a high rate, which ultimately lead to surface scorching [30]. 3. Moisture in Agricultural Products The moisture content of a wet solid in equilibrium with air of given humidity and temperature is termed the equilibrium moisture content (EMC) at that humidity and temperature. Equilibrium moisture content (EMC) point is the point when grain no longer losing or gaining water when contacting with drying air. The final moisture content of the grain is up to the amount of moisture in the drying air, which is the relative humidity. The low relative humidity means air is dry and it has a large potential of picking up water. The lower the relative humidity is, the drier the air is. In general, one-half reduce in relative humidity is caused by 20 degree increase in air temperature [31]. A plot of EMC at a given temperature versus the relative humidity is termed sorption isotherm. An isotherm obtained by exposing the solid to air of increasing humidity gives the adsorption isotherm, while that obtained by exposing the solid to air of decreasing humidity is known as the desorption isotherm. Clearly, the latter is of interest in drying as the moisture content of the solids progressively decreases. A phenomenon known as hysteresis, occurs when the path describing the two isotherms are not identical. Figure 3. Comparing two EMC models using desorption data of corn Source: [32]. According to reference [33], the temperature dependence of the equilibrium moisture content can be correlated by: :;<=>;= =?@ (9) where M* is the dry-basis equilibrium moisture content, T is the temperature and Ψ is the relative humidity of air. The ranges from to 0.01 K -1 [33]. This correlation may be used to estimate the temperature dependence of M* if no data are available.

6 6 Chinweuba Dennis Chukwunonye et al.: Thin Layer Drying Modelling for Some Selected Nigerian Produce: A Review 3.1. Drying Curves of Agricultural Products Drying behavior of solids can be described by measuring the function of moisture content loss versus time. Continuous weighing, humidity difference and intermittent weighing are the often used methods [15]. When drying crops using heated air, two drying periods generally occur viz: constant-rate period and falling rate period. Constant rate drying occurs with evaporation of surface water, while in falling rate period moisture movement is controlled by internal resistances. Moisture content as a function of drying time is plotted in figure 4 while an example of drying rate as a function of moisture content is shown in figure 5 for most agricultural materials. Figure 4. Drying Curve, Showing Moisture Content as a Function of Time of a crop (Source: [34, 35]). A. Segment AB represents the initial unsteady-state, warming-up period. This initial unsteady-state period is usually quite short and it is often ignored in the analysis of times of drying [34]. BC is the constant rate period. The same points are marked in Figure 5, where the drying rate is plotted against the moisture contents [35]. During the constant rate period, the surface of the solid is initially very wet and a continuous film of water exists on the drying surface. This water is entirely unbound water and the water acts as if the solid were not present. The rate of evaporation under the given air conditions is independent of the solid and essentially the same as the rate from a free liquid surface [34]. The transition moisture content at which the departure from constant rate drying is first noticed is termed the critical moisture content, indicated by point C. At this point there is insufficient water on the surface to maintain a continuous film of water. In food systems, where liquid movement is likely to be controlled by capillary and gravity forces, a measurable constant rate period is found to exist. With some foods (structured), liquid movement is by diffusion, and therefore the water that is evaporated from the surface is not immediately replenished by movement of liquid from the interior of the food. Such foods are likely to dry without exhibiting any constant rate period. Hot air drying of apples, tapioca, sugar beet root and avocado are given as such foods without exhibiting any constant rate period [35, 36]. Between point C and D is termed the first falling rate period. During this period the rate of liquid movement to the surface is less than the rate of evaporation from the surface, and the surface becomes continually depleted in liquid water. The entire surface is no longer wetted, and the wetted area continually decrease in the first falling rate period until the surface is completely dry at point D. Beyond point D, the path for transport of both the heat and mass becomes longer and more tortuous as the moisture content continues to decrease. This period is called the second falling rate period. Finally, the vapor pressure of the solid becomes equal to the partial vapor pressure of the drying air and no longer further drying takes place. The limiting moisture content at this stage to which a material can be dried under a given drying condition is referred to as the equilibrium moisture content (M e ) [35] Drying Rate Periods Drying curves characteristically display four defined regions or periods. Not every product will display all four, sometimes only one will appear and although the definition of each period is clear it may be difficult to ascertain in practice. Many agricultural products do not display typical drying curves, notably a lack of constant drying time [37]. Figure 5. Drying Rate as a Function of Moisture Content (Source: [34, 35]). At zero time the initial moisture content is shown at point A. In the beginning, the solid is usually at a colder temperature than its ultimate temperature. Alternatively, if the solid is quite hot to start with, the rate may start at point Initial Drying Period There is often an initial drying rate where the drying rate increases as the surface of the product is heated to the temperature of the immediate ambient air. A sufficient temperature gradient is required between the air and the product s initial temperature to vapourise the moisture [14].

7 American Journal of Food Science and Nutrition Research 2016; 3(1): Constant Rate Period After the initial period, curves display a constant drying rate through a limited time. During this time the surface of the product still contains free moisture, which is vapourised, diffused into the air and taken away by the air [14]. The rate is controlled by the diffusion process for water removed from the surface and into the air [13]. Critical moisture content (MC cr ) is defined as the moisture content at the end in the very last instant of the constant rate period [13] First Falling Drying Rate Period Although a general falling rate period is normally described, it is due to two different phenomena, which sometimes can be seen clearly by a change in the rate of change of the drying rate. These are called the first and second falling rates. Some products only display one or the other. The falling rate as a whole is described as the time from the critical moisture content until the equilibrium moisture content [38]. Equilibrium moisture content is the point at which the moisture vapour pressure in the solid is equal to the partial pressure of the vapour in the air [13]. During the first falling rate period moisture must be transferred from within the solid to the surface (modelled as capillary flow) [13]. This is caused by the gradient between the air vapourisation pressure and the vapour vapourisation pressure at the surface [14]. This continues until the surface film of liquid is entirely evaporated [13] Second Falling Drying Rate Period The second falling rate commences when the drying process is controlled by the rate at which moisture can move through the solid. The two possibilities that could be the limiter are the material heat conduction rate and the material mass diffusion rate. Several other factors come into play in this period shrinkage may cause internal pressures or case hardening can occur, both of which hinder the drying process. This continues until the product reaches the equilibrium moisture content for the prevailing conditions [13]. Although there are mathematical descriptions available to attempt to describe this period, they often are simplified and dependent on geometry (for which only highly simple cases are solved). Reference [38] describes the time for the falling rate for an infinite plate, sphere and cylinder if the diffusion of the moisture is modelled with Crank s basic solution of diffusion, although each situation requires a unique solution based on geometry. But even this contains errors which are presumed to be due to the isothermal assumption Drying Rate Constants Fick s diffusion equations are commonly used to determine the drying constant and effective moisture diffusivity during food and crop drying [39]. Hence the following Fick s second law of diffusion is applied to in conjunction with the experimental data, as given by equation (2.10). A A B D D (10) Where, M = moisture content (dry basis) t = time (s) D e = effective diffusion coefficient (m 2 /s), which describes how fast an object diffuses. B = Mass transfer gradient. It is noticed that the drying curves took a linear form when the ln [MR] is plotted against time [40]. The slope of the straight line obtained when logarithm of moisture ratio (ln MR) is plotted against time (t) represents the drying rate constant (k) Thin Layer Drying Kinetics In 1960, Hukill in a study of the drying rate of fully exposed grain kernels, observed that the drying process was divided into an initial warming up period, constant rate and falling rate periods [41]. These rate periods are illustrated in figure 6. Figure 6. Constant and falling rate periods in thin-layer drying of high moisture grain [42]. Experimental evidence shows that a single drying constant almost invariably over-estimates the drying rate in the final stages of drying. During the convective drying, heat-transfer between the sample and the surroundings is controlled by the humidity-ratio of the air at the surface, the temperature of the plenum and temperature of the sample surface [43]. Heatedair drying refers to the removal of free and bound moisture from a sample, by using heat energy in a specially designed dryer. During drying, there is simultaneous transfer of heat, to evaporate and transfer moisture to the surface and as vapor from the surface into the hot air stream, within an optimal period of time. Movement of moisture through the sample is in the form of water-vapor within the cell-cavities and bound water. Bound water is hydrogen-bonded to the hydroxyl groups of the polysaccharides. Therefore, the driving force responsible for moisture-transport is a combination of

8 8 Chinweuba Dennis Chukwunonye et al.: Thin Layer Drying Modelling for Some Selected Nigerian Produce: A Review diffusion along the moisture concentration-gradient and difference of vapor-pressure due to temperature gradient. The transfer of liquid within a drying sample may occur by the following mechanisms: a. Diffusion in the continuous homogeneous solids, b. Capillary flow in the granular and porous solids, c. Flow caused by shrinkage and pressure gradients, and d. Flow caused by sequence of vaporization and condensation. The attainment of critical moisture-content depends on the drying conditions (humidity and temperature) and the characteristics of the samples (shape, size, density, area and specific heat-capacity). Moisture in excess of free moisturecontent, in equilibrium with the air, can only be removed upon prolonged contact of the sample with hot drying air. The general theory of drying is based on the consideration of inert solid wetted with moisture and exposed to heated current of air. The air supplies the sensible heat, heat of vaporization and also acts as a carrier of the evaporated moisture. Thus drying is a process of simultaneous heat and mass transfer. For the purpose of analysis, drying is usually subdivided into two categories, namely; i. Single kernel or thin layer drying: this is considered as the drying process involving material depth of not more than ten particles (depth<10 F(GHIJKLM) diameter. ii. Deep bed drying: this consists of agglomeration of particles above ten particle diameter ( *LFHh > 10 F(GHIJKL *I(OLHLG). Since warming up period is often short and represents only 0.25% of the total drying period/time, it is often neglected in drying analysis. At constant rate period, the rate of mass transfer balances the rate of heat transfer and so the temperature of the drying surface remains constant at the wet bulb temperature of the drying air. The driving force causing vapor movement through the stagnant air film is the vapor pressure gradient between the drying surface and the main air stream. The rate of mass transfer can be put mathematically as: PQ P 6 R2S. = T U V+F S F ) (11) WhLGL, PQ 6 =*GYI)Z G(HL P R2S. T U =O(MM HG()M[LG J\L[[IJIL)H,TZ/O A=surface area of drying material, m 2 P s =water vapor pressure at material surface P a = partial pressure of water vapor in air The rate of heat transfer to the drying surface is: P^ P 6 R2S. =h R V+/ / S ) (12) h c = convective heat transfer coefficient, J/hm 2 C T a =dry bulb temperature of air T s = temperature of the drying surface, C Since a state of equilibrium exists the following equation can be written; PQ 6._=P^ 6 P R2S. P R2S. Where, L = heat of vaporization of moisture at T s, J/Kg Combining equations 13 and 14, PQ P 6 R2S. (13) = '`.ab c.p.d e +/ / S ) (14) Where, f g8ghij PkSlm 2n 'k Qkoli. Rearranging and integrating equation (14), Q` p *O= Q q '`.ab 8` +/ c.p.d / S )p *H e 8 (15) O O R = '`a+ # ) c.p.d e.h R (16) In this equation, O O R,J() be defined as the amount of moisture removed during constant rate period. m o and m c are initial and critical moisture content respectively. The rate of drying during the constant rate period is a function of three external parameters namely, air velocity, air temperature, and air humidity. From equation (16), time for attaining critical moisture content (m c ), which terminates the constant rate period can be predicted as follows; H R = c.p.d e 3 Q qrq` 5 (17) '` # Where, H R =*sg(hi\) \[ HhL J\)MH()H G(HL FLGI\*. and d = depth of grain bed To predict the drying rate, it is not only the extent of macroscopic convective heat-and-mass-transfer, associated with the sample and the surroundings in the drying chamber that have to be considered, but also the mechanisms of microscopic heat and mass diffusion within the sample must be included in the analysis. The rate of heat or mass-transfer is determined by multiplying the respective transfer-coefficient and the driving force. The drying bed is modeled by considering a thin layer of a slab-shaped crop bed of thickness dz and then combining many of such thin layers to form the deep bed of thickness z o. By consecutively calculating the air and moisture changes that occur during short intervals of time as the drying air passes from one layer to the next, the continuous drying process was simulated. The procedure adapted assumes that each layer is dried for a short time interval, dt, using air leaving the preceding layer. The process is repeated with consecutive short increments of time until the desired final moisture content of the crop bed is achieved. Relevant independent partial differential equations are normally needed to predict the changes in the crop temperature, moisture content, air temperature and relative humidity. Changes in the gas phase concentration are assumed negligible compared with that of the solid phase changes [44]. These equations are: the drying rate equation, the mass balance equation on the drying air, the heat balance equation on the drying air and the heat balance equation on the crop [45] Thin Layer Drying Models Development Thin layer drying models (moisture ratio equations) that describe the drying phenomenon of agricultural materials

9 American Journal of Food Science and Nutrition Research 2016; 3(1): mainly fall into three categories, namely theoretical, semitheoretical and empirical. The first takes into account only internal resistance to moisture transfer while the other two consider only external resistance to moisture transfer between product and air [46]. Similarly, reference [23] categorised thin-layer drying models as theoretical, semitheoretical and empirical models. The semi-theoretical model based on the theory and the drying kinetics experimental, is derived from the simplification of Fick s second law of diffusion or modification of the simplified model, which has been widely used to describe the drying characteristics. Semi-theoretical models offer a compromise between theory and ease of use; they require small time compared to theoretical thin layer models and do not need assumptions of geometry of a typical food, its mass diffusivity and conductivity [47]. Among semi-theoretical thin layer drying models, the Newton (Lewis) model, Page model, the modified Page model, the Henderson and Pabis model, the logarithmic model, the two-term model, the two-term exponential, the diffusion approach model, the modified Henderson and Pabis model, the Verma et al. model and the Midilli Kucuk model are used widely [46]. Empirical models derive a direct relationship between average moisture content and drying time. They neglect fundamentals of the drying process and their parameters have no physical meaning. Therefore they cannot give a clear accurate view of the important processes occurring during drying although they may describe the drying curve for the conditions of the experiment. Among them, the Thompson model and the Wang and Singh model have been found application in the literature. The Thompson model was used to describe shelled corn drying for temperatures between 60 C and 149 C and the Wang and Singh model was used to describe drying of rough rice [47]. Similarly, reference [48] reported that theoretical models could be used for different materials and conditions, but contain diffusion or heat and mass transfer equations, and thus, the usability of these models decreases; semi-theoretical models contain parameters directly related to material properties and the empirical equations give a satisfactory fit to all the experimental data and take less computing time in comparison to the theoretical equations. Several assumptions are made for thin-layer drying models [49]. These include: homogenous and isotropic particles material characteristics (including size) are constant pressure variations are negligible evaporation occurs only at the surface initial moisture content is independent of other parameters moisture equilibrium occurs at the surface temperature distribution within the product is uniform and equal to air temperature internal heat transfer is due to conduction exclusively external heat transfer is due to convection exclusively effective moisture diffusivity is constant Semi Theoritical Models - LEWIS MODEL Lewis in 1921 proposed that the change in moisture content in the falling rate period is proportional to the instantaneous difference between the moisture content and the expected moisture content when it comes into equilibrium with drying air [49]. This essentially assumed that the material is thin enough, the velocity high enough and the drying conditions constant enough that: P P?t +? k- (18) Where K is the drying constant for thin layer concepts this will encompass the moisture diffusivity, thermal conductivity, interface heat and mass coefficients. If K is independent of the moisture content then: u v u exp+?th- (19) Where K, can be obtained from experimental data. This is known as the Lewis (or Newton). - NEWTON MODEL Newton model describes that the moisture transfer from the foods and agricultural materials can be seen as analogous to the flow of heat from a body immersed in cool fluid [50]. This model assumes negligible internal resistance, which means no resistance to moisture movement from within the material to the surface of the material. By comparing this phenomenon with Newton s law of cooling, the drying rate is proportional to the difference in moisture content between the material being dried and equilibrium moisture content at the drying air condition as: LzF+?TH- (20) where, MR = moisture ratio, dimensionless k = drying rate constant, h -1 t = drying time, h This model was used primarily because it is simple. The only drawback, however, it underestimates the beginning of the drying curve and overestimates the later stages. - PAGE MODEL Page model suggests a two constant empirical modification of the Newton model to correct for its shortcomings. This model has produced good fits to describe drying of many foods and agricultural products [50]. This model is expressed as: exp+?th - (21) where, MR = moisture ratio, dimensionless k = drying rate constant, h -1 t = drying time, h n = constant The value of n varies for each material being considered. The Page model has produced good fits to describe drying of many agricultural products and is also convenient to use

10 10 Chinweuba Dennis Chukwunonye et al.: Thin Layer Drying Modelling for Some Selected Nigerian Produce: A Review compared to more rigorous theoretical diffusion moisture transfer equations, which take more computing time in fitting the data [51]. Reference [52] modified Page s model for their model of drying soybeans: exp+?th- (22) This is also known as the Modified Page-I Model. Reference [53] optimised the arrangement of the coefficients for drying of soybeans to produce what is known as the Modified Page-II Model: exp+?+th- - (23) Subsequently, reference [54] formulated the Modified Page-III Model which is slightly different from the original Page equation to describe the drying of sweet potatoes: exp{?t { i } } (24) - HENDERSON AND PABIS MODEL The Henderson and Pabis model is a single-term exponential model. Henderson and Pabis suggested that for sufficiently long drying times only the first term of the solution is needed. Provided the effective moisture diffusivity is constant this is expressed as: (LzF+?TH- (25) Where a is an indication of shape generally called a model constant that is normally obtained from experimental data. It was used successfully to describe drying of corn [48]. - LOGARITHMIC OR ASYMPTOTIC MODEL The Logarithmic or Asymptotic model is a modification of the Henderson and Page Model, developed by reference [55]: (LzF+?TH-J (26) Where c is an empirical dimensionless constant. Reference [56] successfully used it to describe the drying of laurel leaves. Reference [57] included a time dimension to the Henderson and Pabis Model, which they applied to the drying of pollen, mushrooms and pistachios in various drying methods. - MIDILLI et al. MODEL The Midilli et al. Model is expressed mathematically as: (LzF+?TH-~H (27) Where b is an empirical constant of units S -1. This model is also called the Midilli-Kucuk Model. Reference [58] proposed a Modified Midilli Model which excluded the shape model constant a,: LzF+?TH-~H (28) This was not applied to a food material but worked sufficiently well for flax fiber [58]. Another Modified Midilli Model was put forward for the drying of green table olives by including the Modified-I Page model [59]: (LzF+?TH- ~ (29) - HII et al. MODEL A new semi-theoretical model was put forward by Hii et al. (2009) for the air drying of cocoa beans that combined the Page and Two-Term models, called the Hii et al Model: ( LzF+?T H - J LzF+?ZH - (30) This was also used to describe the hot air drying of carrot pomace [60]. - TWO TERM MODEL A two-term solution similar to that, which uses the first two terms of a general series solution of Fick s second law of diffusion, this model is better since its take into consideration the different drying characteristics of the material components [51]; 2koQ (LzF+?T H- ~LzF+?T H- (31) -THREE TERM MODEL Where K 1 and K 2 are drying constants (min -1 ), a and b are empirical constants. Reference [61] continued to add a third term to the general solution of Fick s Second Law of Diffusion, in an attempt to further reduce errors, named the Three Term Model: 'okkkoq ( LzF+?T H- ~ LzF+?T H- J LzF+?T H- (32) Where a, b and c are geometric constants and the K s are drying constants all obtained from experimental data. Reference [61] explains that the third term describes the beginning part of a drying curve (whilst the first term explains last part and the second describes the middle part of the drying curve) Empirical Models Empirical models use experimental data and fit them to mathematical equations. They tend to have similar characteristics to semi-theoretical models and provide minimal explanations for particular drying behaviours [37]. The Thompson Model mathematically described as: H( ƒ) +-~ ƒ) +- (33) Was developed by reference [62] using data from the drying of shelled corns but was successfully used by reference [63] for the drying of sorghum. Similarly reference [64] created a model for the intermittent drying of rough rice: 1+~H+ (H (34) Where b has S -1 units and a has S -2 units both obtained from experimental data. This is referred to as the Quadratic or Wang and Singh model. Kaleemullah created a model called the Kaleemullah Model =LzF+ %)/+~H & (35) Where C is, 1/ Cs, b is 1/s and p is 1/ C and n is

11 American Journal of Food Science and Nutrition Research 2016; 3(1): dimensionless. This was applied to the drying of red chillies successfully by Kaleemullah and Kailappan [65]. A model, known as the Diamante et al Model that has the form: ƒ)+?ƒ)-(~ +ƒ) H-J +ƒ) H- (36) Was introduced by Reference [66] and applied successfully towards to drying of apricots and kiwi fruit. Corzo proposed the use of a statistical model for the description of drying and used the Weibull Distribution which had only been used for rehydration characteristics and osmotic dehydration [67]. The normalized Weibull distribution: exp?{ }g (37) Equation 37 was used to adequately describe the drying of coroba slices [67] Mathematical Modelling of Thin Layer Drying Processes The most relevant aspects of drying technology are the mathematical modelling of the process and the experimental setup. The modelling is basically based on the design of a set of equations to describe the system as accurately as possible [22]. Mathematical modelling serves to be a most effective way to know the depth of drying in post-harvest processing of agricultural materials. Numerous mathematical equations can be found in literatures that describe drying phenomena of agricultural products. Linear and nonlinear regression analyses are important tools to find the relationship between different variables, especially, for which no established empirical relationship exists. Thin layer drying equations require MR variation versus time t. Therefore, MR data plotted with time t and regression analysis is performed with the selected models to determine the constant values that supply the best appropriateness of models. The validation of models can be checked with different statistical methods [68]. The most widely used method in determining the goodness of fit of the selected drying model(s) to the experimental data is using three statistical parameters, namely; coefficient of determination (R 2 ), Sum of square errors (SSE) and root mean square error (RMSE). These parameters can be calculated by using the following equations: ˆ Š ˆ k"&,l? &okp,l l8 (38) ˆ Š Œˆ k"&,l? &okp,l l8 (39) Where: MR exp = Experimental moisture ratio MR pred = Predicted moisture ratio N = Number of observations n = Number of constants The higher R 2 values and the lower SSE and RMSE values are goodness of fit [69, 70]. Thin layer drying models has extensive application due to its simplicity of use [71]. Thin-layer drying models for describing the drying phenomenon of agricultural products are usually based on liquid diffusion theory, and the process can be explained by the Fick s second law [72]. Many mathematical models have been used to describe the drying process of agricultural products. A considerable amount of work has been done on thin layer drying of different agricultural products. Some of the thin layer models reported were for drying of olive fruit [73], date palm [22], cocoa [20], potato mash [1], litchi [74], sorghum [75, 76], hazelnuts [47] and finger millet [2]. 4. Thin Layer Drying Models of Some Farm Produce in Nigeria Major crops grown in Nigeria include cashew nuts, cassava, cocoa beans, groundnuts, maize (corn), melon, millet, cocoyam, plantains, scent leaves, sorghum, soybeans, yams etc [77]. Table 1 shows the suitable model for each crop. Several drying models are available in the literature for the description of thin layer drying kinetics of agricultural products out of which, models such as page and Midilli et al, dominates in the description of farm produce in Nigeria within the limits of twenty produce selected adequately Table 1. Findings of suitable thin layer drying models for some Nigerian farm produce. S/ CROPS/SEEDS/VEGETA SUITABLE N BLES MODEL REFERENCES 1 Bitter Kola Page [78] 2 Bitter Leaves Modified Page and Page [79] 3 Breadfruit Two-term [80] 4 Carrot Midilli et al [81] 5 Cashew kernels Page [82] 6 Cassava Exponential [83] 7 Cocoa Henderson and Pabis [84] 8 Cocoyam Logarithmic [85] 9 Corn Logarithmic [86] 10 Groundnut (Bambara) Two-term & Logarithmic [87] 11 Melon Midilli et al [88] 12 Millet Modified Page & Page [89] 13 Okra Logarithmic [90] 14 Scent Leaves Page [79] 15 Sorghum Page [75] 16 Soybeans Midilli et al [91] 17 Sugarcane Midilli et al [92] 18 Sweet Potato Page [93] 19 Tomatoes Logarithmic [94] 20 Yam Midilli et al and Verma et al [95] describe the drying kinetics of some banana varieties.