Wood fibers were obtained from Arian Sina factory. In order to investigate the drying rate of wood fibers above the FSP point, they were combined with water in equal weight ratios for 24 hours and then stored in a sealed polyethylene bag at 3 ° C to 5 ° C for seven days. The sample was mixed every day to ensure that the wood fibers had a consistent moisture level. Finally, wood fibers with a moisture content of 170% (based on dry weight) were subjected to the drying process.
Moisture Analyzer Halogen model MB45, manufactured by OHAUS, was used to dry wood fibers at three different temperatures: 105 ° C, 120 ° C, and 135 ° C. The MB45 has a sample capacity of 45g, with a readability of 0.001g and repeatability of 0.015% (using a 10g sample). The heater type of MB45 is a halogen lamp, and the operating temperature range is 50º C to 200º C in 1º C increments. The sample was heated in halogen hygrometers by absorbing the IR radiation produced by the halogen lamp. The weight difference before and after drying was used to determine the mass and moisture content of the sample continuously throughout the drying process. Halogen hygrometers work on the Loss on Drying (LOD) principle like oven dryers. However, there are various benefits such as quick drying time, ease of use, and direct measurement without computations compared to the oven dryer. To investigate the drying kinetics of wood fibers, 4 g of wet fibers were dispersed on a stainless steel tray placed on a precise and sensitive scale in the dryer compartment. The fiber was distributed on a tray carefully to prevent the fibers from accumulating at one point. After adjusting the temperature of the dryer chamber in the scope of this study, the weight loss values of the samples at a specified time interval, every 30 seconds, were presented and recorded online on the hygrometer display. The wood fibers continued to dry until the sample's moisture content was nearly zero. The tests were performed three times for each temperature, and the mean moisture content measurements were used to design and fit the drying curves for each temperature.
Drying kinetics of wood fibers
The moisture content of wood fibers was measured according to Equations 1 and 2.
Where MR is the moisture ratio (dimensionless), Mt is the moisture content at time t (kg of solids/kg of water), Me is the equilibrium moisture (kg of solids/kg of water), and M0 is the initial moisture content (kg of solids/kg of water).
It should be noted that due to the insignificant value of Me in comparison with Mt and M0, it can be saved. Therefore Eq. 1 can be simplified to Eq 2. (Ertekin and Firat 2017; Doymaz 2007a).
The drying rate of wood fibers was measured using Equation 3 (Ertekin and Firat 2017).
Where Mt and Mt+dt are the MC at t and MC at t+dt (kg moisture/kg dry matter), respectively, t is drying time (s). Equation 2 was used to obtain the moisture ratio of wood fibers at each temperature. Then, the experimental drying data of moisture ratio versus time was fitted to thin drying layer models using MATLAB 2016 software (Table 2). The models listed in Table 2 have already been widely used to investigate the drying kinetics of food, agricultural products, and municipal waste. The performance of these models was examined through comparing the coefficient of determination (R²), sum squares of error (SSE), and root mean squared error (RMSE) which were calculated in relation to 4 to 6, respectively. The best thin drying layer model is the one with the smallest error value and the greatest coefficient of determination.
Where MRprei and MRexpi are the predicted and experimental moisture ratios (MR) at ith observation, respectively. MRexp is the mean value of the explanatory variable, N is the number of observations, and n is the number of model parameters
Artificial Neural network model
Artificial neural network (ANN), as a nonlinear modeling method, is generally used to model complex physical phenomena such as the drying process of wood and lignocellulosic materials. The ANN configuration used in this study was a Multi-layer perceptron (MLP) consisting of one input layer, one or two hidden layers, and one output layer, as shown in Fig.1. The general form of the MLP output can be expressed mathematically in equation 7.
Where Y is the prediction value of the dependent variable; Xi is the input value of ith independent variable; Wij is the weight of the relationship between the ith input neuron and jth hidden neuron; βj is the bias value of the jth hidden neuron; vj is the weight of the relationship between the jth hidden neuron and output neuron; θ is the bias value of output neuron; g (.) and f (.) are the activation functions of output and hidden neurons, respectively (Saxena et al. 2022). The input variables in the input layer were temperature, and drying time and the output variables in the output layer were moisture ratio. For ANN model building, the input data is split into 3 sets: training (70 %), testing (15 %), and validation (15 %). The number of the hidden layer and the number of neurons in these layers were determined by trial and error. The neural network was trained using the Levenberg-Marquardt (LM) learning algorithm. The transfer function of the hidden layer and output layer were hyperbolic tangent sigmoid and linear, respectively. The hyperbolic tangent sigmoid transfer function was as follows:
Where f (x) and x are the output and input values of neurons, respectively.
The coefficient of determination (R2), mean squared error (MSE), and mean absolute error (MAE) were used to predict the ANN performance. Equations 9 to 11 include the formulas for computing these statistical characteristics.
Where y exp is the actual data values, y pred is the predicted data values, is the average of the actual values, and n is the number of data.