## . Modellization

The main purpose of the drying tests is to obtain a mathematical model that describes the performance of the dryer under any given condition. The drying curves can be modelled using theoretical or semi-theoretical equations [8]. The model expressions concern the simultaneous heat and mass transfer equations that describes the process. Moisture ratio equation is the common theoretical expression to model the drying process, described in Equation 1:

Where MC is the moisture content at any time, MC0 is the initial moisture content and MCeq is the equilibrium moisture content obtained as the asymptotic value of the weight of the sample when it remains constant [9].

Many researchers have described the solar drying process for common products like crops, fruit, leaves, etc. using different mathematical expression, all based on equation 1. The Page model equation, equation 2, resulted in a simple expression, similar to the theoretical expression that employs two constants: k and n, to describe with high degree of precision the woodchip drying performance [9]. Thus each drying test is described by two constants as it is shown in the table 2.

MR = exp(-ktn ) (2)

Table 2 shows the values of the constants k, n for 5 tests, described before in Table1, selected to build a global model that describes the drying process for woodchip. The statistical values, correlation coefficient, R, and mean square of deviations, X2, shows the good agreement between data and modelled values for the Page model.

Table 2: Constant values к and n for 5 selected tests.

 k(min ) n R2 X2 test1 0.068747 1.285319 0.999008 0.00008690 test2 0.176961 1.158643 0.995203 0.00036985 test3 0.123004 1.323546 0.99714 0.00024686 test4 0.516446 1.13697 0.995961 0.00021541 test5 0.572723 1.045855 0.998157 0.00008684

The effects of temperature and drying velocity on the moisture ratio were investigated using a multiple regression analysis to account for the drying variables on the Page model constants. The values of constants к and n were regressed against those of drying air temperature and air velocity using multiple regression analysis. All possible combinations of drying variables were included and tested in the regression analysis [10]. The multiple combinations of different parameters which gave the highest R[7] [8] were finally included in the model. The model equation was as follows:

MR = exp(-(0.1288 • V + 0.0008) • (-0.0009 • T[9] [10] [11] + 0.5559 • T + -2.0808) • t(-9-5259V+3-3147V+Ы768)) (3)

Validation of the Page model was confirmed by comparing the estimated or predicted moisture ratio at any other particular drying condition. The validation of the Page model at different air temperatures and air velocities is shown in Figure 3, where the experimental data of 4 tests is compared with the predicted values obtained from the model giving a good fitness.

Fig 3: Comparison of experimental and predicted MR for 4 new tests.

on the transpired plate type: the collector was a wooden box that comprised a perforated absorber plate made of 1.6 mm thick Aluminium. The area of the collector is 1.80 m2 has been drilled forming a distribution of 2 mm diameter holes spaced 20mm apart. The lower section of the collector frame had 35 holes of 20 mm diameter for air inflow. At the rear backing plate on the top, the fan has been mounted to deliver the air into a 150 mm flexible duct. The gap between the bottom of the collector and the absorber plate was 110 mm. In addition, considering the operating temperatures predicted at higher levels of irradiance, the channelled transparent polycarbonate cover is held 4 cm from the absorber plate to minimise convective heat loss. [5]