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Research material and selection of drying equipment.

Basic equipment and instrumentation. For this study, an experimental combined convective infrared drying unit model Asia, which is available in the TSTU laboratory, was used (Fig. 1). The diagram of the unit shows a 0.40 m × 0.65 m bearing plate with 3 infra-red emitters arranged in parallel and alternating with each other at different wavelengths. The tray is placed at distances of 10 and 12 and away from the infra-red emitters. In this experiment, the distance between the stationary material and the infra-red lamp is 12 cm.



Figure 1. Schematic diagram of an experimental combined convection-infrared drying equipment: 1 - fan; 2 - power control on/off; 3 - infra-red radiator on/off; 4 - wind speed button; 5 - infra-red radiators; 6 - tray.
Testing methodology. Fresh mulberries were placed in a single layer in a tray with fine wire mesh. Drying tests were carried out at different drying temperatures (65, 70 and 75 °C) with a wind speed of 0.2 m/s and an infrared radiation power of 260 W. The quality of the samples was measured at half-hour intervals until the weight of the samples no longer changed. Similarly, the drying tests were carried out at a wind speed of 0.2 m/s and a drying temperature of 70 °C at different infra-red radiation powers (230, 260 and 280 W).

3. Mathematical calculation of the drying curve and drying speed curve

Moisture ratio. The formula for calculating the moisture ratio ( ) is given in the equation
(1)
where is the initial moisture content of the dry mulberry base (g/g); is moisture content in the dry mulberry fruit base at drying equilibrium; is moisture content of the dry mulberry base at drying time t, respectively.

If is much less than , equation (1) can be simplified to equation (2).

(2)
Drying speed. The drying speed ( ) is used to denote the rate at which the material is dewatered. The formula is shown in equation (3).
(3)
where and are the moisture content of the dry mulberry base at during drying.


Effective moisture diffusion coefficient. The effective moisture diffusion coefficient is an important characteristic of the mass transfer of a material that indicates the capacity or diffusion rate of moisture during drying and is important for the calculation and modelling of the drying process. The drying characteristics of fruits and vegetables during the drying period with reduced speed can be described by the second Fick's diffusion equation. According to Fick's equation, the linear equation (4) for the time dependence can be used to describe the effective diffusion coefficient for moisture in the material as follows.
(4)
In this equation t is the drying time (s); L is the thickness of the material (m). The slope method is used to calculate the effective diffusion coefficient. From equation (4) it follows that is plotted as a straight line, and the slope of the line corresponds to equation (5).
(5)
Drying activation energy. Drying activation energy indicates the energy required to remove a unit mole of water during the drying process. Since the relationship between the effective moisture diffusion coefficient and the drying temperature of a material can be expressed by the Arrhenius equation as:
(6)
where is diffusion base in the material, constant, m²/s; is activation energy of drying of the material, kJ/mol; - molar constant of the gas, with a value of 8.314 J/(mol/k); is material drying temperature, °C.
If you take the natural logarithm of both sides of equation (6), you get
(7)
The natural logarithm of the effective moisture diffusion coefficient is linearly related to with the slope of equation (7). Since is related to is known, so the slope can be used to find the value of .
Mathematical models. After a literature review, the six most commonly used classical model equations shown in Table 1 were chosen to fit the data from the drying experiments.