Modeling algorithm of heat-and-mass transfer processes at microwave heating of capillary-porous materials Modeling algorithm of heat-and-mass transfer processes at microwave heating of capillary-porous materials

1. Subject of research: External conditions - Vapor evacuation speed: S(p) - System volume: V 0 -Microwave power: P micro - Body capacity(typical size):V t - Porosity: Φ - Weight part of water in the product: s - Dielectric parameters: ε ’ r, ε ’’ r (Φ, s, T) - Thermo physical parameters:, Product characteristics A product: it mostly has vegetable or animal origin. As a rule a product has many components and each component has its С i (Φ, s, T) and λ i (Φ, s, T). Thus for such products they determine some С eff (Φ, s, T) and λ eff (Φ, s, T).

The main equations that describe these processes are a thermal conductivity equation and continuity equation, Pores with air (porosity Φ = V pores / V product ) Dry framework (waterless structure) Water (the whole water content in the product) Product dry air water If we suppose that product porosity does not significantly change in drying process 2. Modeling algorithm Main equations

Dielectric parameters ε ’ r, ε ’’ r (Φ, s, T) are separate for the framework, pores with water and air, then they are summed up. 2.1 The general formulas for determination ε ’ r, ε ’’ r (Φ, s, T) - ε ’ r, ε ’’ r does not depend on temperature; - porosity Φ also changes in heat-and-mass exchange process - m – exponent that depends on the way of mixing of components and their interference 2.2 Assumptions: ε ’ r (Φ, s)= (Φ ּ s) m ּε ’ rw + [Φ ּ(1-s)] m ּε ’ ra +(1- Φ) m ּ ε ’ rd ε ’’ r (Φ, s)= (Φ ּ s) m ּε ’’ rw +(1- Φ) m ּ ε ’’ rd

2.3 Product humidity effect on its dielectric parameters All the dependence graphics are made with the help of program package MATLAB 7 From previous points it follows that in this model ε’ r and ε’’ r are humidity functions [ε’ r (s) and ε’’ r (s)] 2.4 Depth of electromagnetic field penetration into the product If we know functions ε’r(s) and ε’’r (s) we can determine δ(s) – dependence of depth of electromagnetic field penetration into the product from the product humidity, following the law: where λ 0 – length of electromagnetic field wave λ 0 ≈12 sm

For this model the function δ(s) looks like: 2.5 Switch to the one-dimensional model We have considered dependences of different parameters from humidity. Now if we want to switch to the one- dimensional model, we should introduce dependence of humidity itself from coordinate x: Simplified heating scheme with the help of microwaves. For х=0 the middle of the sample is taken, d=0,1 м the middle of the sample

Function graphic s(x): The function s(x) can be presented like: s(x)=-80ּx Thus function graphics ε’r(s) and ε’’r (s) can look the following way:

δ(х) - dependence of depth of electromagnetic field penetration into the product from х Then we can calculate bulk density of heating sources following the formula: When electromagnetic field penetrates inside the product, it gives its energy to the molecules which form heating sources inside the sample. where F 0 – microwave radiation power flow Penetration depth

According to preliminary calculations this dependence of heating resources from coordinates will look the following way: This data allow us to conclude that at microwave heating in capillary porous materials energy that is generated in the form of heat does not distribute uniformly. Thus to control heat-and-mass exchange processes we need to have their computer modeling, as it helps to visualize energy and substance flows inside the product, to provide a clearer understanding of all the processes.