PSI - Issue 36

Anatolii Pavlenko et al. / Procedia Structural Integrity 36 (2022) 3–9 Anatolii Pavlenko, Andrii Cheilytko, Serhii Ilin, et al. / Structural Integrity Procedia 00 (2021) 000 – 000

7

5

where n b - the average number of pores in the thickness of the material b along the heat flux; П b - the total porosity of the material. G - geometric characteristic of a closed-pore porous material equal to the ratio of the pore cross-section length to the surface area of the material in cross section with the pore (the greater the dimension, the smaller the difference between the heat channel and the heat pipe of the porous material):

(4)

2 S n d   − d

,

G

=

2

2

4

where S - the intersection area of the heat pipe. Then, the effective coefficient of thermal conductivity for closed porous constructions can be written: 2 2 . =   b tr mat b П r H n S   The decrease in the coefficient of thermal conductivity of the porous material due to the pores will depend on the coefficient of thermal permeability and geometric characteristics of the porous structure. The equation describing the transfer of thermal energy in open porous constructions is derived taking into account the dependence of thermal resistance on thermal operating conditions: (5)

2 G grad T G C T G C T   , ( ) =    + +

(6)

Q

1

2

mat

O

O

where С – integration constants, G 0 - the geometric characteristic of open porosity, m.

,

(7)

1

G

=

O

2

1 3 1 + + d C d C 

4

where χ is the coefficient expressing the thermal permeability of the material for convection currents:

2

2 2 g K K K         +             

(8)



=

K - permeability of porous material, Pa -1 ; - coefficient of dynamic viscosity, Pa∙s; - coefficient of kinematic viscosity, m 2 /s. A detailed summary of the above formulas is presented in, Pavlenko et al. (2019). The equation describes not only the transfer of thermal energy in the duct pores but also takes into account the existing closed pores in the material. The study of the technique was carried out on a modern design of thermal protection. The design consists of a flexible ceramic fabric and a thin basalt sheet according to the scheme shown in Fig. 2. Basalt sheet 1 with a thickness of 3 mm is soldered to the basalt surface of ceramics 2. The combination of high heat resistance and ability of the insulating properties of ceramics provide a strong and water-repellent system of thermal protection, which can be used in severe weather and operating conditions. Knowledge of the coefficient of permeability of systems and the effective coefficient of thermal conductivity of porous materials is very important for the calculation of thermal power equipment, so the value of thermal