PSI - Issue 65

Emelyanov I.G. et al. / Procedia Structural Integrity 65 (2024) 83–91 Emelyanov I.G., Puzyrev P.I. / Structural Integrity Procedia 00 (2024) 000–000

89

7

Thus, to use the computational program for unsteady thermal conductivity, you need the thermal diffusivity coefficient a, coefficient of thermal conductivity λ and heat transfer coefficient α multiplied by the reduction factor of the diffusion process k D . Therefore, equation (9) will have the form: 1 1 c c c For equation (10), it is necessary to set the appropriate boundary conditions. Boundary conditions for diffusion problems can be specified in several ways. There are boundary conditions of types I, II, III, IV, Bekman (2016). In boundary conditions of the first kind, it is required to find solutions to the equation in a certain region of space, which takes on given values at the boundary of the region. Consequently, the distribution of the diffusant concentration over the surface of the body is specified. If we accept the assumption of rapid mixing of the hydrogen containing medium, then we can set the boundary conditions I kind. By analogy with (3), on the inner surface of the shell under study we set: D r z z r r r k a t                         (10)

,        2 h t  

c

c

(11)

0

where c 0 the initial hydrogen concentration near the surface of the shell. In boundary conditions of the second kind, the distribution of the diffuser flux density is specified for each surface point as a function of coordinates and time. Boundary conditions of the third kind can be linear, nonlinear and non-stationary. Under linear boundary conditions, the law of convective mass transfer between the surface of the body and the environment is specified in the form of a connection between the desired function and its normal derivative at the boundary:

c







k c c

 

(12)

s

0





k s - proportionality coefficient characterizing the intensity of the concentration interaction of a medium with a given diffusant concentration with the surface of the body. Boundary conditions of the fourth kind determine the conditions on the contact surface of two solid bodies. They correspond to the mass transfer of the surface of the body with the environment of the solid bodies in contact. Boundary conditions of the fourth kind are used when solving problems of diffusion in multilayer bodies with different diffusion and absorption properties in each layer. If the boundary conditions for thermal conductivity problems (3) and (4) can be attributed to physical conditions that depend on temperature, then the boundary conditions for diffusion equations (11) and (12) apparently refer to physicochemical conditions that should depend on the hydrogen concentration in a medium, pressure of a hydrogen containing medium p, from temperature T and on the properties of the material. Various options for determining the hydrogen concentration on the surface of various metals were proposed in, Ivanyts’kyi, Hembaraand and Chepil (2015), Hisamatullin (1990), Capelle, Gilgert and Dmytrakh(2008). The hydrogen concentration on the surface of the steel shell under study in ppm can be determined using the relation from, Hisamatullin (1990):

H



( c K exp  

p

)



(13)

 R T



H

0

0

2

273



2