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

86 4

,        2 h t  

T

T

(3)

0

where T 0 is initial temperature. For third-kind boundary conditions, with the law of convective heat transfer on the inner surface of the shell, the boundary conditions are expressed as:   0 T T T        (4) where α is heat transfer coefficient,γ is vector of the outer normal to the surface. To solve the thermal conductivity problem, we use an approach based on the fact that the thermal conductivity equation is replaced by an equivalent variational equation, Shevchenko, Babeshko and Piskun (1980). This equation is solved by the finite element method using an explicit scheme for solving the heat conduction problem. When testing the computational program given in Shevchenko, Babeshko and Piskun (1980), the results of the solution for a cylindrical rod were compared with the results for the problem with an analytical solution presented in Lykov (1967). Numerical results for solving equation (1) for determining temperature can be found in Emel'yanov and Mironov (2018), Shevchenko, Babeshko and Piskun (1980), Emel'yanov (2019). As noted above, the problem of thermal conductivity of the shell can be solved using the software package ANSYS Workbench Transient Thermal. This module allows users to perform temporal thermal analysis, which is especially useful for investigating processes where temperature and heat distribution change over time. The module provides tools for modeling various types of thermal loads, including steady-state and transient heat generation, convective heat transfer, radiation, and conduction. In addition, the module is integrated with other ANSYS modules, which allows you to transfer solution results between different types of analysis.

4. Example of solving heat conduction problems

In Emel'yanov and Mironov (2018), the temperature field of a steel shell of rotation was determined using the thermal conductivity equation (1).

Material: Stainless Steel. Geometric parameters:

wall thickness h = 0.018 m, median radius of the cylindrical shell R = 0.65 m.

Loads:

internal pressure of hydrogen-containing gas p = 2.5 MPa, gas temperature can vary from 20 ºС to 200 ºС.

Boundary conditions: on the inner surface of the shell were taken in the form of the law of convective heat transfer (4), the outer surface of the shell is thermally insulated. Initial conditions: shell temperature T = 20 ºС, ambient temperature inside the diffusion apparatus with T = 200 ºС. Thermophysical parameters of the process: thermal conductivity coefficient λ = 16.28 W/(m·K), density ρ = 7850 kg/m3,

thermal diffusivity coefficient a = 1.2·10-5 m2/s, heat transfer coefficient α = 767.6 W/(m2·K).