Investigation of the heat transfer process in a cylindrical fuel element
Abstract
Investigation of the heat transfer process in a cylindrical fuel element
Incoming article date: 13.07.2021the presented work is devoted to the study of the temperature state of a fuel element (fuel element) – a cylindrical solid body with an internal heat source of constant power. Using the integral method of heat balance with the introduction of an additional desired function, an approximate analytical solution of the corresponding boundary value problem of thermal conductivity is obtained. The conditions of external heat transfer at the boundary of the studied region were set according to the Newton-Richman law (a boundary condition of the third kind). When obtaining the solution, trigonometric coordinate functions were used. Their use made it possible to reduce the number of terms in the desired solution due to the a priori fulfillment of the boundary condition in the center of the fuel element. It is shown that when using only three terms in the analytical solution (the first approximation), an accuracy sufficient for engineering applications is achieved. The error of the developed method was estimated by comparing the results obtained with a numerical solution based on the finite difference method. The article presents graphs of the temperature distribution at different power values of volumetric fuel element heat sources. The developed method can be used to determine the time of the system's exit to the stationary mode, estimate the maximum fuel element temperature at various values of the dimensionless Bio and Pomerantsev numbers, and determine temperature stresses.
Keywords: internal heat sources, boundary conditions of the third kind, additional desired function, heat balance integral, heat-generating element, approximate analytical solution, numerical solution, heat conduction problem, Bio number, Pomerantsev number