Определение температуропроводности материала по трем точкам несимметричного температурного поля пластины

Abstract

Relatively simple formulas are derived for calculating the thermal diffusivity by a numerical-analytical method in the asymmetric temperature field T (x, τ) of an infinite plate of thickness R obtained as a result of a physical experiment. By solving the inverse heat conduction problem, the thermal diffusivity values are calculated for each time interval Δτ i = τ i – τ i – 1 by the temperatures at three points of the plate with the coordinates x = 0, z, R (0 < z < R) for the time moments τ i . We estimated the complexity and accuracy of the thermal diffusivity determination a t (T) from the test (initial) temperature field of a steel plate (thickness R = 0.07 m) calculated by the method of finite differences with a given thermal diffusivity a s (T) under boundary conditions of the second and third kind. The function a t (T) is set by a broken line and the magnitude of ax varied almost threefold during numerical experiment. The root-mean-square deviation of a t (T) from the initial dependence a s (T) for the entire time range is 3%. The largest errors are observed after change in the sign of the derivative das(T)/dT. On the linear part of the function a s (T), the error of a t (T) determination did not exceed 2%. The method presented in the article does not require strict compliance with the standard boundary conditions: constant temperature of the ambient media, the same heat flow, adiabatic conditions on one of the plate surfaces, which simplifies the organization of the experiment to be carried out in real conditions of the material operation. The method is relatively simple and illustrative and data processing data processing can be easily programed using Microsoft Excel.