Abstract

Thermal diffusivity is a parameter of fundamental importance in heat transfer studies of solids. This parameter can be determined from the transient Fourier heat conduction equation using different techniques. In this research, a new algorithm based on Talbot’s method was proposed to determine the thermal diffusivity using a one-dimensional Fourier heat conduction equation. Furthermore, a free and open-source program was developed to perform the calculations. Experimental data in heating and cooling conditions of ham were used to test the programming. It was found that n and ω are strongly related and affect the results. The developed program in Scilab using Talbot’s method, the Levenberg-Marquardt algorithm of optimization (lsqrolve routine), n = 100 and ω = 1.8 obtained r² of 0.999 and 0.998; thermal diffusivities of 0.98 × 10⁻⁷ m²/s and 1.13 × 10⁻⁷ m²/s with the time required to run the programming from 0.6 to 1.1 s.

摘要

热扩散率是固体传热研究中一个非常重要的参数。该参数可以使用不同的技术从瞬态傅里叶热传导方程确定。在这项研究中，提出了一种基于 Talbot 方法的新算法，使用一维傅里叶热传导方程来确定热扩散系数。此外，还开发了一个免费的开源程序来执行计算。火腿的加热和冷却条件下的实验数据用于测试编程。发现n和ω密切相关并影响结果。使用 Talbot 方法在 Scilab 中开发的程序，Levenberg-Marquardt 优化算法（lsqrolve 例程），n  = 100 和ω  = 1.8 得到r ²为 0.999 和 0.998；^{0.98 × 10 -7} m ² /s 和 1.13 × 10 ^-7 m ² /s的热扩散率，运行编程所需的时间为 0.6 至 1.1 s。