This work presents a novel direct estimation approach for the simultaneous identification of spatially variable thermal conductivity and thermal capacity in heterogeneous media. The fundamentals of the new methodology reside in the direct application of the integral transformed temperature measurements into the integral transformed heat conduction equation. The parameters that model the sought functions are then estimated with a simple minimization problem, which does not require the iterative execution of the direct problem solution, leading to a computationally fast procedure. The methodology is illustrated with some numerical examples representing different scenarios, demonstrating the feasibility and robustness of the approach.

这项工作提出了一种新颖的直接估计方法，用于同时识别异质介质中的空间可变热导率和热容。新方法的基本原理在于将积分转换后的温度测量值直接应用到积分转换后的热传导方程中。然后，通过简单的最小化问题来估计对所寻找函数建模的参数，该问题无需迭代执行直接问题解决方案，从而实现了计算快速的过程。通过一些代表不同场景的数值示例说明了该方法，证明了该方法的可行性和鲁棒性。