Study on Thermal Contact Resistance Estimation in Planar Medium

二维两层介质界面接触热阻的反辨识研究

Received: 25 April 2017

Abstract

Thermal contact resistance(TCR) is one of the important parameters in heat transfer problems of engineering, and it is necessary to estimate the value of TCR effectively in many engineering fields. Considering the limitation of current estimation methods of TCR such as only focusing on one-dimensional thermal conduction, getting a single value of TCR merely, and the temperature measuring points only being placed in temperature gradient direction of mediums, boundary element method(BEM) and conjugate gradient method are combined to estimate the TCR in planar mediums. The value of TCR in relation to the position of contact interface line is estimated with this method, and the positions of temperature measuring points can be selected randomly because of the characteristic of BEM that there is no necessity to discrete the inner area and it is sufficient to discrete the boundary. The analysis of calculation examples base on heat transfer model of planar medium demonstrates that:this method can estimate the TCR effectively, but the ill-posedness is also existed in this method which is one of the inverse problems, and the calculation error of TCR is increased with the distance from temperature measuring points to contact interface, the estimation precision and stability can be improved after optimization with least square method.

摘要

接触热阻是研究工程传热问题的重要参数，很多工程领域都需要有效辨识出接触热阻。针对目前接触热阻辨识方法局限于一维两层介质传热，只能求出一个接触热阻单值，以及温度测点必须布置在介质温度梯度方向上等问题，采用边界元法与共轭梯度法相结合的方法，对二维两层介质界面接触热阻进行反辨识研究。该方法可以求解出随界面接触线位置变化的接触热阻，并且边界元算法只需离散边界，不需要对内部区域进行离散，因此温度测点位置可以任意选取。建立二维两层介质传热模型作为算例并进行分析：该方法可以有效求解接触热阻，但作为反辨识方法的一种同样存在不适定性，并且温度测点距离接触界面越远误差越大，采用最小二乘法对求解结果进行优化处理可以有效提高辨识精度和稳定性。