應用簡單最佳化預測法輔助熱探棒法來同時預測熱傳導系數、熱容量及熱擴散系數之探討

The Investigation of Applying a Simple Optimization for Thermal Probe Method to Simultaneously Predict Thermal Conductivity, Heat Capacity and Thermal Diffusivity

林宜弘(Yi-Hong Lin) ； 廖建貴(Chien-Kuei Liaw)

《農業機械學刊》 4卷4期 (1995/12) Pp. 1-15

https://doi.org/10.30062/JAM.199512.0001

摘要

本文應用共軛梯度參數預估最佳化法來輔助熱探棒法之分析來同時預測k、C及α值，此預測法是將問題解析成(一)直接問題、(二)敏感度問題、(三)梯度方程式等三個疊代步驟，本文將有詳細推導過程。經測試結果有如下優點：初始猜值較不敏感而易於設定、疊代次數少且預測值相當可靠、準確。本文採用此方法經測試結果顯示：單一溫度量測點就足以輔助熱探棒法來預測k、C及α值，當採單一量測點時，欲提高k、C及α等預測值的準確性可埋設此量測點位置距探棒5mm附近及延長量測時間；當採兩點溫度量測點，若一點放置在探棒表面、另一埋設位置愈靠近探棒表面，則預測精度將大幅度提高。

關鍵字

熱探棒法 ； 最佳化法 ； 共軛梯度法 ； 熱傳導系數 ； 熱容量 ； 熱擴散系數

並列摘要

This paper employs thermal probe method aided by a simple optimal method to simultaneously predict thermal conductivity, heat capacity per unit volume and thermal diffusivity. The conjugate gradient method associated with numerical finite difference method are used here. The conjugate gradient method divides the optimal computational procedure into three problems as (1) direct problem, (2) sensitivity problem, (3) gradient equation. The derivation for the present optimization are detailly introduced in this paper. The simulated results of the present method demonstrate some advantages including the wide ranges for choosing the initial guesses of k and C, as well as the rather certainness, high reliability and accuracy of estimated values. The results of analysis point out that only a single measured temperature point embeded at the position of 5mm away from the surface of the thermal probe, together with longer measured time are available for obtain good estimation. Futher, the two measured points will robustly determine k, C and a. Also, the arrangement of locating one measured point at the surface of thermal probe and second point near that will considerablly raise the accuracy of the precdicted values. The concluding remarks are drawn in this paper for providing the guiding line of designing the measurement system of experimental apparatus.

並列關鍵字

Thermal probe method ； Optimization ； Conjugate gradient method ； Thermal conductivity ； Heat capacity ； Thermal diffusivity