逆拉普拉氏轉換在二維溫度場之應用

Inverse Laplace transform applied in two dimensional temperature field

簡連廷(Lien-Ting Chien)

指導教授 ： 王金樹

國立臺北科技大學/機電學院/製造科技研究所/碩士(2012年)

https://doi.org/10.6841/NTUT.2012.00409

摘要

本次論文主要是對與廠商所共同開發之有機肥料發酵機進行二維溫度場分析，機臺主要運作為將廚餘與有機廢棄物置入機臺發酵槽內，添加生物菌酵素組合物，利用加熱器將發酵槽內進行加熱，提高生物菌酵素組合物之活性，能有效消滅有機廢棄物中的有害微生物，並使得有機廢棄物可於24小時內成為有機肥料；本論文將針對二維溫度場進行運算並探討其外在環境改變時，對於發酵槽內部溫度之影響為何；其理論分析主要是在空間上進行中央差分法，將內部由連續空間離散轉換為格點空間，再進行拉普拉氏轉換處理系統之時間域，最後以逆拉普拉氏轉換解得發酵槽內之二維溫度場，再針對不同之case進行探討外在環境對發酵槽內之影響。
結果顯示由本文模擬之可變參數，其均溫和所要求之兩小時內整體溫度約需達到90℃相符，且機臺在大陸鄭州、蘇北實際量測結果相符；其改變外在環境參數，結果也與物理意義相符，相當具有參考價值。
未來可進一步分析逆向熱傳導問題，進而估計有機肥料發酵機所需之熱通量，使發酵槽內能夠達到溫度均勻，使得發酵槽內部攪拌時即能達到良好的發酵效果。

關鍵字

中央差分法 ； 逆拉普拉氏轉換

並列摘要

This thesis is mainly focusing on the two-dimensional temperature field analysis of the organic fertilizer fermented machine. The operation method of this organic fertilizer fermented machine is to drop kitchen waste, organic disposal, and composition of biological bacteria enzymes into the fermenter. Then, the heater will heat up the fermenter so that the activity of the enzyme composition of biological bacteria will rise. And it helps in eliminating harmful micro-organisms in the original kitchen waste and organic disposal. And the original kitchen waste and organic disposal will turn into organic fertilizer within 24 hours. This thesis concerns about the computing of two-dimensional temperature field, and also study how the changes of eternal resources will influence the fermenter: This theory uses central difference method in space to transfer internal space from the continuous space into grid space, then using Laplace transform to deal with time domain of system. Therefore the two-temperature field of fermenter can be solved by using Inverse Laplace transform. Finally discussing how the changes of eternal resources will influence the fermenter in different cases.
The result indicates that the mean temperature in this simulation is identical to the overall temperature requirement in two hours (90℃). Besides, the results we obtained in China Zhengzhou and Subei are consistent; The physical meanings are also consistent while changing the eternal environment variables. The future outlook is to analyze the Inverse Heat Transfer Problems (IHTP) to estimate the requirement heat flux for the organic fertilizer fermented machine. This will help the temperature in fermenter in consistency, and thus lead to a better fermentation effects.

並列關鍵字

Central difference method ； Inverse Laplace Transform

參考文獻

[13] 廖雪吩，應用數值拉普拉斯逆轉換法於壓電材料動力破壞之研究

[14] 鍾文貴、王弘祐和胡竣傑，「靜不定樑的拉普拉斯變換解法」，

[3] 陳述文，以混合逆算法預測十二吋矽晶圓在快速熱製程中所加入的

[4] 鄭仲庭，異向垂直循環流場溶質傳輸分析，碩士論文，國立中央大學

[5] 陳建銘，二維逆向熱傳導問題於各種邊界條件下之探討，碩士論文