Study of the unknown strength of a plane heat source using Grey Theory

• Main Authors: Chin-Chih Hsu, 許晉誌
• Other Authors: 賈明益
• Format: Others
• Language: zh-TW
• Published: 2016
• Online Access: http://ndltd.ncl.edu.tw/handle/93582482449766990426

碩士 === 國立中興大學 === 應用數學系所 === 104 === This study tries to find out the inverse processing of heat conduction problems to estimate the unknown strength of a slab heat source through the finite difference method (FDM). With the Grey Model of the Grey Theory, it improves the predicted heat source with interference caused by the temperature measurement errors, and makes the predictions more stable and accurate. This paper explores the inverse plane heat conduction problem to predict the heat source function. In the heat conduction equation, we have the thermal conductivity, density, and specific heat be known a prior and the predicted heat source be an unknown item. To take equal spacing of the grid in the space, to discrete the governing equations by finite difference method, and to arrange in matrix form through the matrix operations forecasts the heat source. In the article, we have discussed the different heat source distribution, measurement errors, measurement points, and smooth points, etc. which affect to predict the heat source in the heat conduction system. Finally, comparing the error change between the heat of the predictive results and the analytical values. It is found that using the Grey Theory can effectively reduce the interference temperature measurement errors and cause the prediction of heat sources more accurate.