Identification of heat transfer coefficient through linearization: explicit solution and approximation. (17th November 2017)

• Record Type: Journal Article
• Authors: Bazán, F S V; Bedin, L
• Is Part Of: Inverse problems. Volume 33:Number 12(2017:Dec.)
• Publication Date: 2017-11-17
• Subjects: inverse heat transfer -- singular value expansion -- Morozov's discrepancy principle; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/aa97c1
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: We derive an explicit reconstruction formula for the heat flux on the internal surface of a duct based on external temperature data. With the heat flux at hand we determine the internal convective heat transfer coefficient. Technically, by determining explicitly the singular system of a compact operator and assuming noise-free data, the heat flux is expressed as an infinite singular value expansion, whereas for noisy data, the truncated expansion is used as regularized solution. An error bound is derived for the case where the truncation parameter is determined by the Morozov's discrepancy principle. The method has high flexibility in that it is readily adapted to the finite data case without any substantial modification. Moreover, it does not require any linear system solver and it is therefore easy to implement and extremely inexpensive when compared to existing heat transfer coefficient estimation techniques. The method is illustrated by means of numerical results using both synthetic and experimental data.