Abstract
The reciprocity function method is presented in this work as a powerful tool for the transient inverse estimation of steady internal heat transfer coefficients in ducts, using only external boundary data. This paper extends our previous results in a sense that transient measurements can now be used to recover a steady heat transfer coefficient without the need to reach the steady-state regime. In this method, only data from the external (accessible) surface are necessary to estimate the unknown function on the internal (inaccessible) surface. Transient temperature measurements taken on the outer surface are used to estimate internal steady heat transfer coefficients in a non-iterative and non-intrusive process. Different profiles for the internal heat transfer coefficient are considered and noisy synthetic measurements are used to verify the method. Results show that the methodology is able to recover these functions in a short computational time, with good accuracy.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Data availability
All data included in this study are available upon request by contact with the corresponding author.
References
Andrieux S, Ben Abda A (1993) The reciprocity gap: A general concept for flaws identication problems. Mech Res Commun 20(5):415–420
Benkhedda M (2010) Transferts thermiques dans un conduit cylindrique annulaire muni d’ailetttes. Universite Mentouri Constantine, Departement de Physique, Magister en Physique
Bozzoli F, Cattani L, Rainieri S, Bazán FSV, Borges LS (2014) Estimation of the local heat transfer coefficient in the laminar flow regime in coiled tubes by the Tikhonov regularisation method. Int J Heat Mass Transf 72:352–361
Cebula A, Taler J (2014) Determination of transient temperature and heat flux on the surface of a reactor control rod based on temperature measurement at the interior points. Appl Therm Eng 63(1):158–169
Colaço MJ, Alves CJ, Bozzoli F (2015) The reciprocity function approach applied to the non-intrusive estimation of spatially varying internal heat transfer coefficients in ducts: numerical and experimental results. Int J Heat Mass Transf 90:1221–1231
Kakaç S, Bergles AE, Mayinger F, Yüncü H (1999) Heat transfer enhancement of heat exchangers, vol 355. Kluwer
Kakaç S, Yener Y, Pramuanjaroenkij A (2013) Convective Heat transfer. CRC Press
Lu T, Liu B, Jiang P, Zhang YW, Li H (2010) A two-dimensional inverse heat conduction problem in estimation the fluid temperature and wall temperature in pipeline. Appl Thermal Eng 30(13):1574–1579
Mocerino A, Colaço MJ, Bozzoli F, Rainieri S (2018) Filtered reciprocity functional approach to estimate internal heat transfer coefficients in 2D cylindrical domains using infrared thermography. Int J Heat Mass Transf 125:1181–1195
Noh JH, Cha KU, Ahn ST, Yook SJ (2016) Prediction of time-varying heat flux along a hollow cylindrical tube wall using recursive input estimation algorithm and thermal resistance network method. Int J Heat Mass Transf 97:232–241
Noh JH, Cha KU, Yook SJ (2017) Three-dimensional inverse heat conduction modelling of a multi-layered hollow cylindrical tube using input estimation algorithm and thermal resistance network. Int J Heat Mass Transf 106:793–803
Rainieri S, Bozzoli F, Pagliarini G (2004) Wiener filtering technique applied to thermographic data reduction intendedfor the estimation of plate fins performance. Exp Thermal Fluid Sci 28(2–3):179–183
Rainieri S, Bozzoli F, Pagliarini G (2012) Experimental investigation on the convective heat transfer in straight and coiled corrugated tubes for highly viscous fluids: preliminary results. Int J Heat Mass Transf 55(1–3):498–504
Tougri I, Colaço MJ, Bozzoli F, Cattani L (2018a) Internal heat transfer coefficient estimation in three-dimensional ducts through the reciprocity functional approach—an analytical approach and validation with experimental data. Int J Heat Mass Transf 122:587–601
Tougri I, Colaço M J (2017) Estimation of internal heat transfer coefficients in three-dimensional ducts through the reciprocity functional approach: preliminary results. In: 24th ABCM International Congress of Mechanical Engineering, December 3–8, 2017, Curitiba, PR, Brazil.
Tougri I, Padilha R S, Colaço M J (2018b) An analytical extension of the reciprocity functional approach to estimate thermal contact conductances between different material using transients measurments. In: Proceeding of the 16th international heat transfer conference, IHTC-16, August 10–15, 2018b, Beijing, China.
Volle F, Maillet D, Gradeck M, Lebouché KM (2009) Practical application of the inverse heat conduction for wall condition estimation on a rotating cylinder. Int J Heat Mass Transf 52(1–2):210–221
Acknowledgements
This work was supported by Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES), and Fundação Carlos Chagas Filho de Amparo a Pesquisa do Estado do Rio de Janeiro (FAPERJ), Brazilian agencies for fostering science, education, and technology. The support provided from the Brazilian Regulatory Agency for Oil, Gas and Biofuels (ANP/PRH8), from Università degli Studi di Parma and Erasmus Plus were also essential to conclude this work.
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by Antonio C.G. Leitao.
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Tougri, I., Colaço, M.J. & Bozzoli, F. Inverse problem estimation of internal heat transfer coefficients in ducts through a time-dependent reciprocity functional method. Comp. Appl. Math. 42, 26 (2023). https://doi.org/10.1007/s40314-022-02169-7
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/s40314-022-02169-7