{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,20]],"date-time":"2026-03-20T22:42:34Z","timestamp":1774046554612,"version":"3.50.1"},"reference-count":32,"publisher":"MDPI AG","issue":"20","license":[{"start":{"date-parts":[[2021,10,19]],"date-time":"2021-10-19T00:00:00Z","timestamp":1634601600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004225","name":"Petrobras (Brazil)","doi-asserted-by":"publisher","award":["2017\/00702-6"],"award-info":[{"award-number":["2017\/00702-6"]}],"id":[{"id":"10.13039\/501100004225","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100006182","name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Esp\u00edrito Santo","doi-asserted-by":"publisher","award":["88336650"],"award-info":[{"award-number":["88336650"]}],"id":[{"id":"10.13039\/501100006182","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e Tecnologia","doi-asserted-by":"publisher","award":["CEECIND\/00034\/2018"],"award-info":[{"award-number":["CEECIND\/00034\/2018"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e Tecnologia","doi-asserted-by":"publisher","award":["UIDB\/50025\/2020"],"award-info":[{"award-number":["UIDB\/50025\/2020"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e Tecnologia","doi-asserted-by":"publisher","award":["UIDP\/50025\/2020"],"award-info":[{"award-number":["UIDP\/50025\/2020"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The assessment of heat transfer is a complex task, especially for operations in the oil and gas industry, due to the harsh and flammable workspace. In light of the limitations of conventional sensors in harsh environments, this paper presents a fiber Bragg grating (FBG)-based sensor for the assessment of the heat transfer rate (HTR) in different liquids. To better understand the phenomenon of heat distribution, a preliminary analysis is performed by constructing two similar scenarios: those with and without the thermal insulation of a styrofoam box. The results indicate the need for a minimum of thermal power to balance the generated heat with the thermal losses of the setup. In this minimum heat, the behavior of the thermal distribution changes from quadratic to linear. To assess such features, the estimation of the specific heat capacity and the thermal conductivity of water are performed from 3 W to 12 W, in 3 W steps, resulting in a specific heat of 1.144 cal\/g \u00b0C and thermal conductivity of 0.5682 W\/m \u00b0C. The calibration and validation of the HTR sensor is performed in a thermostatic bath. The method, based on the temperature slope relative to the time curve, allowed for the measurement of HTR in water and Kryo 51 oil, for different heat insertion configurations. For water, the HTR estimation was 308.782 W, which means an uncertainty of 2.8% with the reference value of the cooling power (300 W). In Kryo 51 oil, the estimated heat absorbed by the oil was 4.38 kW in heating and 718.14 kW in cooling.<\/jats:p>","DOI":"10.3390\/s21206922","type":"journal-article","created":{"date-parts":[[2021,10,20]],"date-time":"2021-10-20T21:31:26Z","timestamp":1634765486000},"page":"6922","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["FBG-Based Sensor for the Assessment of Heat Transfer Rate of Liquids in a Forced Convective Environment"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8344-2933","authenticated-orcid":false,"given":"Renan","family":"Lazaro","sequence":"first","affiliation":[{"name":"Graduate Program in Electrical Engineering, Federal University of Espirito Santo (UFES),Vit\u00f3ria 29075-910, Brazil"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0687-3967","authenticated-orcid":false,"given":"Anselmo","family":"Frizera-Neto","sequence":"additional","affiliation":[{"name":"Graduate Program in Electrical Engineering, Federal University of Espirito Santo (UFES),Vit\u00f3ria 29075-910, Brazil"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8596-5092","authenticated-orcid":false,"given":"Carlos","family":"Marques","sequence":"additional","affiliation":[{"name":"Physics Department & I3N, University of Aveiro, 3810-193 Aveiro, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4154-5683","authenticated-orcid":false,"given":"Carlos Eduardo Schmidt","family":"Castellani","sequence":"additional","affiliation":[{"name":"Graduate Program in Electrical Engineering, Federal University of Espirito Santo (UFES),Vit\u00f3ria 29075-910, Brazil"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9075-0619","authenticated-orcid":false,"given":"Arnaldo","family":"Leal-Junior","sequence":"additional","affiliation":[{"name":"Graduate Program in Electrical Engineering, Federal University of Espirito Santo (UFES),Vit\u00f3ria 29075-910, Brazil"}]}],"member":"1968","published-online":{"date-parts":[[2021,10,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S1573-4374(98)80004-6","article-title":"Chapter 1\u2014Definitions, Nomenclature, Terms and Literature","volume":"Volume 1","author":"Brown","year":"1998","journal-title":"Handbook of Thermal Analysis and Calorimetry: Principles and Practice"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"130","DOI":"10.1016\/j.tca.2005.07.003","article-title":"Rapid thermal conductivity measurement with a hot disk sensor: Part 2. Characterization of thermal greases","volume":"436","author":"He","year":"2005","journal-title":"Thermochim. Acta"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1309","DOI":"10.1007\/s10973-014-3811-6","article-title":"Measuring the thermal conductivity of heat transfer fluids via the modified transient plane source (MTPS)","volume":"116","author":"Harris","year":"2014","journal-title":"J. Therm. Anal. Calorim."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"82","DOI":"10.1016\/j.yofte.2017.11.006","article-title":"Multi-interface level in oil tanks and applications of optical fiber sensors","volume":"40","author":"Marques","year":"2018","journal-title":"Opt. Fiber Technol."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1161","DOI":"10.1364\/OL.42.001161","article-title":"Zeonex-PMMA microstructured polymer optical FBGs for simultaneous humidity and temperature sensing","volume":"42","author":"Woyessa","year":"2017","journal-title":"Opt. Lett."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"12719","DOI":"10.1109\/JSEN.2020.3040987","article-title":"Diaphragm-Embedded Optical Fiber Sensors: A Review and Tutorial","volume":"21","author":"Marques","year":"2021","journal-title":"IEEE Sens. J."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"7657","DOI":"10.1109\/JSEN.2021.3049574","article-title":"FBG-Based Measurement Systems for Density, Specific Heat Capacity and Thermal Conductivity Assessment for Liquids","volume":"21","author":"Lazaro","year":"2021","journal-title":"IEEE Sens. J."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"114938","DOI":"10.1016\/j.applthermaleng.2020.114938","article-title":"Investigation of the scatter in reported pool boiling CHF measurements including analysis of heat flux and measurement uncertainty evaluation methodology","volume":"169","year":"2020","journal-title":"Appl. Therm. Eng."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"16651","DOI":"10.1109\/JSEN.2021.3078731","article-title":"Linear Temperature Distribution Sensor Using FBG in Liquids\u2014Local Heat Transfer Examination Application","volume":"21","author":"Chakravartula","year":"2021","journal-title":"IEEE Sens. J."},{"key":"ref_10","unstructured":"Incropera, F., DeWitt, D., Bergman, T., and Lavine, A. (2007). Fundamentals of Heat and Mass Transfer, Wiley."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Czichos, H., Saito, T., and Smith, L. (2006). Springer Handbook of Materials Measurement Methods, Springer.","DOI":"10.1007\/978-3-540-30300-8"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1739","DOI":"10.1007\/s11663-014-0109-9","article-title":"The Measurement of Thermal Conductivity Variation with Temperature for Sn-Based Lead-Free Binary Solders","volume":"45","author":"Demir","year":"2014","journal-title":"Metall. Mater. Trans. B"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"407","DOI":"10.1617\/s11527-013-0192-4","article-title":"Design, construction and validation of a guarded hot plate apparatus for thermal conductivity measurement of high thickness crop-based specimens","volume":"48","author":"Dubois","year":"2015","journal-title":"Mater. Struct."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1913","DOI":"10.1016\/j.rser.2010.03.017","article-title":"Techniques for measuring the thermal conductivity of nanofluids: A review","volume":"14","author":"Paul","year":"2010","journal-title":"Renew. Sustain. Energy Rev."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1088\/0143-0807\/24\/4\/353","article-title":"On thermal diffusivity","volume":"24","author":"Salazar","year":"2003","journal-title":"Eur. J. Phys."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"3429","DOI":"10.1016\/j.ijheatmasstransfer.2010.03.042","article-title":"In situ High Temperature Heat Flux Sensor Calibration","volume":"53","author":"Pullins","year":"2010","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Zhao, D., Qian, X., Gu, X., Jajja, S.A., and Yang, R. (2016). Measurement Techniques for Thermal Conductivity and Interfacial Thermal Conductance of Bulk and Thin Film Materials. J. Electron. Packag., 138.","DOI":"10.1115\/1.4034605"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"7179","DOI":"10.1109\/JSEN.2019.2915031","article-title":"Optical Fiber Sensing for Sub-Millimeter Liquid-Level Monitoring: A Review","volume":"19","author":"Marques","year":"2019","journal-title":"IEEE Sens. J."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"80582","DOI":"10.1109\/ACCESS.2020.2991551","article-title":"A Dual-Cavity Fabry\u2013Perot Interferometric Fiber-Optic Sensor for the Simultaneous Measurement of High-Temperature and High-Gas-Pressure","volume":"8","author":"Cui","year":"2020","journal-title":"IEEE Access"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"6093","DOI":"10.1109\/JSEN.2019.2909097","article-title":"Fabry\u2013Perot Interferometer-Based Absolute Pressure Sensor With Stainless Steel Diaphragm","volume":"19","author":"Ghildiyal","year":"2019","journal-title":"IEEE Sens. J."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Ahsani, V., Ahmed, F., Jun, M., and Bradley, C. (2019). Tapered Fiber-Optic Mach-Zehnder Interferometer for Ultra-High Sensitivity Measurement of Refractive Index. Sensors, 19.","DOI":"10.3390\/s19071652"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1263","DOI":"10.1109\/50.618320","article-title":"Fiber Bragg grating technology fundamentals and overview","volume":"15","author":"Hill","year":"1997","journal-title":"J. Light. Technol."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"5962","DOI":"10.1109\/JSEN.2020.2974931","article-title":"FPI-POFBG Angular Movement Sensor Inscribed in CYTOP Fibers With Dynamic Angle Compensator","volume":"20","author":"Theodosiou","year":"2020","journal-title":"IEEE Sens. J."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"414","DOI":"10.1109\/LPT.2020.2977324","article-title":"Glass 3D Printing of Microfluidic Pressure Sensor Interrogated by Fiber-Optic Refractometry","volume":"32","author":"Zhang","year":"2020","journal-title":"IEEE Photonics Technol. Lett."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"165159","DOI":"10.1016\/j.ijleo.2020.165159","article-title":"Multi-scale load identification system based on distributed optical fiber and local FBG-based vibration sensors","volume":"219","author":"Zhang","year":"2020","journal-title":"Optik"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"13867","DOI":"10.1038\/s41598-020-70880-8","article-title":"Smart textiles for multimodal wearable sensing using highly stretchable multiplexed optical fiber system","volume":"10","author":"Avellar","year":"2020","journal-title":"Sci. Rep."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"105997","DOI":"10.1016\/j.optlastec.2019.105997","article-title":"Ultra-high sensitivity and temperature-compensated Fabry\u2013Perot strain sensor based on tapered FBG","volume":"124","author":"Zhao","year":"2020","journal-title":"Opt. Laser Technol."},{"key":"ref_28","unstructured":"Udoh, S., Njuguma, J., and Prabhu, R. (2014, January 28\u201330). Modelling and Simulation of Fiber Bragg Grating Characterization for Oil and Gas Sensing Applications. Proceedings of the First International Conference on Systems Informatics, Modelling and Simulation (ICONS 2014), Vienna, Austria."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Marques, C.A.F., Leal-Junior, A.G., Min, R., Domingues, M., Leit\u00e3o, C., Antunes, P., Ortega, B., and Andr\u00e9, P. (2018). Advances on Polymer Optical Fiber Gratings Using a KrF Pulsed Laser System Operating at 248 nm. Fibers, 6.","DOI":"10.3390\/fib6010013"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"38039","DOI":"10.1364\/OE.27.038039","article-title":"Inscription of Bragg gratings in undoped PMMA mPOF with Nd:YAG laser at 266 nm wavelength","volume":"27","author":"Min","year":"2019","journal-title":"Opt. Express"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1109\/JSEN.2017.2768510","article-title":"Liquid Level Measurement Based on FBG-Embedded Diaphragms With Temperature Compensation","volume":"18","author":"Pontes","year":"2018","journal-title":"IEEE Sens. J."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Pereira, K., Coimbra, W., Lazaro, R., Frizera-Neto, A., Marques, C., and Leal-Junior, A.G. (2021). FBG-Based Temperature Sensors for Liquid Identification and Liquid Level Estimation via Random Forest. Sensors, 21.","DOI":"10.3390\/s21134568"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/20\/6922\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T07:17:49Z","timestamp":1760167069000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/20\/6922"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,10,19]]},"references-count":32,"journal-issue":{"issue":"20","published-online":{"date-parts":[[2021,10]]}},"alternative-id":["s21206922"],"URL":"https:\/\/doi.org\/10.3390\/s21206922","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,10,19]]}}}