{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:20:06Z","timestamp":1760149206802,"version":"build-2065373602"},"reference-count":25,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2023,7,17]],"date-time":"2023-07-17T00:00:00Z","timestamp":1689552000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100006108","name":"KEGA","doi-asserted-by":"publisher","award":["023TUKE-4\/2021"],"award-info":[{"award-number":["023TUKE-4\/2021"]}],"id":[{"id":"10.13039\/501100006108","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>Modern heating furnaces use combined modes of heating the charge. At high heating temperatures, more radiation heating is used; at lower temperatures, more convection heating is used. In large heating furnaces, such as pusher furnaces, it is necessary to monitor the heating of the material zonally. Zonal heating allows the appropriate thermal regime to be set in each zone, according to the desired parameters for heating the charge. The problem for each heating furnace is to set the optimum thermal regime so that at the end of the heating, after the material has been cross-sectioned, there is a uniform temperature field with a minimum temperature differential. In order to evaluate the heating of the charge, a mathematical model was developed to calculate the heat fluxes of the moving charge (slabs) along the length of the pusher furnace. The obtained results are based on experimental measurements on a test slab on which thermocouples were installed, and data acquisition was provided by a TERMOPHIL-stor data logger placed directly on the slab. Most of the developed models focus only on energy balance assessment or external heat exchange. The results from the model created showed reserves for changing the thermal regimes in the different zones. The developed model was used to compare the heating evaluation of the slabs after the rebuilding of the pusher furnace. Changing the furnace parameters and altering the heat fluxes or heating regimes in each zone contributed to more uniform heating and a reduction in specific heat consumption. The developed mathematical heat flux model is applicable as part of the powerful tools for monitoring and controlling the thermal condition of the charge inside the furnace as well as evaluating the operating condition of such furnaces.<\/jats:p>","DOI":"10.3390\/computation11070144","type":"journal-article","created":{"date-parts":[[2023,7,18]],"date-time":"2023-07-18T01:31:32Z","timestamp":1689643892000},"page":"144","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Modeling of Heat Flux in a Heating Furnace"],"prefix":"10.3390","volume":"11","author":[{"given":"August\u00edn","family":"Varga","sequence":"first","affiliation":[{"name":"Department of Thermal Technology and Gas Industry, Institute of Metallurgy, Faculty of Materials, Metallurgy and Recycling, Technical University of Kosice, Letn\u00e1 9, 042 00 Kosice, Slovakia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1035-9415","authenticated-orcid":false,"given":"J\u00e1n","family":"Kizek","sequence":"additional","affiliation":[{"name":"Department of Process Technique, Faculty of Manufacturing Technologies with a Seat in Presov, Technical University of Kosice, Bayerova 1, 080 01 Presov, Slovakia"}]},{"given":"Miroslav","family":"Rim\u00e1r","sequence":"additional","affiliation":[{"name":"Department of Process Technique, Faculty of Manufacturing Technologies with a Seat in Presov, Technical University of Kosice, Bayerova 1, 080 01 Presov, Slovakia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0389-3073","authenticated-orcid":false,"given":"Marcel","family":"Fed\u00e1k","sequence":"additional","affiliation":[{"name":"Department of Process Technique, Faculty of Manufacturing Technologies with a Seat in Presov, Technical University of Kosice, Bayerova 1, 080 01 Presov, Slovakia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5547-1104","authenticated-orcid":false,"given":"Ivan","family":"\u010corn\u00fd","sequence":"additional","affiliation":[{"name":"Department of Process Technique, Faculty of Manufacturing Technologies with a Seat in Presov, Technical University of Kosice, Bayerova 1, 080 01 Presov, Slovakia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9027-8556","authenticated-orcid":false,"given":"Ladislav","family":"Luk\u00e1\u010d","sequence":"additional","affiliation":[{"name":"Department of Thermal Technology and Gas Industry, Institute of Metallurgy, Faculty of Materials, Metallurgy and Recycling, Technical University of Kosice, Letn\u00e1 9, 042 00 Kosice, Slovakia"}]}],"member":"1968","published-online":{"date-parts":[[2023,7,17]]},"reference":[{"key":"ref_1","first-page":"264","article-title":"Intensifying the process of heating slabs in pusher furnaces","volume":"2","author":"Varga","year":"1992","journal-title":"Trans. Technol. Univ. Ko\u0161ice"},{"key":"ref_2","unstructured":"Brunklaus, J.H. (1962). Building of Industrial Furnaces, Vulkan-Verlag. [2nd ed.]."},{"key":"ref_3","unstructured":"Tati\u010d, M., Luk\u00e1\u010d, L., and S\u00fa\u010dik, G. (2021). Industrial Furnaces in Metallurgical Secondary Production, TU of Ko\u0161ice. [1st ed.]."},{"key":"ref_4","first-page":"469","article-title":"Modernization of the pusher furnace lining in VS\u017d a.s","volume":"2","year":"1997","journal-title":"Acta Metall. Slovaca"},{"key":"ref_5","first-page":"26","article-title":"Effect of varying the power and frequency of insulation maintenance on the heat consumption of a pusher furnace","volume":"47","author":"Horbaj","year":"1992","journal-title":"Hutn\u00edcke Listy"},{"key":"ref_6","unstructured":"Kollerova, I. (2010). The Study of the Wear of the Pusher Furnace Bottom with Steel Scales. [Ph.D. Thesis, Technical University of Ostrava]."},{"key":"ref_7","first-page":"203","article-title":"Application of roof radiant burners in large pusher-type furnaces","volume":"48","author":"Varga","year":"2009","journal-title":"Metalurgija"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1","DOI":"10.5604\/20804075.1049487","article-title":"The verification of the influence of heating steel charge parameters on the thickness of scale layer","volume":"7","author":"Benduch","year":"2013","journal-title":"Adv. Sci. Technol. Res. J."},{"key":"ref_9","first-page":"43","article-title":"Minimization of costs when heating the slabs in the pusher furnace","volume":"49","year":"1994","journal-title":"Hutn\u00edcke Listy"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Setiawan, A.F., Arsana, I.M., and Soeryanto, S. (2022, January 10\u201311). Performance Analysis of Reheating Furnace on Billet Heating Production of Reinforced Iron. Proceedings of the International Joint Conference on Science and Engineering 2022 (IJCSE 2022), Advances in Engineering Research, Surabaya, Indonesia.","DOI":"10.2991\/978-94-6463-100-5_21"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1105","DOI":"10.1016\/j.applthermaleng.2006.07.033","article-title":"Online simulation model of the slab-reheating process in a pusher-type furnace","volume":"27","author":"Vode","year":"2007","journal-title":"Appl. Therm. Eng."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1016\/j.ijheatmasstransfer.2010.07.029","article-title":"A mathematical model of a slab reheating furnace with radiative heat transfer and non-participating gaseous media","volume":"53","author":"Steinboeck","year":"2010","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_13","unstructured":"Feliu Batlle, V., Rivas P\u00e9rez, R., Castillo, F., and Mora, I.Y. (2012, January 14\u201317). Fractional Order Temperature Control of a Steel Slab Reheating Furnace Robust to Delay Changes. Proceedings of the 5th IFAC Workshop on Fractional Differentiation and its Applications, FDA\u201912, Nanjing, China."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"675","DOI":"10.1016\/j.ijheatmasstransfer.2015.08.056","article-title":"Prediction of the heating characteristic of billets in a walking hearth type reheating furnace using CFD","volume":"53","author":"Prieler","year":"2016","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"928","DOI":"10.1016\/j.enconman.2017.04.005","article-title":"Analysis of slab heating characteristics in a reheating furnace","volume":"149","author":"Wang","year":"2017","journal-title":"Energy Convers. Manag."},{"key":"ref_16","first-page":"78","article-title":"Internal Model Control based Preheating Zone Temperature Control for Varying Time Delay Uncertainty of the Reheating Furnace","volume":"4","author":"Radhika","year":"2015","journal-title":"Int. J. Sci. Res. (IJSR)"},{"key":"ref_17","first-page":"257","article-title":"Numerical model of steel slab reheating in pusher furnaces","volume":"32","author":"Marino","year":"2002","journal-title":"Lat. Am. Appl. Res."},{"key":"ref_18","first-page":"249","article-title":"Control of Pusher furnaces for steel slab reheating using a numerical model","volume":"34","author":"Marino","year":"2004","journal-title":"Lat. Am. Appl. Res."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Andreev, S. (2019). System of Energy-Saving Optimal Control of Metal Heating Process in Heat Treatment Furnaces of Rolling Mills. Machines, 7.","DOI":"10.3390\/machines7030060"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1016\/j.applthermaleng.2016.02.124","article-title":"Optimal set values of zone modeling in the simulation of a walking beam type reheating furnace on the steady-state operating regime","volume":"101","author":"Yang","year":"2016","journal-title":"Appl. Therm. Eng."},{"key":"ref_21","unstructured":"Steel 11 375 Non-Alloy Steel of The usual Qualities Suitable For Welding For Steel Constructions. Standard No. STN 41 1375. Available online: https:\/\/docplayer.cz\/19932075-Csn-41-1523-nelegovana-konstrukcni-jemnozrnna-11-523-stn-41-1523-ocel-vhodna-ke-svarovani-znacka.html."},{"key":"ref_22","unstructured":"R\u00e9dr, M., and P\u0159\u00edhoda, M. (1991). Fundamentals of Thermal Engineering, SNTL. [1st ed.]."},{"key":"ref_23","unstructured":"Sazima, M., Kmon\u00ed\u010dek, V., and Schneller, J. (1989). Heat, SNTL. [1st ed.]."},{"key":"ref_24","unstructured":"Cengel, Y., and Ghajar, A. (2019). Heat and Mass Transfer: Fundamentals and Applications, McGraw Hill. [6th ed.]."},{"key":"ref_25","unstructured":"Ha\u0161ek, P. (1980). Tables for Thermal Engineering, V\u0160B. [11th ed.]."}],"container-title":["Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2079-3197\/11\/7\/144\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T20:13:42Z","timestamp":1760127222000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2079-3197\/11\/7\/144"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,7,17]]},"references-count":25,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2023,7]]}},"alternative-id":["computation11070144"],"URL":"https:\/\/doi.org\/10.3390\/computation11070144","relation":{},"ISSN":["2079-3197"],"issn-type":[{"type":"electronic","value":"2079-3197"}],"subject":[],"published":{"date-parts":[[2023,7,17]]}}}