Modeling and Energy Consumption of Unilateral Heating Process of Flat Wood Details

A methodology has been suggested for mathematical modeling and research of two mutually connected problems: the temperature distribution along the thickness of flat wood details subjected to unilateral heating and the energy consumption of this process. For the realization of the methodology, a 1-dimensional mathematical model has been created and solved for the transient linear heat conduction in flat wood details during their unilateral heating at arbitrary initial and boundary conditions encountered in the practice. Based on the integration of the model’s solutions, a numerical approach has been suggested for the computation of the specific energy consumption (for 1 m2) and the specific heat flux needed for the heating of the details and for the covering of their heat emission in the surrounding environment during unilateral heating aimed at wood plasticizing and bending. This paper presents solutions of the model concerning the non-stationary temperature distribution along the thickness of spruce details with thicknesses of 6, 8 and 10 mm and the non-stationary change in the specific energy consumption and in the specific heat flux during unilateral heating at temperatures of the electrically heated metal band equal to 100, 120, and 140 ºC aimed at plasticizing and bending of the details in the production of outside curved parts of the body of string musical instruments. The obtained results can be used for technological and energy calculations and for analysis of processes of unilateral heating of wood details at different boundary conditions, as well as in software for systems for model based automatic control of such processes aimed at bending of the heated and plasticized details.Autori u radu daju prijedlog metodologije za matematičko modeliranje i istraživanje dvaju međusobno povezanih problema: raspodjele temperature u smjeru debljine ravnih drvenih elemenata izloženih jednostranom zagrijavanju i potrošnje energije tog procesa. Za realizaciju metodologije izrađen je jednodimenzionalni matematički model i riješen za linearni tok topline pri provođenju topline u ravnim drvenim elementima za vrijeme njihova proizvoljnoga jednostranog zagrijavanja, s početnim i rubnim uvjetima koji se mogu susresti u praksi. Na temelju integracije rješenja modela, predložena je numerička metoda za izračunavanje specifi čne potrošnje energije (za 1 m2) i specifičnoga toplinskog toka potrebnoga za zagrijavanje elemenata i za nadoknađivanje emisije topline u okolinu za vrijeme jednostranoga grijanja radi plasticiranja i lakšeg savijanja drva. U radu su prikazana rješenja modela koja se odnose na nestacionarnu raspodjelu temperature smrekovih elemenata debljine 6, 8 i 10 mm po debljini i na nestacionarnu promjenu specifi čne potrošnje energije i specifičnoga toplinskog toka za vrijeme jednostranog zagrijavanja na temperature električno grijane metalne trake koje su iznosile 100, 120 i 140 °C. Elementi su zagrijavani radi plasticiranja i savijanja drvenih elemenata u proizvodnji vanjskih zakrivljenih dijelova korpusa žičanih glazbenih instrumenata. Dobiveni se rezultati mogu koristiti za tehnološke i energetske izračune i za analizu procesa jednostranog zagrijavanja drvenih elemenata u različitim rubnim uvjetima, kao i za softver za modeliranje sustava koji se temelji na automatskom upravljanju procesima usmjerenima na savijanje zagrijanih i plastifi ciranih drvenih elemenata