Acta Montanistica Slovaca Ročník 3 (1998), 2, 137-142 Mathematical model of thermal aggregates Imrich Pokorný 1 a Karol Kostúr 1 Matematický model tepelných agregátov Tepelné agregáty môžme charakterizovať jako priemyselné pece s veľkou spotrebou energie. Jednou z možných ciest zníženia spotreby energie je optimalizácia a priebežné riadenie priemyselných tepelných agregátov pomocou simulačných modelov. Východiskom pre tvorbu simulačných modelov je matematický model. Matematické modelovanie tepelných procesov je založené na riešení parciálnych diferenciálnych rovníc a nelineárnych algebraických rovníc popisujúcich základné procesy prenosu tepelnej energie. V príspevku je popísaná základná metodika tvorby matematického modelu zónovou metódou vrátane efektívneho riešenia. Prínosom príspevku je rozpracovanie analytického postupu riešenia nelineárneho systému bilančných rovníc, ktorého použitie značne urýchľuje priebeh simulácie v porovnaní s numerickým riešením. Introduction Industrial furnaces belong to the group of the biggest appliances of energy and their heating regime influence of quality of metallurgical semi-products. For this reason it is necessary to optimize the design of heat aggregates. One of effective ways to design a new heat aggregate or to reconstruct the old heat aggregate is simulation (Dvořáček et al., 1990). The creation of simulation models requires high-professional knowledge of the furnace’s heattechnics and considerably programmable capacity. For the creation of simulation models is needed typically long time, which is often in contradiction with the requirements of users. This contradiction leads to abandoning traditional simulation models as effective tool to construct heat aggregates. Mathematical models of processes play an important role more and more in our time and they have a very important place as a software of Automated System of Coíntrol of Technological Processes (ASC TP). We can realise the control of processes more effectively because of the predicting property of the model. The purpose was to obtain the mathematical model of heating of batches in such a way that it makes possible optimisation of heating. As a fuel we can use a mixed gas, which is composite by earth gas, coke gas and gas from blast-furnace. Input of fuel is shown on the Fig. 1 as a vertical arrow. The worked area of furnace we divided on the smaller part - modules. There are usually two modules together - top and bottom. We suppose the homogenity of processes in module. Then e.g. the temperature of fire and walls of furnace is constant in module. In the module each batch is described by one-dimensional thermal field, if it is possible. ⇐ Fig.1. Scheme of pairs of modules. Model of combustion By stechiometric calculations we can define structure and quantity of fuel in the modules. Volume flow of combustion products in the i-th module can be given by following 1 Karol Kostúr, Assoc.Prof., PhD. and Imrich Pokorný, Dr. univ., PhD. Department of Management and Control Engineering, Faculty of Mining, Ecology, Process Control and Geotechnologies, 042 00 Košice, Boženy Němcovej 3, Slovakia (Referees: Imrich Koštial, Prof., PhD. and Vladimír Strakoš, Prof., PhD., accepted in revized form April 29, 1998) 137