Practical aspects of heat conduction simulation in household heating optimization tasks

Abstract

Mathematical model selection for simulation heat conduction processes in household heating optimization task is considered. The essence of the matter is that the heat transfer dynamics properties are very diversified, so simulation procedure formulae and parameters should be properly selected to avoid excessive modeling errors with reasonable calculation time being held. The typical state-space model and analytical formulae for step response of the heat conduction across a homogeneous wall are presented and compared in terms of modeling errors. Formal and numerical problems of heat losses simulation are discussed. Semi-analytical step-response formulae for multilayer walls are derived and their accuracy is compared with effects of simulation based on the state-space model. Some recommendations for time and space discetization parameters are given.