An inverse method based on CFD to determine the temporal release rate of a heat source in indoor environments

Highlights: • An inverse strategy can be used to determine the temporal release rates of a heat source from only one sensor. • Tikhonov regularisation coupled with least-squares optimisation is analysed. • The convolution integral with a thermal response factor is used to accelerate the computations. - Abstract: The rapid and precise determination of the heat flux of a heat source is crucial to the creation of a comfortable thermal environment. Current inverse models can determine the heat flux of the heat source but cannot quantitatively determine its temporal release rates. This paper presents an inverse modelling procedure that combines Tikhonov regularisation and least-squares optimisation using computational fluid dynamics (CFD) to quantify the temporal release rate of a heat source based on information about temperature at a monitored point. To accelerate the computational procedure, the cause-effect relation between the target temperature and the heat source is described by an energy transport matrix. The energy transport matrix is expressed as a series of thermal response factors. The temperature response due to arbitrary release from a heat source can be expressed as the convolution integral of the temporal release and the thermal response factor for a unit impulse release. The proposed method is applied to determine the temporal release rates of a heat source in a three-dimensional cavity. The results show that the inverse method can accurately and efficiently determine the temporal release rates of a heat source in indoor environments by providing a temperature time-series at a monitored point. The errors between the inversely determined release rates and the actual release rates are 31%.