Model

In order to study the radiator dynamics and to analyze the respective influence on the overall system behaviour, a dynamic radiator model is required. When considering the radiator from an Eulerian perspective, the radiator dynamics can be modelled according to a dynamic heat balance in which the lumped thermal capacitance is assumed to be concentrated in the exhaust temperature node. 

Psu is the thermal power supplied to the radiator and equals the net difference between the incoming and leaving heat flows as illustrated in figure below. The heat emission P_emission is described by means of the exponential relationship between the radiator performance and the logarithmic mean temperature difference
according to the 2 equations below. The exhaust temperature of the radiator changes according to the supplied thermal power and the heat emission. The exponent n_rad in the equation below determines the characteristic of the used end-unit. In case of a radiator it is (1,2 ... 1,34) and a convector (1,25 ... 1,45).