Dynamic Thermal Modeling of a Hydronic Heating System

A refined thermal model is presented to describe both the early-stage behavior and the dynamic temperature response of cast iron radiators during heating system operation. In the initial phase, the radiator is conceptually subdivided into three thermally distinct subdomains: the region progressively filled with hot water due to fluid motion, the cast iron wall, and a complementary zone where the fluid remains at its initial (ambient) temperature. Once the radiator is filled with hot fluid, this early stage concludes; however, a downstream adiabatic "short volume" is introduced to account for the delay observed in the outlet temperature rise associated with the fluid transit time through the radiator. The proposed modeling framework offers a physically sound and computationally efficient strategy to simulate both start-up transients and the longer-term dynamic thermal response of radiator-based heating systems.