Water Boiler Heat-Exchanger / Thermostat Limit Cycle

[JanisErdmanis]

Dyad / ModelingToolkit model. A boiler is heated at constant power; a hysteresis thermostat runs the circulation pump when the boiler reaches the upper set-point and stops it at the lower one. Running the pump couples the boiler to a radiator that dissipates heat to ambient (P = k·(Tpipe−Touter)). Switch scenarios to see how heating power and set-point band reshape the cycle

Built with a prompt:

I would like to build a water heat exchanger system. There is a water boiler which is heated with some power and then there is a circulation pump that let's the water thtrough the piping to dissipate heat (heat the house or etc). The water pump is on the on position when certain upper termperature is reached in the boiler and in an off position when boilder temperture has some lower temperature and the cycle repaets that way. The dissipation to the outer pipes is driven by the temperature difference between the circulation pipe and the ambient temperature (soemthing like P_dissipate = k(T_pipe - T_outer)). I would like to learn more about the system. In particular how the boiler temperature depends on the time, what power is dissipated with the heat exchanging system. And would like to understand that for different on/off temprature intervals and heating powers. While the ambient temperature can be taken constant.

Ran out of credits. Still needs a model for startification of the water in the boiler and gradient in the radiator due to finite water flow.