We consider that only conduction plays an important role in the heat transfer between neighbor elements. Energies transferred to the inferior element and from the superior element within a time step (p) are:

3.1 Energy input from the electrical heater

The auxiliary electrical heater has a 2kW power. Experiments showed that during heating water in the tank is mixed up in the entire volume just above the heater. We consider in this model that all elements are brought at the same temperature after one time step of electrical heating. Thus, the set-up temperature is reached by all elements above the heater in the same time, after one time step or more. If during a time step of heating the hot water temperature might rise above the set-up temperature, the electrical heater will stop even if the time step is not over.