Equilibrium temperature of heat exchanger

[Escheresh]

In a closed loop with a heater and a fan cooled finned heat exchanger where water flows between the two, is it right to assume that the water will reach an equilibrium temperature?
If so, is there an equation that can get the equilibrium temperature?
The power of the heater and cooler, the flow rate, volume of water and initial temperature are known.

 

[KLoux]

I don't think the system will reach an equilibrium temperature, but it can reach an equilibrium state.

If the water doesn't boil, we can assume it has a constant specific heat, and I don't know what your specifics are, but it might also be safe to assume that the heat flux from the heater is a constant. If this is true, then the temperature rise of the water between the inlet and outlet of the heater is a constant.

So, if everything is at ambient temperature before you "switch it on," the water will start to flow and the water leaving the heater will be at some elevated temperature (ambient temperature + some constant temperature rise). The efficiency of the heat exchanger depends on the difference in temperature between ambient air and the water, so it might not (probably will not) be cooled back to ambient temperature. After several passes, the water might be hot enough that the temperature drop at the heat exchanger is equal to the temperature rise at the heater, so now your system is at its equilibrium state. But the water is still changing temperature.

-Kerry