# How to vary, according to a given sinusoidal profile, the water temperature in a tank, independently of the temperature of the environment?

The water tank in Fig. 1, that is placed in a closed space, has a heat source inside (an experimental device) that liberates 20 to 50 kW of heat. However, the water temperature in the tank has to be kept, at each moment of time, as close as possible to the sinusoidal profile in Fig.2.

I believe that, if the outdoor temperature is between 0 and 4 C, a simple radiator placed outdoors, together with a pump whose flow can be controlled, will be enough to keep, for the water in the tank, the temperature profile in Fig. 2. However, for cases when the outdoor temperature is above 4 C some cooling is required. Also, for below zero temperatures special measures have to be taken to avoid ice formation in the heat exchanger.

Question: Can you suggest a heating/cooling system that is able to keep the temperature profile in Fig. 2 for the water in the tank?

Fig. 1. Water tank with a heat source inside.

Fig. 2. The profile of temperature the water must have at each moment of time.

If I have a suggested heating-cooling system with some relatively simple formulas, I can dimension it but I can not run a thermal analysis in ANSYS, for example.

I calculated that the experimental device in the tank, while emitting its maximum power in the water, can not heat the content of the tank with more than 10.75 C per hour or a single liter of water with more than 11.94 C/sec which means that if each second 1 liter of water is evacuated then cooled by 11.94 C and reintroduced in the vessel then the temperature of the water inside the tank can be kept constant.

UPDATE 1:

One solution would be to use a heat exchanger like the one in Fig. 3 but with the difference that the left side (labeled indoor unit) has to be placed directedly in the tank with water, not in air.

Fig. 3. Heat exchanger.

UPDATE 2:

Fig. 4 shows the working principle of the commercial heat pump (a water chiller) in Fig. 5.

As the water tank in Fig. 1, already has a heat source inside a water chiller like the one in Fig. 5 might be enough to keep the temperature profile in Fig. 2, assuming the water chiller can be somehow controlled from an external Programmable Logic Controller.

① Compressor, ② High pressure gauge, ③ Condenser, ④ Dry filter, ⑤ Expansion valve, ⑥ Water supply, ⑦ Evaporator, ⑧ Low pressure gauge, ⑨ Water tank, ⑩ Drain, ⑪ Refrigerated water, ⑫ Pump.

An efficiency issue might arise from the fact that the water in the tank with the heat source (Fig.1) has a variable pressure that can reach 6 bars and is mixed with chemicals, sand and mud in low concentrations. In other words the pump (12) can not pump directedly the water from the tank (9) of the chiller in Figs. 4 and 5 into the tank with the heat source, but through a serpentine (a heat exchanger), connected to the output - input (11), and placed in the tank in Fig.1. I do not know how much energy will be lost by applying this trick with two cascaded heat exchangers.

• As close as possible- how much power are you willing to put into heating and cooling? Calculate from the thermal mass what you would need in order to make it follow your curve assuming no input from environment. Then add on worst case environmental inputs- insolation temperature outside, etc heating and cooling against what you want. Finally, double it for a factor of safety and go purchasing and installing refrigeration and heating equipment according to those numbers.
– Abel
Jun 11, 2022 at 23:14
• @Abel , I added to my question some simple calculations I made. However, I can not run complex thermal analysis in ANSYS, for example, so what I am asking for is a heating / cooling system already designed that might work in my case with simple adjustments. I can not design such heat exchangers from zero, especially for the case when a refrigeration device is needed. The electric energy I want to consume for keeping the temperature profile in Fig. 2 is, of course, the minimum possible as long as 1 kW costs 0.35 Euro. Jun 11, 2022 at 23:50
• Use a heatpump to get reject the heat - that takes care of the external temperature. Check your simulation model for dimensions units etc - any error will be one you made. Jun 12, 2022 at 6:41
• @SolarMike , From what I see on the net, a heat pump heats or cool the air in a building (see: youtu.be/14MmsNPtn6U?t=54 ). In my case the water in a tank has to be directedly cooled or heated not the air in the room where the tank is placed. Jun 12, 2022 at 14:33
• Heatpumps can take heat from below the ground to add to a tank of water, which is why I suggested it, perhaps you should check out variations of not only air : air, but air : water, water : air and water : water. Jun 12, 2022 at 14:36