# What is the quantity of electric energy necessary to cool the water in a tank heated by P = 30 kW?

A pump draws cold water from the reservoir of industrial chiller and pumps it at a flow q in a 5 m3 tank filled with water. The tank has a 30 kW parasitic heat source inside (see Fig. 1). The temperature of the environment is 30°C, both around the water chiller and the tank. The heat absorbed from the environment by the tank of the water chiller and the heat radiated/absorbed to/from the environment by the tank with the heat source are considered negligible.

Fig. 1. Tank filled with water heated by a parasitic source and cooled by an industrial chiller.

Question 1: How much electric power the chiller has to draw from the grid to maintain the temperature of the water in the tank constant?

Question 2: Assuming that the initial temperature in the tank was 30°C, what is the power absorbed by the chiller from the grid to lower the temperature in the tank to 4°C in 3 hours?

I have arrived at a formula for the temperature inside the tank (see the calculations below) but I do not know if it is correct. Anyway, the enormous amount of power the chiller has to draw from the grid is discouraging.

Note: I mention that I do not know what assumptions I have to make regarding the efficiency of the industrial chiller which is a water refrigerator. In the calculations above I took it as one.

• chillers/air conditioners move more heat than they consume in electricity. Also, you will have trouble getting water to 4 C without some type of glycol system, otherwise the coils would freeze. Commented Jun 19, 2022 at 22:49
• @TigerGuy , I am in a case where all over the place, indoors and outdoors, the temperature of the environment is 30 C. Had the outdoors temperature had been 2 C, it would have been possible to cool the water in the tank just by installing an outdoor radiator and then, with a small pump (say 1 kW or less), forcing the water in the tank into the radiator and back into the tank. However, in my case, how can I extract those 30 kW generated by the parasitic source of heat by consuming less than 30 kW of electricity with the chiller? Commented Jun 20, 2022 at 3:01
• Commented Jun 20, 2022 at 5:34
• Heat exchanger efficiency see Heat Transfer by J.R. Simonson Commented Jun 20, 2022 at 6:18
• @SolarMike , I would not have opened this topic had the comments of engineering.stackexchange.com/q/51329/10902 furnished an answer for my current question. However, the book " Heat Transfer by J.R. Simonson" is useful. I will read it. Commented Jun 20, 2022 at 6:19