Chilled Water Coil – Confusion About Delta T and Heat Transfer

[Josef M.]

Hi everyone,

I'm a mechanical engineer currently working as a site manager. From time to time, I need to do some HVAC-related calculations, and this particular one is driving me a bit crazy.
I'm hoping someone can help me understand what I'm missing here.

I have a chilled water coil system with inlet and outlet water temperatures, as well as air-side inlet and outlet temperatures across the evaporator.
Here's what's confusing me:
If the chiller lowers the absolute temperature of the water but keeps the ΔT (temperature difference) the same, the amount of heat removed (Q) stays the same—assuming a constant water flow rate.

For example, with water going from 10°C in to 12°C out or from 20°C in to 22ºC out, the heat transfer comes out the same. That doesn’t seem intuitive to me, especially if the air temperature around the coil is constant.
So my questions are:

• How is it possible for the same amount of heat to be removed in both cases, assuming the environment and airflow are the same?
• Why don’t we consider the air temperature around the coil in these calculations?
• If the surrounding air is, say, 25°C, wouldn’t colder water remove more heat due to a larger temperature difference, even with the same ΔT? Shouldn’t that mean you’d need less water flow to achieve the same Q? How is the same flow, with lower temperatures removing the same heat? if the temperature difference is bigger to outside, and the time that water goes through is the same, how can it be that the Q removed is the same?

Sorry if this is a silly question—it’s more about curiosity than an urgent issue. I'd really appreciate any insights.

Thanks!

 

[Btutiful]

1. How is it possible for the same amount of heat to be removed in both cases, assuming the environment and airflow are the same? Your intuition is correct here, in that not all substances will transfer heat at the same rate when it's cold vs. when it's hot. The generic heat transfer equation that is used usually looks like: Q = mdot*cp*(T1-T2). However, this equation is derived assuming cp (specific heat, or the amount of heat necessary to change a substance's temperature by a single degree) is constant. In your application, water has a pretty stable cp across the temperatures you are working with, which is why a temperature difference between 10°C - 12°C and 20°C - 22°C will give you the same heat transfer from/to the water with a very small error.
2. Why don't we consider the air temperature around the coil in these calculations? It really all just depends on what you want to keep constant or what the system inherently adjusts. For example, in a chilled water system, your biggest concern is getting that water temperature where you want it. So, you will calculate the heat the water needs to give up in order to drop the temperature to that point. This same amount of heat then goes to your air (through whatever process is used). At this point, this no longer affects your chilled water system per se, but if you have to pick out the chiller that is making this heat transfer or you have to design the chiller itself, then the calculations for air temperature do become important. If you slow down the flow of air, the temperature difference for your air will be larger and vice-versa. (This is assuming dry air.) However, if air is the important temperature for your system, then this process would work the same way, but backwards.
3. If the surrounding air is, say, 25°C, wouldn't colder water remove more heat due to a larger temperature difference, even with the same ΔT?... Not with the same temperature difference, no. Colder water, by intuition, does remove more heat, but that is only because you have adjusted the temperature difference. If you try to remove heat with water at 20°C and the water gets to 25°C, then you try it with 15°C water, the rate of transfer will be the same, but now you can heat the water 10 degrees instead of 5. So more heat in total can be removed, but the rate stays the same. There are some assumptions made here as well, though. One of which is that the heat exchanging method used doesn't see a change in its heat transfer coefficient because of a change in temperature (kind of similar to the cp thing). Ultimately, if you are talking about Q as in heat flow rate, then no it doesn't change, but if you are talking about Q as in total heat, then without getting into specifics yes, it would change.

Hope this helps!