Calculating Cooling Time for a Large Building

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Discussion Overview

The discussion revolves around calculating the cooling time for a large building, specifically how to determine the time required to cool a 60'X60'X50' structure filled with outside air from 96°F to 65°F using 14,250 CFM of supply air at 55°F. The conversation explores theoretical and practical approaches to this problem, including the application of Newton's Law of Cooling and concepts of thermal mass and airflow efficiency.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • Some participants note the complexity of the cooling calculation due to factors like thermal mass and airflow efficiency.
  • Newton's Law of Cooling is mentioned as a potential method for estimating cooling time, but its application may not fully account for airflow.
  • One participant suggests that the situation simplifies to a dilution scenario, involving a weighted average of temperatures.
  • Another participant expresses uncertainty about how to apply Newton's Law of Cooling and the concept of weighted averages.
  • The equation T(t)=T_a + (T_o - T_a)e^(-kt) is referenced, but its connection to the cooling process remains unclear to some participants.
  • There is a suggestion to perform calculations in one-minute increments to determine the temperature after each mixing interval.
  • Participants discuss the need to sum the number of intervals to find the total time to reach the desired temperature.

Areas of Agreement / Disagreement

Participants express varying levels of understanding regarding the application of Newton's Law of Cooling and the concept of weighted averages. There is no consensus on how to effectively integrate these concepts into a solution for the cooling time calculation.

Contextual Notes

Participants highlight limitations in their understanding of how airflow impacts cooling and the specifics of calculating weighted averages. Some assumptions about the system's behavior and the definitions of terms used remain unresolved.

Who May Find This Useful

This discussion may be useful for individuals interested in HVAC systems, thermal dynamics, or those involved in real-life projects requiring cooling calculations for large spaces.

mknott
How do you calculate the time to cool down a 60'X60'X50' building filled with outside air at 96°F to 65°F with 14,250 CFM of supply air at 55°F?
 
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mknott said:
How do you calculate the time to cool down a 60'X60'X50' building filled with outside air at 96°F to 65°F with 14,250 CFM of supply air at 55°F?
This is a surprisingly difficult question because you have to consider the thermal mass of the building and it's contents and how efficient the airflow is. If you just want a rough estimate of how fast it can cool the air, Newton's law of cooling (or the dilution/mixing equation) can be solved numerically in a spreadsheet in about 30 seconds...
 
So, what is the Newton's Law of Cooling equation and how would you solve this problem with it?
 
mknott said:
So, what is the Newton's Law of Cooling equation and how would you solve this problem with it?
Is this homework or a real life situation? Either way, we like to teach here rather than spoonfeed, so you should be able to take partial answers and nudges in the right direction and move them along yourself...

With that in mind, note the late edit to my post. In this situation, Newton's Law of cooling simplifies to a dilution situation. Dilution is just a weighted average. Do you know how to calculate a weighted average?
 
This is a real life project. I've looked up Newton's Law of Cooling, but what I was seeing was it doesn't take into account air flow. I'm not sure what you are talking about in how it simplifies to a dilution situation. I'm not sure how to calculate weighted average either.
 
This is the equation I was looking at: T(t)=T_a + (T_o - T_a)e^(-kt)
 
mknott said:
I'm not sure how to calculate weighted average either.
A weighted average is the amount of air at one temperature plus the amount of air at another temperature divided by the total amount of air.
(V1T1+V2T2)/V3=T3
 
So, how does the weighted average pertain to the equation above? I still have two variables that are unknown.
 
mknott said:
So, how does the weighted average pertain to the equation above? I still have two variables that are unknown.
Just use the weighted average. You have only one unknown; the temperature after each mixing interval(T3). Do a series of 1 minute increments using that equation and you'll get your answer.
 
  • #10
So once I calculate all the temperatures after each interval until I reach the desired 65F, how then am I able to calculate the time to get to that temperature? Sorry if I'm not understanding you correctly.
 
  • #11
mknott said:
So once I calculate all the temperatures after each interval until I reach the desired 65F, how then am I able to calculate the time to get to that temperature? Sorry if I'm not understanding you correctly.
Each interval is 1 minute, so you add up the number of intervals (number of calculations). The fact that the same calculation gets repeated several times is why a spreadsheet works so well...
 
Last edited:
  • #12
Ok, I understand. Thank you for your help.
 

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