Heating/cooling a volume of air.

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Discussion Overview

The discussion revolves around the heating and cooling of air within two different box sizes, focusing on the time required to change the air temperature from 60F to 80F and potentially to 90F or cool to 50F. Participants explore the implications of box volume, heating mechanisms, and the influence of air circulation on temperature change.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant seeks a formula to determine the heating time for a larger box, noting that the relationship is not linear due to the volume differences.
  • Another participant emphasizes the need for additional information regarding the dominant heat transfer mechanism (natural convection, forced convection, or radiation) to apply the correct formula.
  • A different participant calculates that the second box's volume is 27 times larger than the first, suggesting it would take approximately 27 times longer to heat, while also noting potential heat losses due to surface area.
  • One participant proposes a formula involving specific heat, volume, and heater power, but cautions that the same equation cannot be applied to cooling without more information.
  • Another participant provides additional context about the air dispersion rate from a fan and attempts to calculate heating times for both boxes, while acknowledging that existing air temperature affects these calculations.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between box volume and heating time, with some suggesting a linear relationship while others argue against it. There is no consensus on the appropriate formula for cooling scenarios, and the discussion remains unresolved regarding the exact impact of various factors on heating and cooling times.

Contextual Notes

Limitations include assumptions about insulation, the specific heat of air, and the need for clarity on the heat transfer mechanism. The calculations presented do not fully account for the existing temperature of the air in the boxes.

Who May Find This Useful

This discussion may be of interest to individuals exploring thermodynamics, heat transfer principles, or practical applications in HVAC systems and thermal management.

rolinger
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I have a box that is 5'w x 5'l x 3.3'h and the air temperature within the box is 60F. If I have a device that can heat the air in the box to 80F in 7 minutes, then what formula could I use to determine how long it would take that same device to heat a box exactly 3 times the size of the first box (15'w x 15'l x 10'h) from 60F to 80F?

I know its not going to be a linear (7min x 3 = 21 min) equation because larger volumes of gas or liquid take longer to cool or heat than smaller volumes.

In addition, could this same formula be applied to determine how long it would take either boxes to heat from 60F to 90F, or possibly to cool from 90F to 50F? I am hoping to find a general formula that can be applied to a variety of heating/cooling scenarios.

Thank you.
 
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You're going to need a little more information to apply the right heat transfer formula. What is the current dominant mechanism when heating the box? Natural convection? Forced convection? Radiation?
 
In simple terms (assuming the air mixes and is well insulated) it is linear.
But it is not 3x, the second box is not3 times the volume it is 27 times (3x3x3) the volume so will take 27times as long to heat the air.
In the real world there are probably losses from the surfaces which are 9 times as large so it will take a bit longer than 27x.
 
rolinger said:
I have a box that is 5'w x 5'l x 3.3'h and the air temperature within the box is 60F. If I have a device that can heat the air in the box to 80F in 7 minutes, then what formula could I use to determine how long it would take that same device to heat a box exactly 3 times the size of the first box (15'w x 15'l x 10'h) from 60F to 80F?

I know its not going to be a linear (7min x 3 = 21 min) equation because larger volumes of gas or liquid take longer to cool or heat than smaller volumes.

In addition, could this same formula be applied to determine how long it would take either boxes to heat from 60F to 90F, or possibly to cool from 90F to 50F? I am hoping to find a general formula that can be applied to a variety of heating/cooling scenarios.

Thank you.

If the heater is at a much higher temperature of the box then the power transferred per unit time should be roughly constant. In which case you can assume

\Delta T = C_p V_1 P_{heater} t_2 \Delta

\Delta T = C_p V_2 P_{heater} t_1 \Delta
C_p is the specific heat
V_1 is the volume of box 1
V_1 is the volume of box 1
\Delta T is the change in temperature.
t_1 is the time to heat box 1
t_2 is the time to heat box 2
P_{heater} is the power of the heater.

You cannot apply the same equation to cooling because you would need more information as the above poster mentioned. See:
http://en.wikipedia.org/wiki/Heat_conduction#Newton.27s_law_of_cooling
 
Last edited:
Some more info to assist the question:

I have a fan that disperses air at 8 CFM, the air is heated to 80 F.

Assuming a fully insulated box that is 5'x5'x3 = 75 Cubic Feet. Thus 75CF / 8CFM = 9.3 minutes to heat, but this basic equation doesn't take into account the existing temperature of the air in the box.

The same equation should apply to a 15'x15'x10 box. 2250CF / 8 CFM = 4.7 hours, again, not taking into account the current temperature of the box.

If the known temperature of either box is exactly 60F...this should be enough info to compute a more accurate amount of time to heat the box, right?
 

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