# Convective Flow due to Stack Effect

One way to ventilate a building that is hotter or colder on the inside than outside is to use what is known as "stack effect". Because of the temperature difference, the air inside the building is either more or less dense than the air outside. If there is an opening high in the building and another low in the building, a natural flow will be caused. If the air in the building is warmer than the outside, this warmer air will float out the top opening, being replaced with cooler air from outside. If the air inside is cooler than that outside, the cooler air will drain out the low opening, being replaced with warmer air from outside.

One common use for stack effect would be nighttime flushing of a building's interior, to cool it for the next day.

The rate at which air flows depends on several factors, the inside and outside air temperatures, the area of the openings, and the height difference between the top and bottom openings.

The 1997 ASHRAE Fundamentals handbook gives the following relationship:

```Q = 60 * Cd * A * sqrt(2 * g * (Hn - Hb) * ((Ti - To) / Ti))

where

Q = flow rate in cfm,
Cd = 0.65 (for unobstructed openings),
A = opening area, square feet,
Ti = indoor temp (Rankine),
To = outdoor temp (Rankine),
Hn = height of "neutral pressure point" (for simple systems, assume
1/2 way between top and bottom openings).
Hb = height of bottom opening
g = gravity.
```

To calculate flow rate, fill in the boxes below.

Area:square feet.
Height difference:feet.
Indoor Temperature:F.
Outdoor Temperature:F
Flow Rate:CFM.

For a more complete discussion of this, and especially of unusual situations, please see the discussion in the ASHRAE Fundamentals handbook.

You might want to compare the flow rates of this natural ventilation to those of forced ventilation. For example, a typical "whole house fan", available at Home Depot for \$130, is rated at 4500 CFM (but consumes about 200 watts of electricity).

Note also that for stack effect, flow rate diminishes as the ventilation proceeds, bringing the temperature difference down.

The purpose of ventilation is to flush the indoor space out with outdoor air. As the outdoor air replaces indoor air, it either adds heat to or removes heat from the inside space. Knowing the flow rate, the specific heat of air, the density of air, and the temperature difference, we can calculate the effective heating or cooling rate, and express the result in BTU per hour, or BTUH (for reference, air conditioners are often rated in "tons" of cooling capacity, one ton being 12,000 BTU per hour):

Heat Transfer Rate:BTUH, which is about Watts.

You can see that the potential for stack effect cooling is rather low, compared to mechanical refrigeration. However, it does work, has no moving parts, and requires no extra energy input. Consider it as part of a complete plan that includes a significant effort to reduce daytime heat gain (especially from the sun).

An interesting variation on this theme is the so-called "solar chimney". Imagine that at the top of the building, air flows through a duct that is heated by the sun. The added height and temperature difference could combine to significantly increase air flow, if designed carefully.

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