When is a Cubic Foot Not a Cubic Foot?
November 1, 2006
We all know that in convection ovens and furnaces, air is heated by a burner or electrical elements and then is pushed or pulled over and through the workload by a circulating fan. Coming into contact with the workpieces, the air transfers some of its heat to the product before going out the exhaust or being recirculated to the heating chamber. It’s a pretty straightforward process, but how do oven designers figure how much circulating airflow is needed?
There are two major considerations -- the rate of heat transfer and the temperature uniformity in the load -- and they have to be balanced against each other if the oven or furnace is to perform successfully. Before I get into greater detail, though, I’ll look at air and its heat content at elevated temperatures, with particular attention to how the airflow is measured. Overlooking this has occasionally been the cause of design errors, resulting in ovens and furnaces that didn’t perform up to expectations.
The most reliable way to measure the heat content of air is by expressing it in BTU per pound of air, because a pound is a pound, regardless of the air temperature. Visualizing, let alone measuring, airflow in pounds per hour is difficult, so we fall back to units of volume, cubic feet per minute or cubic feet per hour, because they’re easier to relate to oven volumes and air changes and to pressure differentials that can be used to estimate flow. This is where the problems crop up. We often see flows expressed in standard cubic feet (scf), actual cubic feet (acf), or simply cubic feet (cf). What’s the difference?
Scf is the volume of air measured at so-called standard conditions -- ambient temperature and sea level barometric pressure (29.92 inches or 760 mm of mercury). Here’s where another problem comes up -- there’s no universal agreement on which ambient temperature to use: 60oF, 70oF, 25oC and even 0oC are used in various situations. This is important to know if you’re calculating conversions, but for this discussion, I’ll use 60oF (15.5oC). At 60oF and sea level pressure, one standard cubic foot of air weighs 0.0765 lb, or, looking at it the other way, one pound of air occupies 13.07 ft3. There is a fixed relationship between the weight and volume, so you can use standard cubic feet as another way of expressing weight flow.
When air is heated, it expands and becomes less dense. At 400oF (204oC), a cubic foot of air now weighs only 0.0463 lb, and one pound of air now occupies 21.6 ft3. This upsets that nice weight-to-volume relationship, so you have to specify the air temperature to correct for the difference in density. You do this by expressing the air volume in actual cubic feet (acf), along with the temperature at which the volume or flow rate was measured. The trouble starts when we simply use cf without specifying the reference temperature. This is a meaningless term because we can’t be sure how it relates to weight flow.
All right -- now you can figure how much air you need to do a specific heating job. Because circulating airflows are usually described in cubic feet per minute, we’ll express everything on a per minute basis. We’ll also assume the oven design permits the desired rate of heat transfer at the flow we select.
So, suppose you have to heat a load at a rate of 2,400,000 BTU/hr -- that’s 40,000 BTU/minute. Maximum load temperature is 300oF (149oC), and we decide to heat the incoming air to 400oF (204oC) and let it leave the work area at no less than 350oF (176oC). That gives us a 50oF (28oC) temperature differential to work with. How much air do we need?
The specific heat of air at 400oF is 0.244 BTU/lb-oF, so we can calculate the weight flow of air:
Airflow = 40,000 BTU/min ÷ (0.244 BTU/lb-oF x (400 - 350oF)) = 3,279 lb/min
That’s equal to
3,279 lb/min ÷ 0.0765 lb/ft3 = 42,859 scfm
So, you go out and buy a fan rated at around 43,000 scfm, right?
Nope. At a given speed, a fan will move roughly the same volume of air, hot or cold, so our 43,000 scfm fan is also a 43,000 acfm fan. When it’s handling 400oF air, it will be moving only 1,991 lb/minute, and that’s not enough to do the job. One of two things will happen -- either the heating rate will suffer (24,191 BTU/min), or the air temperature will decrease more than we specified, in this case, 82oF (45oC).
One way out is to raise the incoming air temperature higher than 400oF, but that may expose you to product overheating, if you’re lucky enough to have extra heat input capacity and can get a higher heat transfer rate to the product. To do it right, you have to oversize the fan -- at least 70,855 scfm. This will offset the natural downrating that takes place when the air is heated.
This little sizing exercise also points out the tradeoffs you have to make between airflow and temperature uniformity. If you want no more than, say, a 25oF (14oC) temperature drop in your heated air, you have to use a fan with double the flow capacity. This is the fact that underlies that oft-made statement, “If you want tighter temperature uniformity, you have to use more airflow.”