## Convective Heat Transfer: How Do We Use It?

Vortex Tubes have been studied for decades, close to a century. These phenoms of physics and the theory behind them have been discussed on this blog before. Many customers gravitate toward Vortex Tubes when needing parts and processes cooled. The fact of the matter is there is still more to be discussed on how to correctly select the which product may be needed in your application. The reason being, area, temperatures, and air flow volumes play a large role in choosing the best product for cooling. The tendency is to say, well I need to cool this down as far as possible so I need the coldest air possible which leads to the assumption that a Vortex Tube will be the right solution. That isn’t always the best option and we are going to discuss how to best determine which will be needed for your application. The first step, is to call, chat, or email an Application Engineer so that we can learn about your application and assist with the implementation of the Vortex Tube or other cooling product for you. You may also want to try and take some initial readings of temperatures. The temperatures that would help to determine how much cooling is going to be needed are listed below:
• Part temperature
• Part dimensions
• Part material
• Ambient environment temperature
• Compressed air temperature
• Compressed air line size
• Amount of time desired to cool the part: Lastly desired temperature

With these bits of information, we use cooling equations to help determine what temperature and volume of air will best suit your needs to generate the cooling required. One of the equations we will sometimes use is the Forced or Assisted Convective Heat Transfer. Why do we use convective heat transfer rather than Natural Heat Transfer? Well, the air from EXAIR’s Intelligent Compressed Air Products® is always moving so it is a forced or assisted movement to the surface of the part. Thus, the need for Convective Heat Transfer.
Calculation of convection is shown below: q = hc A dT Where: q = Heat transferred per unit of time. (Watts, BTU/hr) A = Heat transfer area of the surface (m2 , ft2) hc= Convective heat transfer coefficient of the process (W/(m2°C), BTU/(ft2 h °F) dT = Temperature difference between the surface and the bulk fluid (compressed air in this case) (°C, °F)

The convective heat transfer coefficient for air flow is able to be approximated down to hc = 10.45 – v + 10 v1/2

Where: hc = Heat transfer coefficient (kCal/m2 h °C) v = relative speed between the surface of the object and the air (m/s)

This example is limited to velocities and there are different heat transfer methods, so this will give a ballpark calculation that will tell us if we have a shot at a providing a solution.  The chart below is also useful to see the Convective Heat Transfer, it can be a little tricky to read as the units for each axis are just enough to make you think of TRON light cycles. Rather than stare at this and try to find the hidden picture, contact an Application Engineer, we’ve got this figured out.

1 – Engineering ToolBox, (2003). Convective Heat Transfer. [online] Available at: https://www.engineeringtoolbox.com/convective-heat-transfer-d_430.html [02/10/2021]

## Battling Heat Transfer

If you haven’t read many of my blogs then this may be a surprise. I like to use videos to embellish the typed word. I find this is an effective way and often gives better understanding when available.  Today’s discussion is nothing short of benefiting from a video.

We’ve shared before that there are three types of heat transfer, more if you go into sub-categories of each. These types are Convection,  Conduction, and Radiation. If you want a better understanding of those, feel free to check out Russ Bowman’s blog here.  Thanks to the US Navy’s nuclear power school, he is definitely one of the heat transfer experts at EXAIR.  If you are a visual learner like myself, check out the video below.

The Application Engineering team at EXAIR handles any call where customers may not understand what EXAIR product is best suited for their application. A good number of these applications revolve around cooling down a part, area, electrical cabinet, or preventing heat from entering those areas.  Understanding what type of heat transfer we are going to be combating is often helpful for us to best select an engineered solution for your needs.

Other variables that are helpful to know are:

Part / cabinet dimensions
Material of construction
External ambient temperature
If a cabinet, the internal air temperature
Maximum ambient temperature
Desired temperature
Amount of time available
Area to work with / installation area

Understanding several of these variables will often help us determine if we need to look more towards a spot cooler that is based on the vortex tube or if we can use the entrained ambient air to help mitigate the heat transfer you are seeing.

If you would like to discuss cooling your part, electrical cabinet, or processes, EXAIR is available. Or if you want help trying to determine the best product for your process contact us.

Brian Farno
Application Engineer
BrianFarno@EXAIR.com
@EXAIR_BF

Video Source: Heat Transfer: Crash Course Engineering #14, Aug 23, 2018 – via CrashCourse – Youtube – https://www.youtube.com/watch?v=YK7G6l_K6sA

## What Is A Btu?

A Btu, or British Thermal Unit, is a traditional unit of energy and is a measure of the heat content of fuels.

Originally, the Btu was the amount of energy needed to increase the temperature of 1 pound of liquid water by 1 degree Fahrenheit.  The term became common among engineers in the late 1800’s.

A single Btu is insignificant in terms of the amount of energy used by a single household or by an entire country. In 2013, the United States used about 98 quadrillion (written out, 1 quadrillion is a 1 followed by 15 zeros) Btu of energy.

One Btu is approximately equal to the energy released by burning a match.

Interesting Energy Conversion Factors

 Energy source Physical units and Btu (averages,¹ 2012) Electricity 1 kilowatt hour = 3,412 Btu Natural gas 1 cubic foot = 1,025 Btu Motor gasoline (10% ethanol) 1 gallon = 120,524 Btu Diesel fuel 1 gallon = 138,690 Btu Heating oil 1 gallon = 138,690 Btu Propane 1 gallon = 91,333 Btu Wood 1 cord = 20,000,000 Btu (Estimated)

1Weighted averages across different contexts of each fuel such as imports, exports, production, and consumption. Source:  www.eia.gov/EnergyExplained by the U.S . Energy Information Administration

EXAIR manufactures the Cabinet Cooler System.  The Cabinet Cooler System is a low cost, reliable way to cool and purge electronic control panels.  They incorporate a vortex tube to produce cold air from compressed air – with no moving parts! EXAIR Cabinet Cooler Systems are available for NEMA 12, 4, and 4X type enclosures.  For the most efficient way to operate Cabinet cooler, a thermostat control system would be utilized. The standard thermostat control systems include an adjustable thermostat factory set at 95F.  Also, available is the ETC Electronic Temperature Control, providing precise control with easy adjustability and a digital readout.

In the United States, the power of HVAC (Heating Ventilating and Air Conditioning) systems is often expressed in BTU/hr.

The EXAIR Cabinet Cooler Systems are available with cooling capacities ranging from 275 to 5,600 Btu/hr.  To cool the down the equivalent of 98 quadrillion Btu’s of energy used by the US in 2013, it would take 17.5 trillion of our largest Cabinet Cooler Systems!

If you would like to find out how many Btu’s of cooling your electrical cabinet needs, please fill out and send in the Cabinet Cooler Sizing Guide and we can let you know.

Brian Bergmann
Application Engineer
Find us on the Web

Match Photo courtesy of Samuel M. Livingston via Creative Commons License

## The Effect of Back Pressure on a Vortex Tube Part 2, Calculating Btu/Hr.

My previous blog post was about how Vortex Tubes react when there is back pressure due to a restriction on either the hot or cold discharge of the Vortex Tube.  In it I mentioned that there is a formula to calculate what the cooling capacity (Btu/Hr) will be if there is no way to avoid operating the Vortex Tube without back pressure on the discharge. That is the calculation focus of this blog – calculating Btu/hr of a Vortex Tube with back pressure.

To continue with the same example, the calculations from the previous blog are shown below.  Last time the example Vortex Tube was operating at 100 psig inlet pressure, 50% cold fraction, and 10 psi of back pressure. We will need some additional information to determine the Btu/Hr capacity. The additional information needed is the temperature of the supplied compressed air as well as the ambient air temperature desired to maintain.  For the example the inlet compressed air will be 70°F and desired ambient air temperature to maintain will be 90°F.

(100 psig + 14.7 psia) / (10 psig + 14.7 psia) = X / 14.7 psia
4.6437 = X / 14.7
X= 14.7 * 4.6437
X = 68.2628
(Values have been rounded for display purposes)

The calculation above gives the compensated operating pressure (X = 68.2628) which will be needed for the BTU/hr calculation. The rated air consumption value of the Vortex Tube will also need to be known.  A 30 SCFM rated generator will be used for this example, the normal BTU capacity of a Vortex Tube with a 30 SCFM generator is 2,000 BTU/hr.

First, determine the new consumption rate by establishing a ratio of the compensated pressure (68.2628 psi) against the rated pressure (100 psi) at absolute conditions (14.7 psia).

(68.2628 PSIG + 14.7 (atmospheric pressure)) / (100 PSIG (rated pressure) + 14.7) = .7233
.7233 x 30 SCFM  = 21.7 SCFM Input

Second, the volumetric flow of cold air at the previously mentioned cold fraction (50%) will be calculated.  To do this multiply the cold fraction setting (50%) of the Vortex Tube by the compensated input consumption (21.7 SCFM) of the Vortex Tube.

50% cold fraction x 21.7 SCFM input = 10.85 SCFM of cold air flow

Third, the temperature of air that will be produced by the Vortex Tube will need to be calculated.  For this consult the Vortex Tube performance chart which is shown below. To simplify the example the compensated operating pressure (68.2628 psi) will be rounded to 70 psig and to obtain the 70 psig value the mean between 80 psig and 60 psig performance from the chart will be used.

For the example: A 70 psig inlet pressure at 50% cold fraction will produce approximately an 88°F drop.
Fourth, subtract the temperature drop (88°F) from the temperature of the supplied compressed air temperature (70°F).

70°F Supply air – 88°F drop = -18°F Output Air Temperature

Fifth,  determine the difference between the temperature of the air being produced by the Vortex Tube (-18°F) and the ambient air temperature that is desired (90°F).

90°F ambient – -18°F air generated = 108°F difference.

The sixth and final step in the calculation is to apply the answers obtained above into a refrigeration formula to calculate BTU/hr.

1.0746 (BTU/hr. constant for air) x 10.85 SCFM of cold air flow x 108°F ΔT = 1,259 BTU/hr.

In summary, if a 2,000 BTU/hr. Vortex tube is operated at 100 psig inlet pressure, 50% cold fraction, 70°F inlet air to maintain a 90°F ambient condition with 10 psi of back pressure on the outlets of the Vortex Tube the cooling capacity will be de-rated to 1,259 BTU/hr.  That is a 37% reduction in performance.  If a back pressure cannot be avoided and the cooling capacity needed is known then it is possible to compensate and ensure the cooling capacity can still be achieved.  The ideal scenario for a Vortex Tube to remain at optimal performance is to operate with no back pressure on the cold or hot outlet.

Brian Farno
Application Engineer Manager
BrianFarno@EXAIR.com
@EXAIR_BF