## Build, then Design, then Regret

I have to admit that I only looked at the design of the air exchanger after building two complete units (Air Exchanger and Air Exchanger Again!). If I had done so beforehand I may (would) have done things differently. As it turned out, the thickness of the channels that the air runs through is the main driver for heat transfer efficiency since conduction through the air stream is the bottleneck. Using 2mm thick coroplast, rather than the 4mm material I used would have allowed for a more compact design without losing efficiency.

## Background

The exchanger passes air being vented out of the van and air being drawn into the van through channels that are on opposite sides of a thin barrier. I got the idea from the build it solar site. The exchanger allows some of the heat from the inside air to travel to the incoming air, warming it up before it enters the van. To obtain a large surface area, a stack of thin channels is assembled with hot air and cold air channels alternating. This allowed my larger exchanger to contain 24 sq. ft. of heat transfer area in a core that measures 7" x 14" x 6".

The main design consideration is the surface area available for heat transfer. A second consideration is the cross-sectional area that the air has to flow through. Too small a surface area and little heat exchange will occur. Too small a cross-sectional area and it will be hard to push much air through.

The air exchangers I built both have a two stage cross-flow design. This is due mostly to the space that it fits into and the location of the air inlets and outlets. There is an efficiency advantage to this design as well, since it allows for a higher average temperature difference between air streams, increasing the total heat transfered.

The main design consideration is the surface area available for heat transfer. A second consideration is the cross-sectional area that the air has to flow through. Too small a surface area and little heat exchange will occur. Too small a cross-sectional area and it will be hard to push much air through.

The air exchangers I built both have a two stage cross-flow design. This is due mostly to the space that it fits into and the location of the air inlets and outlets. There is an efficiency advantage to this design as well, since it allows for a higher average temperature difference between air streams, increasing the total heat transfered.

The main factors that determine the exchanger design are the space available, and the materials available. Because I wanted to fit the exchanger on the bathroom ceiling there was a hard size constraint, and because I was using readily available 4 mm coroplast as the exchanger material this defined the channels through which the air would flow. However, it helps to run the numbers to see what kind of performance you can get from slightly different configurations and sizes.

## Calculations

I initially hesitated on doing the actual heat exchange calculations because I didn't realize how easy it would be to get an approximate answer (being rather lazy). Eventually curiosity got the better of me and I put some time into sorting out an approximate answer. The approach I used was to model the exchanger numerically by taking advantage of the iterative solvers found in most (?) spreadsheets. By breaking the exchange surface into discrete blocks, and solving for the temperature in each block using the energy balance, it was possibly to estimate the change in temperature as the air flowed through the core. To solve the energy balance it was necessary to have the upstream cell temperature, and the temperature of the block on the other side of the coroplast barrier. This is where the iterative solver comes in, allowing for an array of interdependent equations to be solved at once. In this way, a reasonable answer could be found without excessive cleverness (a rare substance at the best of times).

The main properties in the exchanger core are below. I pulled out my old heat transfer textbook for some convective heat transfer terms - [NOPE! I looked into this further and it appears that those numbers were not particularly valid for narrow channels - fortunately Jo et al. came up with some better numbers that I will use to update this section. [NOPE! Even those numbers aren't quite right - they used water rather than air and narrower channels, the results don't seem to generalize to air. I've estimated some new numbers based on numerical simulations with fully developed laminar flow]].

There are two issues with the heat exchange values I have estimated. They assume fully developed laminar flow and a wide channel. In the heat exchanger cores I am using the air barely has time to reach a fully developed velocity profile, so the actual heat transfer should be higher. Additionally, only one of the air streams goes through a wide channel, the rest travels through the narrow channels created but the coroplast structure. These are less efficient at heat transfer because air stagnates in the corners of each channel. However I have yet to try to work out different heat transfer coefficients for that case.

So I have one factor that should make the heat transfer lower, and one that should make it higher. I have no idea which error is larger, so I'll leave these numbers as is for now.

The main properties in the exchanger core are below. I pulled out my old heat transfer textbook for some convective heat transfer terms - [NOPE! I looked into this further and it appears that those numbers were not particularly valid for narrow channels - fortunately Jo et al. came up with some better numbers that I will use to update this section. [NOPE! Even those numbers aren't quite right - they used water rather than air and narrower channels, the results don't seem to generalize to air. I've estimated some new numbers based on numerical simulations with fully developed laminar flow]].

There are two issues with the heat exchange values I have estimated. They assume fully developed laminar flow and a wide channel. In the heat exchanger cores I am using the air barely has time to reach a fully developed velocity profile, so the actual heat transfer should be higher. Additionally, only one of the air streams goes through a wide channel, the rest travels through the narrow channels created but the coroplast structure. These are less efficient at heat transfer because air stagnates in the corners of each channel. However I have yet to try to work out different heat transfer coefficients for that case.

So I have one factor that should make the heat transfer lower, and one that should make it higher. I have no idea which error is larger, so I'll leave these numbers as is for now.

Parameter |
Value |
Units |
Notes |

coroplast wall thickness |
0.00025 |
m |
- |

coroplast thermal conductivity |
0.1 - 0.22 |
W/m K |
polypropylene |

coroplast channel height |
0.004 |
m |
- |

convective heat transfer (corrugated side) |
5.2 - 15.6 (@ 0.7 - 3.5 m/s flow) |
W/m2 K |
based on laminar flow (Nu ~ 0.9 - 2.6 (velocity dependent)) |

conductive heat transfer coefficient (non corrugated side) |
9.2 - 20.5 (@ 0.7 - 3.5 m/s flow) |
W/m2 K |
based on laminar flow (Nu ~1.5-3.4 (velocity dependent))) |

air density |
1 |
kg/m3 |
- |

air heat capacity |
1000 |
J/kg K |
- |

core thickness (total) |
6 |
inches |
19 layers for cold side, 18 for hot side |

core size |
7 x 14 |
inches |
- |

air thermal conductivity |
0.024 |
W/mK |
- |

I am only looking for the percentage of heat transfered out of the vented air to the intake air, so I only need to calculate a single element of the core. That consists of the section below, which contains a half thickness (0.002 m) of both the vented and intake air, and the 0.00025 mm coroplast barrier. Tc and Th refer to the hot and cold sides. Q refers to the heat transfer through the air on each side and the coroplast material.

The overall heat transfer coefficient (U) through the two air films (corrugated channels and non-corrugated channels) and coroplast skin is calculated in the following way (actual h values depend on the air flow velocity):

This single element is broken up into discrete blocks for solution. It is assumed that the heat with these sub elements is constant for purposes of calculation. This discretization leads to some error, which should drop as the number of blocks increases. However, I didn't pursue very fine blocks. The 7" x 14" core is divided into square blocks with 7/10" sides. The core is therefore represented by 200 blocks on both the 'hot' and 'cold' side.

The energy balance on each of these is as follows:

For each cell the area for heat exchange is around 0.00032 square meters and the cross section for airflow on the hot and cold sides is 0.000018 square meters (based on half of the core cross section of 6" x 7" for each stream). The air velocity ranges from 0.7 m/s at 20 cu. ft./min to 3.5 m/s at 100 cu. ft./min. A screen shot of a solution below shows the 'hot side' on the left and the corresponding 'cold' side on the right. The hot inside air enters from the bottom left. After it passes through the first stage of the exchanger it runs through a fan and enters the second stage above the first.

## Results

The overall calculated efficiency turned out to be pretty good, at least at low flow rates (the efficiency is calculated as the amount the outside air is warmed up, divided by the difference between the inside air and the outside air). It peaks at 43% at 20 cu. ft./min and drops to around 30% at 100 cu. ft./min. Happily, the new exchanger appears to be better than the old one, so I might not have wasted my time building the new one before going through the design process!

I also calculated the efficiency of a cross flow core of the same cross sectional area as the one I built (10" x 10" instead of my 7" x 14" core). It appears to be around 20% less efficient for a give core volume. However, it may be a better configuration depending on where the exchanger has to fit. The calculated efficiencies at different rates are shown below for the old, new, and crossflow designs.

I also calculated the efficiency of a cross flow core of the same cross sectional area as the one I built (10" x 10" instead of my 7" x 14" core). It appears to be around 20% less efficient for a give core volume. However, it may be a better configuration depending on where the exchanger has to fit. The calculated efficiencies at different rates are shown below for the old, new, and crossflow designs.

## Actual Efficiency

I picked up a few thermometers to check the actual performance. I don't know the actual flow rate, other than the fact that it is limited by the fans maximum capacity of 108 cu. ft./min and is likely lower due to flow resistance through the exchanger. However, the results at maximum speed and 'low' speed show higher than predicted efficiencies and little dependence on flow rate, which is notably different than the calculations suggested. The overall higher than predicted efficiency is likely because my home-made convective heat transfer terms neglect the developing flow region.

Flow Rate |
Outside Air Temp (oC) |
Inside Air Temp (oC) |
Warmed Outside Air (oC) |
Actual Efficiency |

High (~100 cu. ft./min) |
7 |
20 |
15.8 |
68% |

High (Test 2) |
4 |
23.5 |
17.4 |
69% |

Low (? cu. ft./min) |
8 |
21 |
16.5 |
65% |

## Conclusion!

So ultimately, what is the effect of the exchanger? At night we usually keep the van around 10 Celcius. If the temperature outside is -15 Celcius and we are venting air at 20 cu. ft./min. the total loss would be around 800 Btu/hr. We would need to run the heater for approximately 8 minutes to heat up the replacement air to 10 degrees. According to the numbers here, by using a heat exchanger we manage to save around 60% of that 800 Btu/hr, which means that we run the heater for 3-1/2 minutes instead of 8 to replace the lost heat. Is this worth it? The electrical savings are negligible because we are comparing a full hour of exchanger run-time against saving 4-1/2 minutes of running a relatively efficient heater (1.8 Amps draw). We save a bit of propane, but 4-1/2 minutes of heating requires only around 17 grams of propane (Propex HS2000 heater). That adds up to about 0.45 pounds of propane in a typical 12 hour period that the exchanger runs in a day. Over a week that is about 3.1 pounds of propane, or 17% of an average '20 pound' tank. On our last winter trip we burned through a full tank in 17 days - this suggests that we would have run out with three days to go.

These are not huge numbers but they aren't bad! This is a pretty easy way to cut heating costs by almost a fifth. It is certainly easier than improving the insulation by 17% (11/32" extra foam?!?). It is definitely a better option than having inadequate ventilation while living in a small box.

These are not huge numbers but they aren't bad! This is a pretty easy way to cut heating costs by almost a fifth. It is certainly easier than improving the insulation by 17% (11/32" extra foam?!?). It is definitely a better option than having inadequate ventilation while living in a small box.

## Design Aid

In case you wanted to build and exchanger but didn't feel like the above process I put together a table from which you can determine the theoretical efficiency of different sized cores at different flow rates. The multi-stage cross flow core like I built measures L x 2L, where my L was 7". The air velocity is the volumetric flow rate divided by the total cross sectional area available for flow. Each hot/cold sandwich provides around half of its thickness for each air stream, so the more you stack, the more cross sectional flow area you get. Roughly, a stack of thickness t provides a total cross sectional flow area of 0.5 x L x t for each stream (roughly because we are neglecting the 0.25 mm thick walls of the coroplast). Once again I am mixing up my choice of units, sorry!

## Improvements?

How could the exchanger be better? More surface area is the key. This could be achieved by either increasing the overall size of the exchanger core, or decreasing the thickness of the coroplast (leading to more layers in the core). I did not realize it at the time, but coroplast can be bought in thicknesses down to 2 mm, which would increase the efficiency of my exchanger by almost 10% without changing the overall size! Replacing the core in the old, smaller exchanger would have been better than building an all new one, and would lead to fewer bashed heads!!!

Interestingly, the convective heat exchange from the corrugated side is lower than the non-corrugated side! This is due to stagnant air getting 'trapped' in the corners of the square channels. I had hoped that the corrugations would act like heat sink fins, but it looks like this is only good for around a 5% boost due to their relatively wide spacing. If you built a core out of thin sheets and spacers, rather than coroplast, you could get a slight efficiency gain.

It has been suggested that using aluminum instead of coroplast would increase the efficiency. Using the above calculations, but increasing the conductivity of the core material from 0.1 W/mK (polypropylene) to 205 W/mK (aluminum) results in the efficiency at 20 cu. ft./min. increasing less than 1%. The main resistance to heat transfer is in the air (0.024 W/mK), not the core material.

Another way of increasing the heat exchange would be by increasing the mixing or turbulence of the air traveling through the core. This would also require a great deal more energy from the fans however. Any way of forcing the air through a more tortuous path would be beneficial.

A more optimal exchanger might be built using 1/16 or 1/32" aluminum sheets (for strength, since you don't have the strength of the corrugations) separated by 2 mm spacers. This would yield efficiencies of 48-64% at 20-100 cu. ft./min, compared to my core that is 30 to 45% efficient over the same range. That said, it's hard to beat a $25 sheet of coroplast for cost and ease of construction.

Interestingly, the convective heat exchange from the corrugated side is lower than the non-corrugated side! This is due to stagnant air getting 'trapped' in the corners of the square channels. I had hoped that the corrugations would act like heat sink fins, but it looks like this is only good for around a 5% boost due to their relatively wide spacing. If you built a core out of thin sheets and spacers, rather than coroplast, you could get a slight efficiency gain.

It has been suggested that using aluminum instead of coroplast would increase the efficiency. Using the above calculations, but increasing the conductivity of the core material from 0.1 W/mK (polypropylene) to 205 W/mK (aluminum) results in the efficiency at 20 cu. ft./min. increasing less than 1%. The main resistance to heat transfer is in the air (0.024 W/mK), not the core material.

Another way of increasing the heat exchange would be by increasing the mixing or turbulence of the air traveling through the core. This would also require a great deal more energy from the fans however. Any way of forcing the air through a more tortuous path would be beneficial.

A more optimal exchanger might be built using 1/16 or 1/32" aluminum sheets (for strength, since you don't have the strength of the corrugations) separated by 2 mm spacers. This would yield efficiencies of 48-64% at 20-100 cu. ft./min, compared to my core that is 30 to 45% efficient over the same range. That said, it's hard to beat a $25 sheet of coroplast for cost and ease of construction.