Radiation

Nov 21, 2024

Complexities of heat transfer

I always loved physics because it deals with the tangible effects of the forces of nature— the interactions between matter and energy—that explain the things that we feel or see on a daily basis. Specifically, I want to delve into the transfer of heat, which seems to be a hot topic in sauna forums.

There are three methods of heat transfer: conduction, convection, and radiation. In a sauna, (and everywhere else, unless you live on a planet at absolute zero: -460 °F) there are all three. Heat always goes from a warmer object to a cooler one, and a closed system is entropic, that is to say, if you sip too slowly, the ice will melt and your drink will eventually all be the same lukewarm room temperature. The transfer of heat is greater when the temperature difference (ΔT) is greater, and it slows over time, until the temperature equalizes in a system, which, for our study, includes not just inside the sauna, but the environment it sits in. Which is to say, no matter how well you insulate it, eventually the sauna will reach the ambient outdoor temp, unless, like a house (or a sauna in a house,) you keep the heat on. This is a factor in freestanding sauna design as we have to assume the starting point is anywhere from 0 to 100°F (unless it is fired up constantly) and the desired bathing temp is 180-220°F. In a house we are trying to hold the temp at about 70°, in the residential sauna, we need it to hold temp for a few hours, at the most.

Conduction is the transfer of heat from one solid or liquid to another by direct contact. You Grab a (foolishly installed) metal doorknob to the sauna that is either 200°F or 10°F, depending on the season, and which way you are going, and the heat rapidly conducts either to your hand or from it, with a resulting shriek. Same is true if someone pushes you against the hot stove as you try to leave the sauna, burning your butt to the point where sitting was impossible for two weeks, as happened to me once. This is conduction which we typically try to avoid in the sauna, but it happens. Less dense materials, like your towel, mitigate conduction, which is why we look for low density boards like cedar, not hardwood, for the benches, which would feel like a hot iron on your posterior.

Convection is the transfer of heat through the movement of fluids. It is in part driven by gravitational forces whereby warmer gasses or liquids are typically less dense and lighter and thus tend to rise as cooler ones sink. This create a convective loop as the heat is circulated to, say, the walls of the room, or you on the top bench, and then the air cools and falls, creating an endless loop. I say typically, because there is this oddball exception: water close to freezing gets less dense and thus freezes on the top of lake or pond, making hockey, ice plunging after a sauna round, and life on this planet, possible. If the movement of air is stopped, say by the fibers of mineral wool or two close layers of glass, it becomes an insulator. Air itself holds very little heat per volume-more than a thousand time less than water, whereas water holds twice the heat energy of granite and about the same as steel. A large volume of this dense, heat holding material is called a thermal mass, which can mitigate the fickle effects of convection, especially when the air is coming and going, by acting as reservoir of heat. That is why we try to keep the door closed in the sauna—all of the air convecting nice warmth around us is disturbed by the cold air rushing in to take it’s place. But that’s not so bad—as we actually want the fresh air—as long we have some thermal mass to mitigate the swings in temperature.

In home construction, the emphasis is on controlling convection: eliminating it inside wall cavities and not allowing warm air to escape from heated (conditioned) spaces, especially up high where it creates a chimney effect, whereby escaping warm air creates negative pressure and sucks in cold air from wherever it can. In a not-so-old house on a cold night, put your hand over the wall outlets—even on interior walls— and you will likely feel cold air being sucked in. More so if a you have a big cozy, romantic, fireplace with an actual chimney and a roaring fire, which feels great, but sucks the heat right out of house.

In a freestanding wood fired sauna, there will be leaks and cold air coming in. That’s ok because we want fresh air, as long as we control where it comes and goes. Air and steam will move the heat around but eventually it settles into strata: hot up high and cold down low. Air movement can help break up this layering of cold to hot, but it is difficult to control. Thus, the upper bench will always be hotter; unless you have an Aufgussmeister to move the heat around with his swirling towel dance.

The last method of heat transfer is Radiation. Sounds bad, like Chernobyl, but radiation is everywhere; all objects with a temperature above absolute zero emit thermal radiation, mostly in the infrared range that we can see with a special camera. At a certain point heat becomes light you can see and the color of the light corresponds exactly to a temperature. The dull red glow of a poker in the fire ( or the top of my sauna stove when I fire it hot) is 1200°F. The surface of the sun burns at 5772°K, which is the color of the sunlight we bask in on the beach. Fortunately, the sun appears relatively small, otherwise we would burn up instantly. We radiate as well; after getting sunburned, your skin will be hotter than the person next to you and will radiate heat to them. In fact all bodies, especially black bodies, which are not necessarily black, radiate and absorb heat, depending on which is hotter. The only things that are not black bodies are things like foil, which reflects most heat directed at it. Surface area and angle of incidence also matter; the more surface area and the more parallel two surfaces are, the more heat transfer. Temperature difference matters too: too much and the effect is intense, like when I pour bronze and have to stand an arms length away from the pot of molten metal, or stand on a subzero surface in winter and feel the heat being sucked from my body.  Too little difference in temperature (ΔT), and radiation is hardly noticeable. Direction is also important. The fireplace heats our front but not our back. I have a story about a cold drizzly camping trip where all we could do to stay dry was to keep putting our jackets on backwards then forwards as we sat by the fire. And in all these situations it is aluminum foil that saves the day: as an apron to wear, a foil surface to stand on, or an emergency blanket over the shoulders. Foil blocks radiation, (but it does need an air gap, lest it become extremely conductive); without any barrier, heat, like light, radio waves and the rest of the electromagnetic spectrum can radiate millions of miles. Those episodes of Leave it to Beaver are still traveling through space.

In the sauna, radiation is really important as it creates this enveloping heat coming at us from everything hotter than 98°F. If the whole room- walls, benches and rocks, is 200° or more, we will feel the heat coming from each of those surfaces. Colder surfaces like a big window, or that guy that just got out of the cold plunge, will suck heat from us. Something too hot—like a blasting fire in a single wall stove pipe— will feel searing. In an electric sauna, the rocks need to cover the elements so we don’t see/feel the searing red heat. The much cooler—but still hot–rocks will then reradiate the softer heat. Foil, behind the cedar wall (or other wood), will reflect the heat back towards the cedar which will re-radiate towards the interior. The walls need to be just so hot. Radiation also mitigates the effect of the constantly changing air. The air may be cool, but the radiation of the hot surfaces will cut through the cold like the winter sun on your face. Speaking of, nothing like a full body sun-bath on a calm, freezing day to boost the sauna experience! The thermal mass mentioned above will continue to radiate heat even as the door is left open. Cool air swirling in will kill the radiation buzz for sure, but as soon as the door is closed that warm fuzzy feeling  will come back.

So how does all of this daydreaming back to high school physics class inform how I build my saunas? A lot. I want the radiant heat off of the stove to work for me, warming me just so, like the sweet spot in the campfire where you should put your skewered marshmallow (but never do). I aim for a soft radiant heat, like a ΔT of a few hundred degrees at most (me: 98°, the rocks 400°,) but also omni-directional heat (which gets all the walls and benches up to 200° before taking a sauna) and not too intense (make sure the fire has died down and the stove pipe, if single wall, is not too hot). A big window is pretty to look out of, but not too big, as it will suck the heat away from you and a cold cascade of negative convection will sweep over the floor. Thermal mass is great, but not too much, because the sauna will take forever to heat up, and no one seems to have to time for the daylong ritual sauna used to be. I have my bathers all facing the rocks and typically the stove is fired from outside, so there is no worry about the intense (visible) radiant heat through the firebox glass door, which, as cozy as it sounds, may feel too much sitting around a hot campfire and is not the kind of heat you want in a sauna. 

Recently I heard, in an online sauna forum, two seasoned sauna veterans saying you don’t want radiant heat in a sauna. I believe they misspoke. You don’t want high intensity radiant heat, but no radiant heat just is not possible, unless everything has reached a state of equilibrium. That is to say, you are as hot as the rocks, thus cooked like a goose (or the sauna is only 100°F). As long as you are cooler than the rocks, stove, walls and benches, heat will radiate to you. It is said that when you close your eyes in a good sauna, you cannot tell where the stove is. 

How do we get there? Fire it hot to get the rocks and the whole sauna hot, but let the intense fire die down before getting in. Use radiant foil behind the wood (with an air gap) so the foil can reflect heat back into the wood, use a high rock capacity stove or heater to hold and radiate the heat, and make sure everyone can see the heater so the radiant heat—which travels as waves, like light— reaches everywhere.

You can always tell when there has been a really good sauna; everyone coming out looks so… radiant!

_____________________________________________________

The Last Word on Foil.

Dec 21, 2021

Lately I have been thinking about the application of the foil I use in my saunas as a radiant vapor barrier. Perhaps this is because it almost Christmas and I was thinking of how we decorated the tree each year. The final touch would be to drape foil tinsel over everything; our mother would have to constantly damp down our enthusiasm by reminding us to place it carefully on each branch, not to throw it. 

NOT sauna foil.
This suspicious “sauna” foil is Aluminum-coated Plastic—upper working temperature of only 55-120° C.

There are tricks to using the foil but the first and most important step is to buy the right stuff. Like the tinsel we put on the tree, the foil may actually be aluminum-coated plastic— which you don’t want to use. That plastic is likely polyethylene which, if you look it up on the material specification sheet that every product has, it has an upper working temperature of 55-120° C, meaning it will likely melt at typical sauna temps. Sauna Foil, available from any of the familiar sauna suppliers, is aluminum foil on a kraft paper backing. I used to find it with fiberglass reinforcing thread, which is helpful because the stuff tears easily. Also helpful is 4 ft. rolls, rather than 3 ft so you can do a wall in 2 passes, but I have trouble finding this too. I recently tried a new supplier selling 4 ft rolls of  “sauna” foil, but upon opening it had a suspicious plastic look to it. That night I put it in the sauna and within seconds it began to distort and curl up like the polyethylene I suspected it was made of. (See illustration above)

The second thing is to design the wall correctly. I read and see a lot of misinformation that touts using no air gap with foil.  The air gap is essential.  The foil works by reflecting radiant heat. All “black bodies” give off and absorb radiant heat that travels in a straight line from one hotter object to another cooler one, the hotter the body, the more heat it emits. The sauna rocks radiate a “soft” heat to you, the walls, and the benches, and that is why you want the sauna to be laid out so that everyone has a view of the rocks. The fire, if seen through a clear glass door, also radiates heat— but at a higher intensity. Too high for a comfortable sauna (but great for ambiance.) When that heat hits foil, it is reflected back into the room or the backside of the cedar—if there is an air gap of at least 1/2″. If it touches the backside of the cedar the foil— also a perfect conductor—pulls the heat away from the cedar and transfers to the wall space behind.

Proper sauna insulating with an air gap on backside of cedar.
Air Gap. A Sauna Building Best Practice.

I’ve understood this for along time. The first semester of college I took a class: Solar Design and the Energy Efficient Home. We learned all about insulation, heat transfer and basic building skills. The first day of lab, where we were building a timber frame house, I was handed a Makita 12″ circular saw. My building career started right then and there.

With the web of misinformation out there I had to think of a way to illustrate this basic principle of thermodynamics that I learned my freshman year. So, one slow day in the shop I rigged up an experiment and photographed it. (see illustration below) I set up a section of cedar wall about 18″ from my infrared shop heater and fastened 2 pieces of foil to the back, one with a 3/4″ air gap, and one with no gap. After an hour the cedar was 250°F on the front—like it is often is in my sauna. The back of the cedar was 121° F, which is impressive by itself. The back of the foil with no gap was 115°F, meaning it was acting as a perfect conductor, and the back of the foil with an air gap was 71°F: room temp. The air gap was clearly making a difference, 45° in this case. 

Sauna thermodynamics by sauna builder Rob Licht Custom Saunas
The thermodynamic experiment begins.
  • After an hour on cedar
  • back of cedar
  • back of foil, no gap
  • air gap makes big difference!

The foil is a perfect vapor barrier rated at zero perms— meaning no vapor moves through it. But unless you layer it properly, with insulation behind it, the moisture will condense on it, or the first cold surface it hits. Even in a perfect build, there might be cold spots in the insulation (typically about the size of a mouse hole), so there likely be some condensation, but not a problem if there is air movement. The air gap behind the cedar allows air to circulate around the cedar, removing any moisture and ensuring that the wood heats and dries evenly and remains stable. Heating one side of a board and wetting or cooling the other is how you make curved boat staves.

There are other tricks to using the foil- like unrolling it and re-rolling it foil-in, or using temporary magnets when working a commercial job with metal studs, but the key is to use care. Use plenty of hi-temp foil tape and patch tears as you go and work with a partner if possible.

I suppose you could build a sauna by putting a heater in a refrigerator box- but that would last about a day and be incredibly wasteful. Cedar touching foil won’t ruin your sauna and neither will plastic melting in the walls where you don’t see it. But if you are going to take the time and bear the expense of building a sauna, you might as well do it right and so it will last generations. I guess my mother was right: applying foil carefully and not just throwing it up is the way to work.