# The Naked Scientists Forum

### Author Topic: floor-air convection  (Read 3234 times)

#### meeotch

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##### floor-air convection
« on: 21/04/2014 20:27:53 »
I'm trying to do a rough calculation to find the "operating temperature" of a concrete floor.  I've found a paper that discusses calculations for rate of heat loss from the slab to the earth: newbielink:http://academic.udayton.edu/kissock/http/EEB/LecturesAndHomework/05_RoofsFloorsBasements/FloorsBasements.docx [nonactive]  (It's a Word file - don't freak out.)  Which gave me a fairly reasonable figure of ~2400Btu/hr (~700W) for heat loss.  Also, I've got the equation for convective heat transfer as:  q = hc*A*dT.    newbielink:http://www.engineeringtoolbox.com/convective-heat-transfer-d_430.html [nonactive]

However, I'm not sure I can just assume that the heat loss to the earth will be exactly balanced by the heat transfer from the air.  Or maybe I can, since the linked paper seems to give the heat loss figures for an equilibrium situation between the slab & the air?  If I do that, and take 10.45 as the convective transfer coefficient (hc), A ~= 1000sf (~93m2), I get something < 1 degree for dT.  That doesn't seem right.

Basically, I'm trying to predict the temperature of the floor, given adequate heating of the interior space by forced air.  (With no air stratification, due to a gigantic fan.)  It doesn't seem intuitive that a bare concrete floor of something like 8" thick would be almost exactly the same temperature as the air.  Have I missed something?

EDIT:  it occurs to me that the convection equation above may not apply anyway, since the action in this case it reversed...  rather than floor heating air, hot air rising - it's air heats floor, cold air stays where it is, unless moved by some external force.  But I'm told that this giant fan (8' diameter!) can reduce stratification to 1deg from ceiling to floor.
« Last Edit: 22/04/2014 02:04:44 by meeotch »

#### alancalverd

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##### Re: floor-air convection
« Reply #1 on: 21/04/2014 23:35:20 »
It all depends on the effective R value of the floor and underlying insulation, the difference between internal and ground temperature, and the area of the floor. Since you haven't given any of those figures, we can't check your arithmetic!

If you add enough heat, stir thoroughly, and wait long enough, the top surface of the floor will be in equilibrium with the air above it but (assuming the earth is colder than the air in the room) you will have to continue adding heat to the air to balance the flow to the ground.

I've just solved the inverse problem, installing underfloor heating in a "new" building (barn conversion). The trick was to start with a very thick insulator (high R value) above the impermeable membrane then to embed the heating pipes in as little concrete as necessary to protect them from the floor load. It's really comfortable, driven by an airsource heat pump with a CoP of about 3. Maintaining a 10 degC indoor/outdoor differential over about 200 sq m requires around 500 watts but I haven't done much analysis as we only heat the barn for concerts, when there are upwards of 30 people inside, adding another 3000W of body heat!

#### meeotch

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• Posts: 11
##### Re: floor-air convection
« Reply #2 on: 21/04/2014 23:45:38 »
Thanks for the reply.  Yes, I probably should have stated my constants.  I was using 70deg for interior air, 40deg for earth (based on just picking a value by looking at some of the graphs in the linked paper), A = 1000sf as mentioned.  R-value I assumed was zero, as I have no reason to believe the builder was careful about providing a thermal break.  (I can say that the building is sandwiched between two others, which I assume mitigates the heat loss horizontally in those two directions.)

p.s. - I originally wanted to go with heated floors, but the expense of the install, plus the complication of pouring an additional ~4" of concrete or ~0.5" of self-leveling cement, then polishing that seemed like it would break my budget.  A hydronic system would be roughly one billion dollars (give or take), due to the fact that this is NYC, and any plumbing requires prostrating yourself in front of the DOB while lighting fire to a pile of cash.  Electric would be cheaper, but have higher operating cost.  So at this point, I'm just trying to determine if going without will be unbearably uncomfortable.  And since it's spring, I can't just try it out.

#### alancalverd

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##### Re: floor-air convection
« Reply #3 on: 22/04/2014 08:19:07 »
I'd strongly recommend getting a quote for underfloor heating - I was surprised how cheap it turned out even though we had to break out half of the original concrete base and level it before adding the insulation. I liked the idea of polished concrete but strangely, that would have been extremely expensive for an indoor domestic finish so we faced it with ceramic tiles.

That said, I assume that if you are concerned about the floor temperature you want to use the space as living accommodation so you will need to cover the concrete with something. So here's the opportunity to increase the R value to 20 - 40 by adding styrofoam or urethane under the floor finish. Having done that, your real problem is going to be heat loss through the outside walls rather than the floor.

#### meeotch

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##### Re: floor-air convection
« Reply #4 on: 22/04/2014 17:55:27 »
I did actually get a few quotes:  A hydronic system looked like it was going to come in around \$15k, plus permits and electrical work.  (Remember:  NYC.)  Electric heat would be about \$6k for parts, which I could presumably lay out myself, and then a couple \$k for an electrician to wire it to the panel properly.

Unfortunately, both of those would then require an additional concrete pour.  Self-leveling was coming in at \$15k-20k.  "Regular" concrete would presumably be a fair bit less.  Then you've got the cost of polishing & sealing.  I hate tile, so I've tried to steer clear of it - but the few that I found that I liked were (of course) high-end stuff that made other options look cheap.  My most recent Rube Goldberg scheme was to lay down sleepers, insulate between them like a wall, then plywood, then these fiber-cement panels I found that are normally used for wall cladding.  That whole thing was looking like about \$15k, but comes with a fair amount of uncertainty as to how they'll wear, since it's an off-label use.  Also, they have to be sealed on all six sides for moisture reasons, which sounded like it was going to be a bit of a trick.

Which brought me all the way back around to just polishing the slab and seeing if it's miserable in the winter.  Worst case, maybe I can wire up some flat heating elements with rugs on top of them, and roll them out during the cold months...

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##### Re: floor-air convection
« Reply #4 on: 22/04/2014 17:55:27 »