Don W. McAdam Ph. D., P.Eng.
So your floors are cold. What can you do about it?
If you ask at your local building store, look on the internet or ask many contractors, they will tell you to put insulation under the floor. This is not good advice. If you followed this advice you would have the cost of the insulation and installation, an increase in your heating bill and your floors would still be cold. Putting insulation under the floor is not the solution. Sound crazy? Read on and I will show you why a floor is not a ceiling turned over, and how to get your floors warm.
The reason heat is transferred is simple, a temperature difference. No temperature difference equals no heat flow. The larger the temperature difference the more heat is lost. As long as there is a high temperature and a low temperature heat will flow. We cannot change this but we can reduce how much is lost. But you must know how heat is lost before you can do anything about it.
There are three ways (or modes) heat is transferred: conduction, convection, and radiation, and the method of reducing this heat transfer is different for each one. All three modes can act simultaneously, however, in many cases one mode predominates.
Conduction requires a medium, which can be a fluid or a solid. There is no conduction in a vacuum. The thickness of the material and thermal conductivity are important. Thermal conductivity (k, BTU/hr ft °F) is a property of the material and values are tabulated.
The familiar way of classifying insulating material is the R -value (thermal resistance) which depends on material and the thickness.
R = thickness of the material/ thermal conductivity
The lower the thermal conductivity (k) the higher the resistance for a given thickness. For given insulating material increasing the thickness increases the resistance and reduces heat loss.
Typical values of thermal conductivity for some materials and the thermal resistance are
There is a direct relation between heat loss and temperature difference and heat flow can be found using the relationship:
where R is the resistance.
Convection requires a fluid. Heat is transferred by convection when a fluid, liquid, or gas moves. There is no convection in a vacuum. The movement can be “forced”, with a fan or pump, or it can driven only by density difference (“free” convection). Hot air rises because the density of hot air is less than that of cold air.
Convection heat transfer is more complicated than conduction. It depends on:
fluid properties, density, specific heat, conductivity, to name a few fluid velocity, which can be forced or free geometry, the direction of heat flow, horizontal or vertical (up or down)
It is characterized by a heat transfer coefficient (h, BTU/hr·ft²·°F) (also called film coefficient) which depends on many variables. Heat transfer coefficients must be calculated using correlations based on experimental results.
Heat transfer per unit area (BTU/hr·ft² ) is given by:
Heat transfer coefficients for air are low, and those for free convection are very low. Some typical heat transfer coefficients (h) for free and forced convection are:
Free convection for outside surface of a horizontal 6″ heating duct in a room at 70 °F
1 – 3 BTU/hr ft²·°F
Forced convection for inside surface of a 6″ heating duct, depending on velocity
5-10 BTU/hr ft²·°F
inside surface for heating water flowing in a 2″ pipe
~2000 BTU/hr ft²·°F
Unlike conduction and convection nothing but a temperature difference is required for radiant heat transfer. Any two surfaces at different temperatures exchange heat by radiation. Radiant energy can be transferred in a vacuum.
How much is heat is exchanged depends on:
temperature of each surface
geometry, how one surface is “sees” the other.
There are other factors that influence radiation heat exchange, for example the wavelength of the energy being emitted from each surface.
Suffice to say that any surface radiates energy. The hotter the surface the more energy it emits.
How Do These Modes of Heat Transfer Apply
Comparing heat transfer from a floor to heat transfer in a wall and a ceiling will show how they differ. The same modes of heat transfer apply to all three.
The direction of heat flow through a wall is horizontal. Heat flows through the gyproc by conduction. Since the gyproc is hotter than the outer surface it radiates energy through the air space to the outer wall. Heat is also conducted through the air even though it is not a good conductor of heat. (There is also heat transfer through studs, which is conduction, but this is not considered here.) The resistance of a 3 ½ inch air space is about 19. So why would R-14 insulation be used in a wall?
Because hot air rises. Air at the inner surface is heated and rises due to density difference. Air at the outer surface is cold and falls so there is circulation in the wall cavity. Adding insulation in the wall cavity eliminates this air movement. Insulation also prevents radiation because the hotter inner surface cannot “see” the colder outer surface. The predominant mode of heat transfer in an uninsulated wall is convection and this can be eliminated by adding insulation so air cannot circulate. The predominant mode of heat transfer through a wall then becomes conduction. Note that the thermal conductivity of glass wool is slightly higher than that for air. The glass wool prevents air from moving.
Heat flow is up at a ceiling. It is conducted through the ceiling into the attic which is at a lower temperature. Adding insulation above the ceiling, increases the thermal resistance and reduces heat flow. The thickness of this insulation in an attic can be large enough to reduce to the temperature of the top surface sufficiently so there is little or no convection loss to the attic. Air at the top surface is close to attic temperature so air movement is minimized. The predominant mode of heat transfer for an insulated ceiling is conduction. There is radiant transfer from the upper surface of the insulation to the roof however the temperature difference between the insulation and the underside of the roof is small it can be neglected. This radiant heat transfer can easily be reduced however.
The difference between a floor above an unheated space (a crawl space or a garage for example) and a ceiling is that the hot surface is above the cold surface and heat flow is down. A floor is NOT a ceiling turned over. Consider how the three modes of heat transfer apply to a floor to see why.
The air immediately under the floor is hotter than the air space below (a crawl space). This is a stable situation. Hot air rises, but this air has no place to go. Even if there are holes in the floor the temperature above the floor is higher than the temperature under the floor (air density above the floor is less than that above the floor). Air can leak out the edges and this would cause air to move toward the edge (slowly) but this does not have much effect because the heat transfer coefficient is so low and it can be eliminated by sealing the rim joist. Convection can be eliminated.
Heat is conducted down from the floor through the air but air is a good insulator. This is similar to an uninsulated wall but there is no circulation below a floor. The R-Value of 9 1/2 inches of air is about 50. We cannot do anything about this conduction loss but adding insulation makes it worse. We cannot reduce conduction loss to zero but a thermal resistance of about 50 is not bad, and it is free. Heat loss from the floor joists can be practically eliminated. This will be discussed later.
Installing R-24 insulation under a floor reduces the resistance from 50 to 24. Halving the resistance doubles heat loss. This is not a good thing to do. Batt insulation prevents air movement, but in this situation there is no air movement, unlike a wall cavity, where heat flow is horizontal, or an attic where heat flow is up. (A thermal resistance of 50 can be achieved by adding insulation above the ceiling but it is not free.) Insulation is beneficial in both walls and ceilings but it is counter productive when installed under a floor.
The direction of heat flow makes all the difference under a floor. What works in a ceiling or wall does not work under a floor. There is little or no convection and conduction is small, but there is always radiation. Radiation is the predominant mode of heat transfer to an unheated space below. Heat is transferred from the floor and from the floor joist to the to the cooler surface below ( crawl space, garage or another heated space) by radiation. This downward radiation occurs all the time (24/7/365), as long as there is a temperature difference.
Now that we know how the heat is transferred we can do something about it.
Radiation always occurs between surfaces at different temperatures. Heat transfer by radiation from the floor to the crawl space floor cannot be eliminated but it can be greatly reduced and it is very simple to do.
How can radiation loss to the crawl space be reduced? By reflecting it back to the floor. Like light, radiant energy can be reflected by a shiny surface. (technically, a surface with low emissivity (ϵ), a property of the surface). Light is radiation that we can see. A piece of aluminum foil (the kind we use in the kitchen) placed under the floor will reflect almost all thermal radiation back to the floor. Aluminum foil is not practical because it is thin and tears easily, but aluminum foil on each side of a plastic film is available. Stapling this to the bottom of the floor joists will reduce radiation heat loss from the floor by over 90%. This is particularly important if there is an under-floor heating system. This represents a major cost saving since almost all of the energy stays at the floor where you want it. No more cold floors.
Compare radiant heat loss from a floor with, and without, a radiation shield to see how effective it is. Some simple formulae will be used to show how much difference a piece of aluminum foil can make.
Figure 1 Heat flow from floor to crawl space
A simple formula for radiant heat loss from a heated floor to a crawl space floor is
where ϵ1 and ϵ2 emisivities of the floor and the crawl space floor. Emissivity is about 0.9 for these surfaces.
is a constant,
T is the absolute temperature, kelvin (K).
could be called a resistance.
Putting in the numbers for emissivity (0.9) the formula becomes:
Adding a radiation shield below the floor joists as shown in Figure 2 adds another resistance.
Figure 2 Radiation shield below floor joists
The formula becomes:
where εs is the emissivity of each side of the radiation shield.
A typical value of aluminum is ϵ = 0.06. The formula becomes
Resistance goes from 1.2 to 33 and radiant heat transfer is reduced by 96%. Not a bad reduction for a piece of aluminum foil. If there is a heated floor, heat flow down to the crawl space is greatly reduced. The resistance to conduction in the air space is still about 50, which is much better than adding R-24 under the floor.
You can try this by standing below a heat source (a radiant heater is an example) and holding a piece of aluminum foil (from the kitchen) between your face and the heater. Without the foil you will feel the heat. With the foil you will feel nothing.
There are two parallel heat paths through a floor and we have considered only the space between the floor joists not the joists, usually 2 x 10. Wood has a low thermal conductivity, but does conduct heat through the joist where it then radiates to the crawl space. If reflective film is stapled to the bottom of the joist (as shown in Figure 2) there will still be a significant reduction in heat transfer, however, the loss below the joists will still be higher than between the joists. This is because one side of the reflective film is in contact with the bottom of the joist and does not reflect anything. Only the side facing the colder surface does any good. This is easily fixed by leaving a small space between the bottom of the joist and the film. Running the shield perpendicular to the joists and stapling it only at the edges will a give an air space under the joists. A small air space is all that is needed. Figure 3 shows how this can be done.
A radiation shield is simple to install under the floor joists. Unroll it and staple it on as shown in Figure 3. It is also inexpensive. The cost for material was $0.20 per square foot.
Figure 3 Installation of shield to reduce loss from joists
The same technique can be used with a radiant floor installation to prevent heat flowing into the room below or a garage ceiling. A heated basement room would be heated both from above and below, and the room above would get less heat. In this case the radiant barrier should be stapled between the joists and close to the floor above to be most effective.
Figure 4 Installation of shield between joists
The shield is not installed on the bottom of the joists in contact with the ceiling because it is not as effective as putting it between the joists as shown. Only the top surface of the shield would be effective. The “low ε” side in contact with the ceiling would be rendered completely ineffective because it would be in contact with the ceiling.
Figure 5 shows an installation of a radiation shield correctly installed under a heated floor.
Figure 5 Radiant shield over a crawl space
© Don W. McAdam 2012