That is certainly a reasonable question for any radiant system designer to answer. After all, unlike relocating a sensor or trimming the impeller of a pump, there is no chance of changing tubing depth once that screed slides over the concrete. The slab's performance over a very long service life is now fixed.
The irreversible nature of such situations should give us pause to consider whether the tubing is being installed in the best manner possible. If the depth of the tubing doesn't have much of an effect on performance, why worry about it? On the other hand, if depth does have a substantial effect on performance, then why ignore it? Why sacrifice performance to the "attitude" of a concrete placement crew who certainly won't be around to apologize if the system doesn't deliver as promised?
Reasonable doubtsThere are several fundamental principles that suggest that tubing depth in the slab will affect the thermal performance of the floor:
- The deeper the tubing, the greater the thermal resistance between the tube surface and the floor surface. The greater this resistance becomes, the slower the rate of heat transfer for a given temperature difference between the tube and the floor surface.
- The closer the tubing is to the bottom of the slab, the lower the thermal resistance between the tube surface and the underside of the slab. Lowered resistance can mean increased heat loss to the soil under the slab with or without underside insulation.
- When the tubing ends up near the bottom of the slab, more of the slab's thermal mass is above the level where heat is being added. This lengthens the time it takes to warm the floor surface to normal temperatures following a call for heat. It also lengthens the cool down time after heat input is interrupted by system controls. This can be a real problem in buildings having significant internal heat gains from sunlight or other sources.
In light of the above, it seems obvious that placing the tubing higher in the slab should improve its performance. The harder question to answer is: How much is performance affected by tubing depth? Moreover, is the change in performance worth the effort of ensuring the tubing will be installed at the proper depth?
Slab simulationsOne way to get a handle on the tube depth issue is through finite element analysis (FEA). This approach uses computer software to simulate the two-dimensional, steady state heat flow through a model of the heated slab. A network of interconnected node points is established within the various materials that make up the floor assembly, as well as the adjacent materials above and below it.
For steady state heat flow conditions, each node must stabilize at a temperature where the net heat flow through it is zero. Stated another way: the heat flowing into any given node from other adjacent nodes at higher temperatures must equal the heat flowing out to adjacent nodes at lower temperatures. The boundaries of the materials are characterized in three ways:
- Adiabatic (e.g., no heat flow through the boundary nodes);
- Fixed temperature (e.g., the node is fixed at a constant pre-specified temperature determined by surroundings); and
- Convective/radiative boundary layer (e.g., heat flow from the node depends on specified surface coefficients and the temperature of an adjacent fluid).
A typical FEA model often contains hundreds, if not thousands, of nodes. The heat balance at each node is represented by a set of equations that are automatically generated as the model is built. The simultaneous solution of these equations determines the necessary temperatures of the nodes to satisfy the condition of steady state heat transfer. The sheer number of equations involved precludes all but computer-based solution methods.
The nodal network of one of the models used is shown in Figure 1. The floor construction modeled is a 4-in. concrete slab sitting on 1-in. (R-5) polystyrene insulation, and covered by 3/8-in. oak flooring. The embedded tubing circuit consists of 1/2-in. PEX tubing spaced 12-in. on center. Several versions of this basic model were developed to simulate tubing at different depths with the slab.
Each time the model is run, the temperatures at each of the hundreds of node points are determined. Using these temperatures, isotherms (lines of constant temperature) can be constructed as shown in Figure 2. Heat flow is always perpendicular to these isotherms.
The curves in Figure 3 show the predicted surface temperature profiles for four different tubing depths. This figure also shows some color contours based on the temperature distribution within the floor assembly. Reds indicate the highest temperatures, and blue the lowest temperatures.
The surface temperature profiles point to the following trends as the tubing is placed deeper in the slab:
- The floor surface temperature directly above the tube decreases due to the greater R-value between the tube and the surface.
- The difference between the floor surface temperature directly over the tube and that halfway between adjacent tubes decreases. This is a desirable effect.
- The area underneath each surface temperature profile is different. This area represents the overall heat output of the floor.
Using the temperature data from several runs of the model, the heat output from the floor was estimated for water temperatures of 100 degrees F and 130 degrees.
For both water temperatures, heat output increases as the tubing is lowered through the upper portion of the slab, and then it decreases as the tubing is placed even deeper in the slab. This means there is an optimal tube depth where the slab delivers maximum heat output. The simulations performed suggest this optimal depth is about 1/4 the slab thickness down from the slab surface. This depth could vary depending on flooring resistance and other factors.
The FEA results were also used to determine the average water temperatures required for heat outputs of 15 and 30 Btuh/sq ft. The results are shown in Table 1. Notice that the average circuit water temperature required to yield 15 Btuh/sq ft is about 7 degrees higher when the tube is located at the bottom of the slab compared to when it is centered in the slab. This increase doubles to 14 degrees when the output requirement doubles.
Can the system's boiler provide the higher water temperatures required when the tubing remains at the bottom of the slab? Sure, if it is a conventional boiler.
However, what if a condensing boiler or hydronic heat pump were used as the heat source? The increased water temperature required to deliver the same rate of heat output lowers the condensing potential of the first, and decreases the COP (efficiency) of the latter. Higher water temperatures also mean reduced capacity through mixing devices, higher piping heat loss, and higher underslab losses.
Bare slab resultsSince uncovered radiant floor slabs are typical in many commercial and industrial buildings, it is prudent to examine the effect of tube depth for such applications. The wood flooring in the original model was changed to concrete, and several more simulations were run. The results are summarized in Figure 4.
The results again show that heat output drops off as tubing depth increases. The highest output (for the cases modeled) occurs when the tube is centered about 3/4-in. below the floor surface (about 25 Btuh/sq ft at 100 degree water temperature). Lowering the tube another inch into the slab reduces output to 24 Btuh/sq ft. Taking it down yet another inch lowers output to 22.3 Btuh/sq ft.
These changes are relatively small. However, look what the model predicts when the tube is located at the bottom of the slab. Here the output is only 16.6 Btuh/sq ft, about 31% lower than when the tube is centered 1.7 in. below the surface. Put another way, the slab with the bottomed-out tubing needs 115 degrees water to yield an output of 25 Btuh/sq ft, compared to only 101 degrees water temperature if the tubing were centered 1.7 in. below the surface.
Global warmingThe graph in Figure 5 shows what the simulations predict for downward heat loss to soil at a constant 65 degree temperature.
For a given water temperature, downward losses are higher when the tube is centered in the slab. You might think this means that leaving the tubing at the bottom of the slab reduces downward heat loss. The problem with this reasoning is that it doesn't consider upward heat output. When water temperatures are adjusted (as shown in Table 1) to allow tubing at the bottom of the slab to produce the same upward heat output as tubing centered in the slab, downward heat loss increases by about 10%.
Other considerationsThere are factors other than thermal performance that affect tubing depth. One of them is protecting the tubing near sawn control joints. The depth of such saw cuts is typically 20% of the slab thickness. I prefer to keep the tubing near the bottom of the slab at such locations to give the blade a wide berth as it passes over. A typical detail is shown in Figure 6.
Another consideration is penetrations by fasteners used to secure equipment to the slab. In most cases, it doesn't make sense to leave all the tubing at the bottom of the slab just to accommodate what might be a future bench or lift post. Find out where such equipment will be placed, and keep the tubing a couple of feet away from where the fasteners are likely to go. Block out and note these areas on your tubing layout drawing. Be sure to leave a copy of the plan with the owner, since nobody will remember where the tubing is a few years after installation.
It is also worth noting that suggested specifications for welded wire reinforcement (WWR), which is often specified for slab-on-grade floors, calls for it to be placed between 1/3 and 1/2 the thickness of the slab below the upper surface. This depth is where the WWR yields its best crack control performance. In most heated slab-on-grade floors, the tubing is tied to this reinforcement. Hence, there are structural as well as thermal performance issues associated with the placement of the WWR and tubing within the depth of the slab.
SummaryFinite element analysis is not guaranteed to predict reality with 100% accuracy. The simulation results are based on assumptions such as soil temperature, flooring resistance, tube spacing, etc.
Still, for the cases modeled the data agrees fairly well with other published performance models. The relative comparisons are also based on the same material and boundary assumptions and thus reveal significant trends.
These results indicate that tube depth does have a nontrivial effect on the thermal performance of a heated floor slab. There is a performance penalty associated with leaving the tubing at the bottom of the slab vs. positioning it near mid-depth of the slab.
The analysis performed was also based on steady state conditions. It doesn't predict the consequences of the longer response times associated with deeper tubing. These could be significant in situations where a building is recovering from a setback condition, or when heat flow from the slab needs to be reduced quickly to accommodate internal heat gains.
Considering the tradeoffs, perhaps it is time we pay more attention to quality control procedures to ensure that performance is not compromised as concrete is poured over radiant tubing circuits.
When future archeologists dig up the ruins of our buildings several centuries from now, will they ponder why we put the heating tubing at the bottom of the slab? Might they wonder if we didn't know any better? Would they conclude that some builders of the time were just too lazy to bother lifting the tubing? Thinking back to how ancient Romans used lead piping for water supplies, perhaps those archeologists will conclude that even after centuries of experience, we still had a hard time doing this pipe thing right. ES