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NREL is operated by Midwest Research Institute ● Battelle Contract No. DE-AC36-99-GO10337 

Pipe Freeze Prevention for 

Passive Solar Water Heaters 

Using a Room-Air Natural 

Convection Loop 

Preprint 

J. Burch 

National Renewable Energy Laboratory 

M. Heater, M. Brandemuhl, and M. Krarti 

University of Colorado

To be presented at Solar 2006 

Denver, Colorado 

July 8–13, 2006 

Conference Paper 

NREL/CP-550-39722 

May 2006 
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PIPE FREEZE PREVENTION FOR PASSIVE SOLAR WATER HEATERS 

USING A ROOM-AIR NATURAL CONVECTION LOOP 

Jay Burch 

National Renewable Energy Laboratory 

1617 Cole Blvd.; Golden, CO 80401-3393 

E-mail: jay_burch@nrel.gov 

Morgan Heater, Mike Brandemuhl, and Moncef Krarti 

University of Colorado 

Architectural, Civil, and Environmental Engineering 

Boulder, CO 80302 

ABSTRACT

With the goal of extending the geographical market for 

passive solar water heaters northward, a room-air natural 

convection loop (NCL) was investigated for providing 

freeze protection for supply/return pipes carrying 

pressurized domestic water through unconditioned space. 

An NCL model was developed based upon balancing 

buoyancy and friction in the loop. Calibration factors 

(Cfric,Cht-trsf) were introduced to scale calculations and 

account for un-modeled details and correlation bias. An 

NCL prototype was constructed with 2”, 4”, and 8” 

diameters. Least-square regression on data from the 4” 

diameter duct yielded (Cfric,Cht-trsf) = (2.05, 1.8). The 

calibrated model was used to provide site-specific design 

guidance, and to estimate energy losses with and without a 

thermostatic control to stop flow whenever Tamb > 0 °

C. 

1. INTRODUCTION

Reducing costs and increasing reliability of solar water 

heaters is believed necessary for a substantial market to 

exist in the U.S. (1). One strategy to achieve these goals is 

increased use of passive solar water heaters (PSWH). 

PSWH include integral-collector-storage and thermosiphon 

systems, as in Fig. 1. PSWH eliminate the pumps, 

controller, sensors, and power needs of active systems, 

saving ~$400-$800 in life-cycle cost and eliminating related 

failures. PSWH also eliminate the need for separate storage 

inside the home, although roof weight is an issue. New 

polymer-based PSWH with potential for >50% cost 

reduction are nearing market entry (1). However, the market 

for PSWH has been limited by the risk of freeze-induced 

bursting of the supply and return lines (2). The supply/return 

pipes carry pressurized potable water through the typicallyunconditioned attic space to the thermal storage, as shown 

in Fig. 1. The pipes are almost always copper because most 

SWH can reach temperatures that will burst polymer 

piping. On the other hand, copper pipe can freeze and burst 

in the attic during freeze spells. A burst attic pipe is 

catastrophic, as one incident may readily cost much more 

than the SWH’s lifetime savings. Therefore, the market for 

PSWH has rightfully been restricted as shown on the left 

side of Fig. 2. Note that if the building top-side insulation 

(normally at the ceiling) is raised to the roof plane, pipe 

freeze is eliminated in the attic. Such exceptions aside, 

lower-cost, more-reliable PSWH are at present generally 

considered unsuited for almost all the continental United 

States. If the pipe freeze problem could be solved, the 

PSWH market becomes limited by non-zero risk of 

collector-storage freeze, as indicated in Fig. 3. In the case of 

an indirect thermosiphon with well-insulated storage, the 

region of zero collector freeze risk would cover the entire 

lower 48 states. 

Fig. 1. Schematic integral-collector-storage and 

thermosiphon SWH. The balance-of-system is very simple, 

lowering costs and improving reliability compared to more 

common active systems. 

1
It is suggested in (3) that a primary piping freeze protection 

(PFP) method combined with freeze-tolerant piping as the 

fail-safe backup to the PFP could be an acceptable solution 

to the pipe freeze problem. If the PFP fails and piping 

freezes, the homeowner must bypass the PSWH to regain 

hot water flow, which is a significant inconvenience. Thus, 

PFP failure must be very rare to be acceptable to the market. 

PFP must be passive to work during power outages and 

satisfy code regulations that any PFP cannot depend on 

electrical power. PFP must be low in cost, as SWH 

generally are marginally cost-effective against current 

conventional electricity. 

= 0

> 0 to 1

> 1 to 10

Freeze 

Probability (%)

Pipe Diameter = 3⁄4 in.

Insulation = 1 in.

> 10 to 100

Fig. 2. Probability of at least one freeze in 20 years, for 3/4” 

copper pipe with 1” insulation. Zero-freeze-probability sites 

are shown as large dots. Map taken from (2). 

PFP recently investigated are water-based methods using the 

supply/return pipes: 1) an NCL driven either by tank heat or 

room air heat (4,5); and 2) a freeze protection valve placed 

just upstream of where the return line crosses back into 

conditioned space (6). For NCL in the pipes, an additional 

pipe (with flow-limiting means) must be added to close the 

loop (4,5), adding plumbing costs. Pipe-based NCL can fail 

because: a) the flow-limiting restriction can become 

plugged; or b) the source of heat can fail (gas/electric 

storage tank, or room air). Similarly, freeze protection 

valves can fail because: a) scale or grit buildup can prevent 

the valve from opening; b) the actuator (e.g., wax 

compound) can degrade; c) the valve can improperly seat 

and leak; or d) water pressure is lost. This work considers an 

air-based, bi-directional NCL circulating room air through 

an insulated duct surrounding the piping, as shown in Fig. 4. 

To provide freeze protection, the exit temperature must be 

above zero when Tamb is set to Tamb,min. A room-air NCL 

may have improved reliability, because it eliminates issues 

with scale, orifice clogging, or plumbing leaks. However, 

there are still failure modes: a) room air too low; b) duct 

obstruction (e.g., insect infestations); or c) holes in the duct 

(e.g., poor installation or mechanical abuse). The air duct 

also presents more area for heat losses compared to pipe 

insulation. The objectives here are to construct and validate 

a model for a bi-directional NCL driven with room air. 

Fig 3. There are two freezing problems for PSWH: pipe 

freeze, and collector-storage freeze. If the pipe freeze 

problem were to be resolved, risk of collector-storage freeze 

damage becomes the limiting factor in freeze risk. 

2. NCL MODEL

A room-air NCL is shown schematically in Fig. 4. Warm 

room air enters the duct on the right, travels up the tube on 

the inlet side of the divided duct, crosses to the outlet side at 

the top of the duct near the connection to the passive 

system, and then descends back into the room. The air 

becomes colder as it traverses the loop, making the exit 

column of air colder and heavier than the entering column 

and providing the net buoyancy force to drive the loop. The 

outlet is shown with an extension into conditioned space 

intended to induce a counterclockwise flow, as shown. 

Fig. 4. Schematic of a room-air natural convection loop. 

Warm room air ascends on the right, and descends on the 

left side of the divided duct that surrounds the pipes. The 

NCL could also have air exiting at the top rather than 

returning to the room (7). 

2
The room-air NCL is modeled as in (8). The driving force 

for the flow is the difference in density of the two columns 

of air in the loop (loop buoyancy): 

Pbuoy = ∫ sdg ( cold −=⋅ ρρρ hot)gH ρρ (1) 

The buoyant pressure Pbuoy is exactly dissipated by the 

friction losses around the closed loop: 

Pbuoy = Pfric,shear + Pfric,hyd = 1⁄2ρv2

*[fLp/Dh +ΣKi] (2) 

Hydraulic losses included here include entry/exit losses for 

rectangular openings, and one 180 bend (ΣKi = 4). The halfcircle duct with occlusion of the water tube was modeled as 

a rectangular duct, using the duct pressure drop correlation 

in (9). The turbulence-tripping effects of wires and other 

protrusions were neglected. A friction calibration factor 

(Cfric) is introduced, which multiplies the sum of computed 

pressure drops. Cfric scales computed pressure drops to 

compensate for the many friction modeling sins. Cfric is 

expected to be greater than 1, due to unmodeled friction. If 

friction were modeled exactly, Cfric would be exactly 1.0. 

For calculation of buoyancy, the heat transfer at the pipe 

wall is modeled similarly to (8). The divider was considered 

adiabatic. At the outside surface of the pipe, a combined 

coefficient was used coupled to Tamb. The entering, exiting 

and mean temperatures are related through the log-mean 

temperature distribution, which applies to the pipe-to-air 

heat exchanger here. The heat transfer was modeled 

explicitly in both the entrance and developed regions, as in 

(8,10). As with friction, it is likely that un-modeled features 

cause higher heat transfer than is predicted from correlations 

for simpler geometries. To compensate, a second calibration 

factor Cht-trsf is introduced that multiplies the inside wall 

convection coefficients. Cht-trsf is expected to be greater than 

1. Cht-trsf would be exactly 1.0 if all heat transfers were 

modeled exactly. No accounting was made for turbulent 

mixing or radiation transfer at the outlet, which tend to 

warm the outlet air for a short distance up the outlet tube. 

Any solar radiation incident on the piping is not modeled. 

The resulting set of coupled equations was solved using the 

Engineering Equation Solver, which also provides for easy 

creation of a stand-alone version (11). The stand-alone EES 

model is available for download on the internet at: 

ftp://ftp.nrel.gov/pub/solar_waterheat-out/NCL/AIR.EES. 

The user inputs the pipe/insulation geometry under 

investigation, assumed room-air and ambient conditions, 

and the two calibration factors for friction and convection. 

The flow rate in the duct and temperature at the top and exit 

of the duct are outputs. The same calibration factors derived 

below should be used (these are the defaults), unless data 

are available to calibrate the model for the specific geometry 

of interest (as is the case here in Section 4 below). 

3. PROTOTYPE ROOM-AIR NCL

To test the general concept and provide data for model 

calibration, a prototype room-air NCL was constructed, as 

shown in Fig. 5. The NCL was 10 feet high. There was no 

PSWH at the top of the loop (not needed to test the room-air 

NCL); instead, a small box was placed at the top to provide 

room for piping and air flow to turn and return to the 

interior. The outlet passageway was extended one foot 

below the ceiling plane to induce the outlet on that side of 

the air duct. The loop was tested throughout spring, 

summer, and fall 2005. Three different ducts were 

constructed from schedule 40 PVC piping of 2”, 4”, and 8” 

diameters. In each case, a 1” insulation layer with foil 

covering was applied to the outside of the duct, as was also 

done for the top box. The 4” and 8” ducts were slit in half, 

with the duct divider inserted between the halves. The pipes 

were 3/4” PEX and were not separately insulated. 

Thermocouples were located in the air on each side of the 

NCL at 0’, 3’, 5’, 7’ up the duct, and in the top box at the 

10’ position. Each location had a sensor in the center of the 

air-stream, and a TC fastened to the surface of the PEX 

pipe. Two rugged RTD-based hotwires were constructed 

and calibrated in a wind tunnel, as in (10). In addition, a 

commercial hot-wire (TSI IFA-100) was used for the 8” 

duct. Flow varied significantly across the aperture. A 

number of traverses were done with a hot wire on a 

mounting controlled along two axes to determine total mass 

flow, and this data was used in model calibration. 

Fig. 5. Prototype room-air NCL. Left: NCL outside (4” pipe 

with 1” foil-faced insulation). The box at top provides room 

to make a U-turn with the piping. Right: View of the bottom 

of the NCL inside the building. The pipes are 3/4” PEX, 

attached to the divider board which separates the 4” PVC 

duct into two partitions. 

3
There was no flow induced under moderate freeze 

conditions for the 2” duct; evidently the passageways 

presented too much friction to allow measurable flow, even 

though the simple model predicts flow with any open area. 

There were 10 total flow measurements on the 4” pipe, and 

3 for the 8” pipe. Data were taken only when ambient 

conditions were not changing rapidly, implying stable flow. 

Measured temperature along the flow path are shown in Fig. 

6. Generally, temperatures start at room air and decrease in 

the flow direction, as expected. However, as the flow 

descends to the outlet, there is some influence from the 

warmer room. Perhaps turbulent mixing with room air, fanforced room air currents, and/or infrared radiation 

exchanges are involved. Although of some interest, this 

perturbation has a small affect on the results and was not 

modeled. For the temperature point in the regression in 

Section 4, the temperature at the top of the loop was used. 

4" Duct, NCL Temperatures

-10

0

10

20

30

72 96 120 144

Time [hr]

Temperature [C]

In 0'

In 3'

In 5'

In 7'

In 10'

Out 7'

Out 5'

Out 3'

Tamb

Fig. 6. Variation with temperature along the NCL. The 

bounding Troom, Tamb are shown as heavy lines. The 

temperatures decrease around the loop at night, until the 

pattern is broken with TOUT@3’, which increases due to 

interaction with the room. 

4. MODEL CALIBRATION

The model is calibrated to the prototype data using least 

squares to determine best-fit values of the two calibration 

factors Cfric and Cht-trsf. The χ2 metric used for this regression 

included both flow rate and a temperature: 

χ2

 = Σi{[(Tmod,top,i –Tdata,top,i)/σ∆T]

2

 + 

[(mmod,i –mdat,i )/σm]

2

}/(N-2) (4) 

 

where i labels the different measured conditions. the 

modeled quantities Tmod and mmod are functions of (Cfric,Chttrsf). Contours of χ2

 as a function of (Cfric,Cht-trsf) are shown 

in Fig. 7 for the complete 4” diameter data set. The 

minimum value χ2

min is about 1. The “true” parameters 

could exist within the χ2

 contour bounded by ~2χ2

min, or 

about ± 30% of the values. A more extensive data set with a 

more accurate means of measuring flow, such as with tracer 

gas, could yield more precise values of (Cfric,Cht-trsf). 

Nonetheless, the fit of the model to the data appears 

reasonable, as shown in Fig. 8 for NCL flow rate. 

In the case of the 8” diameter pipe, a similar analysis was 

performed, yielding (Cfric,Cht-trsf) = (~8, 2), unfortunately 

indicating that the parameter adjustments are dependent on 

diameter. This result is somewhat unexpected. As a result, 

one should use the model with default calibration factors 

only for diameters that are reasonably close to 4”, e.g., 3”-

6”. 

Fig. 7. Contours of χ2

 as a function of (Cfric,Cht-trsf) for all the 

data on the 4” diameter room-air NCL. Contour values are 

shown in the boxes, and the minimum is χ2

min ~ 1, located at 

(Cfric,Cht-trsf) = (2.05,1.8). 

 Fig. 8. Average duct flow velocity vs. ∆T = Troom - Tambient

Measured flow rates are shown as the solid dots. The model 

results with (Cfric,Cht-trsf) = (2.05,1.80) are the solid curve. 

4
5. DESIGN GUIDELINES 

The calibrated model can be used to design the geometry of 

the room-air NCL. The design criterion is that at the record 

minimum temperature Tamb,min, the exit temperature of the 

loop must be above 0 °

C. Fig. 9 shows Texit(Tamb) for the 4” 

diameter/10’ long case. The graph shows that if Tamb,min is 

-10 °

C, the insulation must be at least .5”. A greater level of 

insulation than this minimum may be desired to limit the 

thermal losses, as below. 

 

Fig. 9. Exit temperature versus ambient temperature, for a 

vertical 4” diameter duct 10’ long, with insulation 

thicknesses the curve parameter, with values .25”, .5”, 1”, 

1.5”, and 2.5” (respectively, from bottom to top curve). 

Fig. 10 shows the variation of Texit with total effective 

length Leff when keeping the vertical height fixed at 10’. 

[Leff is greater than the vertical height because of horizontal 

components of the duct run and effective lengths added in 

due to fittings and bends. If the length becomes too long for 

a given diameter, the flow will slow and cool down below 

0 °

C when Tamb = Tamb,min. A 30’ length would be just safe at 

the 4” diameter when Tamb,min = -13 °

C. 

Fig. 10. Exit temperature versus ambient temperature, for a 

4” duct with 1” insulation, 10’ in vertical height, and lengths 

of 100’, 60’, 40’, 30’, and 20’ (from bottom to top curve). 

The loop dumps room air heat to the outside, a parasitic loss 

that must be quantified to assess the viability of the loop. 

The model was used to compute the parasitic, which 

depends on temperature difference (Troom – Tamb) in a 

complex manner. Losses from the NCL were computed for 

six cities using a bin method (10), with results given in 

Table 1. Values are given with and without a thermostatic 

control that stops the flow when the air temperature rises 

above 1 °

C. The parasitic losses with no control range 

between ~1%-10% of savings. The losses in northern 

climates could be reduced with added insulation. The 

control significantly reduce the losses, ranging from nearly 

100% reduction in mild climates, but only about 35% 

reduction in the severest climate. A detailed cost study was 

not done, but it is estimated that the NCL could be installed 

for $100-$200. The cost advantage of going to a PSWH vs. 

an active system should be larger than sum of the NCL cost 

plus the monetary value of the parasitic losses from the 

NCL plus the monetary value of any decreased savings from 

going to the PSWH vs. an active system. 

Table 1. Room-air NCL Thermal Losses vs. Location. 

Loss, GJ/yr Loss, %1

Location No cntrl2

 Cntrl2 No cntrl2 Cntrl2

Albuquerque 0.26 0.07 2.80% 0.79% 

Boulder 0.36 0.15 4.58% 1.94% 

Memphis 0.24 0.05 3.31% 0.63% 

Minneapolis 0.65 0.42 9.84% 6.27% 

Phoenix 0.13 0.00 1.39% 0.01% 

Sacramento 0.26 0.00 3.40% 0.00% 

1. Loss expressed as a % of the savings at that location. 

2. “Cntrl” is a damper closing above 1 °

C. 

6. CONCLUSIONS AND FUTURE WORK 

If pipes are protected from freezing, the available 

geographical for PSWH can be extended northward. A form 

of primary pipe freeze protection has been investigated, 

using warm room air circulating in a NCL through a divided 

duct containing the supply/return pipes of the PSWH. A 

simple model for the NCL was developed which balances 

buoyancy and friction, predicting flow rate and NCL 

temperatures. A prototype room-air NCL was built and 

tested. The model agreed well with the data from a 4” duct 

if the model’s friction and heat transfer coefficients were 

roughly doubled [(Cfric,Cht-trsf) = (2.05, 1.8)]. The calibrated 

model was then used to calculate annual parasitic loss from 

the NCL and to generate design guidelines. 

Future work depends on available funding. Field trials of the 

room-air NCL are needed to develop practical details and 

resolve any issues that may arise. Other configurations 

should be investigated, such as circularly-concentric ducts 

with water pipes in the inner duct, and return air flow in the 

outer annulus (12). This configuration will allow lower flow 

5
rates than the split duct configuration, while still providing 

adequate protection. The uni-directional pipe model, where 

the flow exits into the attic at the top of the loop, should also 

be developed and validated, and its projected costs and 

losses compared to bi-directional NCL. 

i Index for fittings or data points 

min Record minimum (temperature) 

mod model 

room Room air 

shear Wall shear 

7. ACKNOWLEDGMENTS 9. REFERENCES

(1) Solar Energy Technology Program: Multi-year 

Technical Plan 2007-2011. The document is available at 

http://www1.eere.energy.gov/solar/about.html. 

The authors acknowledge funding from the U.S. Department 

of Energy’s Solar Energy Technology Program, Solar 

Heating and Lighting (SH&L) sub-program. We gratefully 

recognize encouragement from Tex Wilkins and Glen 

Strahs, SH&L program managers, to pursue PSWH market 

extension concepts. Ron Judkoff, director of the NREL 

Buildings and Thermal Sciences Center, has been a 

masterful enabler of good science. 

(2) Salasovich, J., Burch, J., and Barker, G., “Pipe Freeze 

Probability for Passive-solar Water Heating Systems in 

the United States”, Proc. ASES 2004, ASES, Boulder, 

CO. 

(3) Burch, J, and Heater, M., “Northward Market Extension 

for Passive Solar Water Heaters By Using Pipe Freeze 

Protection with Freeze-tolerant Piping”, to be published 

8. NOMENCLATURE Proc. ASES 2006, July 2006. ASES, Boulder, CO. 

(4) Darbaheshti, M., Burch, J., Gawlik, K., and Johnson, T., 

“Freeze Protection for Potable Water Piping Using 

Natural Convection Loops,” Proc. ASES 1999, ASES, 

Boulder, CO. 

Symbols

C Scale factor for friction or heat transfer 

D Diameter of air duct 

 (5) United States Patent, US005806511A, Method and 

Apparatus to Provide Freeze Protection for Solar Water 

Heating Systems, 1998. Assigned to D. Hart, Watershed 

Energy Systems. 

f Friction factor in Darcy-Weisbach Eqn. 

g gravity 

H Vertical height of natural convection loop 

K Hydraulic friction coefficient 

L Duct length (6) Burch, J., and Salasovich, J., “Water Consumption from 

Freeze Protection Valves for Solar Water Heating 

Systems”, Proc. ASES 2005, ASES, Boulder CO. 

v Average velocity in the duct 

P Pressure 

(7) Richard Bourne, Davis Energy Group, Davis, CA. 

Private Communication, 3/06. 

ρ density 

χ2

 Metric of deviation between model and data 

(8) Roberts, J., Burch, J., and Brandemuhl, M., “Venting 

Overheat Protection in Solar Water Heaters”, Proc. 

ASES 2005, ASES, Boulder, CO. 

∆ Difference 

σ Error 

Σ Summation 

(9) American Society of Heating, Refrigerating, and Airconditioning Engineers (ASHRAE). Fundamentals 

Handbook. pp 32.6-7. Atlanta: ASHRAE, 2005. Subscripts

amb Ambient 

(10) Heater, M., Passive Freeze Protection for Passive 

Solar Thermal DHW Systems, 12/04, M.S. Thesis, 

ACEE Department, University of Colorado, Boulder, 

CO. 

buoy buoyancy 

cold Cold side of the NCL 

data data 

exit exit from the NCL 

(11) Engineering Equation Solver. Available from F-chart 

Software, Madison, WI, USA. 

fric friction 

hot Hot side of the NCL 

(12) Craig Christensen, National Renewable Energy 

Laboratory, Golden, CO. Private Communication, 4/06. 

ht-trsf Heat transfer 

hydr Hydraulic 

6
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4. TITLE AND SUBTITLE

Pipe Freeze Prevention for Passive Solar Water Heaters Using a 

Room-Air Natural Convection Loop: Preprint 

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J. Burch: NREL 

M. Heater, M.Brandemuhl, and M. Krarti: University of Colorado 

5f. WORK UNIT NUMBER

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13. SUPPLEMENTARY NOTES

14. ABSTRACT (Maximum 200 Words)

With the goal of extending the geographical market for passive solar water heaters northward, a room-air natural 

convection loop (NCL) was investigated for providing freeze protection for supply/return pipes carrying pressurized 

domestic water through unconditioned space. An NCL model was developed based upon balancing buoyancy and 

friction in the loop. Calibration factors (Cfric,Cht-trsf) were introduced to scale calculations and account for unmodeled details and correlation bias. An NCL prototype was constructed with 2”, 4”, and 8” diameters. Least-square 

regression on data from the 4” diameter duct yielded (Cfric,Cht-trsf) = (2.05, 1.8). The calibrated model was used to 

provide site-specific design guidance, and to estimate energy losses with and without a thermostatic control to stop 

flow whenever Tamb > 0 °C. 

15. SUBJECT TERMS

solar domestic water heating; solar water heating; cold-climate solar domestic water heating; cold-climate solar water 

heating; thermosiphon solar water heating; freeze-protection for solar water heating 

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