Hydronic Heating with Renewable Energy Heat Sources

Designing for low water temperatures is critical to good performance

This article focuses on using water-based hydronic distribution systems to distribute heat produced by renewable energy heat sources. It’s based on the premise that good hydronic design is the “glue” that holds together nearly all thermally based renewable energy systems that provide space heating and domestic hot water for homes. In other words, pick a renewable heat source, do a good job with the underlying hydronics, and you’ll likely be pleased with the results. Pick any renewable heat source, treat the hydronics as “whatever,” and you’re likely to be disappointed.

A Little History:

I started working in the renewable energy field in 1978 as an applications engineer for Revere Solar & Architectural Products in Rome, NY. In those days, solar heating essentially boiled down to using solar collectors as sunny day substitutes for conventional boilers or water heaters. Designers focussed on the collectors, storage, and control aspects of the solar subsystem, but devoted little thought to a compatible means of distributing solar derived heat within the building.

Most hydronic distribution systems of that era were designed around relatively high supply water temperatures. Most residential system used fin-tube baseboard to release heat from water sent through the piping circuits at temperatures that sometimes exceeded 200 oF.

Many designers of that vintage eventually discovered that the high water temperatures required by conventional hydronic heating systems were beyond what solar collectors could produce on a consistent basis. Sure, there was an occasional “perfect solar day” in December or January, where the storage tank got hot enough to supply the home’s heating load during the following night. However, seasonal performance over a typical Northern heating season was often disappointing. In short, after investing thousands of dollar in collectors, storage tanks, and controls, many of these early systems spent much of their time distributing heat generated by conventional fuels rather than by the sun.

The North America heating industry has long had a tendency to focus overwhelming attention on heat sources rather than overall heating systems. Unfortunately, this mindset continues to limit the performance of not only solar thermal applications, but heating systems supplied by emerging renewable heat sources such as geothermal heat pumps, and wood-fired boilers.

Trending Downward:

All renewable heat sources yield better performance when combined with low temperature distribution systems. To see why we’ll take a look at the thermal performance characteristics of a solar collector, and a geothermal water-to-water heat pump.

Figure 1 shows how the instantaneous thermal efficiency of a flat plate solar collector is affected by the temperature of the Figure 1fluid entering its absorber plate.

Assuming the outdoor temperature and solar radiation intensity remain at the indicated values, which represent a sunny mid-winter day in a Northern US climate, the thermal efficiency of the collector drops rapidly with increasing inlet fluid temperature.

For example: If the fluid entering the collector is at 90 oF, the outdoor air temperature is 30 oF, and the sun is bright (e.g. solar intensity is 250 Btu/hr/ft2), the graph indicates that the solar collector is gathering about 56% of the solar energy striking it. However, if the entering fluid temperature is 160oF, while the other conditions remain unchanged, the collector’s efficiency falls to 33%. That’s a significant “penalty” imparted by forcing the collector to operate at the higher inlet temperature. It’s the result of greater heat loss from a collector to outside air, much like the increased heat loss associated with keeping your house at 75 oF rather than 68 oF.

This relationship between entering load water temperature and efficiency also holds true for hydronic heat pumps. Figure 2 shows the effect for a modern water-to-water geothermal heat pump, operating with an assumed constant earth loop inlet temperature of 45 oF.

Figure 2

The coefficient of performance (COP) is an indicator of the heat pump’s efficiency. Mathematically, it’s the ratio of the heat output rate divided by the electrical input rate. A COP of 4.0 means that the heat pump is sending heat to the load at a rate 4 times higher than the rate of electrical energy input required to operate it. The higher a heat pumps’ seasonal COP, the lower its seasonal operating cost.

Figure 2 shows the COP of this particular heat pump dropping rapidly as the temperature of water entering it from the hydronic distribution system increases. Thus, for the highest possible COP, the water temperature required from the heat pump should be kept as low as possible.

When it comes to wood-fired boilers one might argue that they can produce higher water temperatures, even up to 200 oF. While this is true, it doesn’t negate the benefits of matching wood-fired boiler to low temperature distribution systems. The reason is that these heat sources are best applied in combination with a thermal storage tank. When operating, they add heat to that tank. The heating distribution system draws heat out of that tank. The lower the tank temperature can go, and still supply sufficient heat to the building, the less often the boiler has to be stoked.

 My suggestion is to design hydronic heating systems supplied by either solar collectors or hydronic heat pumps so that the supply water temperature under maximum load conditions doesn’t exceed 120 oF.

Making It Happen:

Now that you know that low water temperature distribution systems enhance the performance of renewable energy heat sources, let’s look at some practical options for building them.

First, it’s critically important to understand what determines the supply water temperature in any hydronic heating system.

Some designers, including an embarrassing high percentage of HVAC professionals, think that it’s the heat source that determines the supply water temperature in a hydronic heating system. This stems from the fact that many boilers come with a control device that has a dial (or perhaps a digital interface) which the installer uses to “set” a water temperature. Many think that by setting this temperature they are guaranteeing that the heat source will produce it. Unfortunately that’s not true. The set temperature is only a limit on how high the water temperature leaving the heat source might climb if conditions allow. This is called a high temperature limit, and it does NOT guarantee that the set water temperature will ever by achieved.

The water temperature in any hydronic heating system only climbs high enough for that system to achieve thermal equilibrium – where the rate of heat release from the distribution system exactly balances the rate of heat input from the heat source. Once this condition is achieved, there is no thermodynamic incentive for the water temperature to climb higher, and it won’t!

It’s the design of the hydronic distribution system, rather than the setting of the heat source’s high limit controller, that determines the water temperature at which the system operates.

Almost everyone who designs heating systems wants to maximize their thermal efficiency. In the context of hydronics, this means moving away from high water temperatures by specifying heat emitters with larger active surfaces, or other details that increase both convective and radiative heat transfer. This allows thermal equilibrium to occur at relatively low water temperatures during both maximum load and partial load conditions.

Although the trend toward lower water temperatures is relatively new in North America, it’s been happening on a worldwide basis for several decades. Those who work with hydronics in Europe accept low water temperature distribution systems as the norm.

Truth be told; North America is perhaps the last place on earth where some hydronic heating systems are still designed around water temperatures of 180+ oF.

Why is this the case? Because most North American hydronic heating systems, especially those used in houses, are designed to keep their installed cost as low as possible.

Standard fin-tube baseboard is one of the best examples. Originally designed as an alternative to cast-iron radiators, most fin-tube baseboard hasn’t changes much over the last several decades. When fin-tube baseboard first entered the market, fuel was cheap, and nearly all boilers operated at water temperatures of 180 oF or higher. You can still find north American manufacturer’s literature that lists the heat output of fin-tube baseboard at water temperatures as high as 240 oF!

The economics are simple: The higher the water temperature, the greater the heat output. The greater the heat output, the shorter the required fin-tube length. The shorter the length, the lower the installed cost.

This was probably justified when fuel was cheap. Even now, standard fin-tube baseboard would probably regain market share against more contemporary and higher cost alternatives if fuel prices reverted to where they were in the 50s and 60s. That’s not going to happen, so the industry needs to move on.

Emitter Evolution:

Fortunately there are several ways to design modern hydronic distribution systems around the low water temperatures that enhance the performance of renewable energy heat sources.

Let’s start with the heat emitters. This term refers to any device intended to remove heat from water flowing through it, and release that heat into the room where it’s located.

Many homeowners in heating dominated climates are used to the look of fin-tube baseboard. While most don’t relish it as a visual enhancement to a room, they understand its purpose, and accept it as a necessary part of the building.

The latest development in low temperature fin-tube baseboard is shown in Figure 3. It’s a product called Heating Edge that’s now available in North America.

[Figure 3] (Courtesy of Smith’s Environmental Products)Screen Shot 2016-01-12 at 11.16.12 AM

From the outside it looks similar to other fin-tube baseboard, but what’s “under the hood” is very different. Heating Edge baseboard has fins that are about three times larger than those on traditional baseboard. It also has two 3⁄4” copper tubes running through those fins. These tubes can be piped for either parallel or series flow. In the latter case, the hottest water flows down the upper tube, makes a U-turn at the end of the element, and flows back along the lower tube.

Assuming an average water temperature of 110 oF, this baseboard releases about 290 Btu/hr/ft when the two pipes are configured for parallel flow, and the total flow rate through the element is 1 gallons per minute (gpm). This increases to about 345 Btu/hr/ft with a total flow of 4 gpm. If the two tubes are configured for series flow the output drops about 10%.

Consider a 12 foot by 16 foot room in a well insulated home, with a maximum heating load of 2880 Btu/hr (e.g. 15 Btu/hr/ft2). This load could be met using a 10 foot length of Heating Edge baseboard operating at an average water temperature of 110 oF and 1 gpm flow rate. To produce equivalent output, a 10 foot length of conventional residential baseboard would require an average water temperature of about 150 oF. This temperature is well above what a typical geothermal heat pump can produce, and would significantly lower the efficiency of solar thermal collectors.

Radiant Solutions:

The key to low water temperature operation are heat emitters with large heated surface areas. The greater the heated surface area, the lower the required water temperature for a given rate of heat output.

By embedding tubing in floors, walls, and ceilings, it’s possible to create very large heated surfaces within a room. Such surfaces are called hydronic radiant panels.

Radiant floor heating is undoubtedly the best known form of radiant panel heating. It can be installed in several proven ways that allow it to operate at relatively low water temperatures.

Tubing embedded in a concrete floor slab is the most common form of radiant floor heating. Figure 4 shows a proven design configuration.

Figure 4Notice that the tubing has been placed at approximately mid-depth within the slab, and that the underside and edge of the slab are well insulated with extruded polystyrene. These details are crucial for good low temperature performance. It’s also important to use low resistance (or even no-resistance) floor coverings. A painted, stained, or stamped slab surface is ideal. If that doesn’t suit you tastes, consider ceramic tile, or vinyl flooring. If you have to have carpet, and still expect reasonable performance, use only 1⁄4” thick commercial level loop carpet, and glue it directly to the slab. If you ignore this advice, and cover that heated slab with 1⁄2” thick urethane pad and Berber carpet, the only consolation I can offer is “better luck next time.”

The graph in Figure 5 can guide your tube spacing and floor covering selections. Assuming you’re satisfied with 70 oF indoor air temperature, this graph gives you the required average water temperature in the floor tubing based on tube spacing, the R-value of the floor covering (if any), and the rate at which heat must leave the floor under maximum heating conditions (in Btu/ hr/ft2).

Figure 5

For example, assume the maximum heating load of a room, divided by the heated floor area, is 15 Btu/hr/ft2 . You’ve decided to install the tubing at 6” spacing, and finish the slab with a sealed stain (Rff=0). The required average water temperature in the embedded tubing in only 83 oF. The supply water temperature is typically 8 to 10oF higher than the average water temperature. Under these assumptions you will only need to supply the slab with 93 oF water under maximum heating load. The supply water temperature will be even lower under partial load conditions.

Such temperatures allow excellent performance of the renewable energy heat source. However, the floor surface temperature will likely only be in the low to mid 70s. That’s as hot as the floor needs to get to release all the heat the room needs. I always stress this point so that occupants understand that the “toasty warm” floor implied by some floor heating advertisements simply don’t occur in low heating load conditions, and in systems optimized for low water temperature operation.

The graph in figure 5 is limited to a maximum finish flooring resistance of 1.5, and a maximum average water temperature of 110 oF, (with the assumption of a maximum supply water temperature of 120 oF). If you’re serious about building a good performing system, don’t exceed these limits. Here are some more suggested limits for using a heated slab floor with a renewable energy heat source:

  • Tube spacing within the slab should never exceed 12 inches
  • The slab should have a minimum of R-10 underside and edge insulation
  • Tubing should be placed at approximately half the slab depth as shown in figure 4. Doing so decreases the required water temperature for a given rate of heat output. For a 4-inch thick concrete slab the average water temperature needs to be about 7 oF higher if the tubing is left at the bottom of the slab during the pour. This will definitely lower the performance of the renewable energy heat source.

Heated Thin-Slabs:

Another common method of installing floor heating uses a 1.5-inch “thin slab” poured over a wooden floor deck. The slab can be either concrete or poured gypsum underlayment, but it should never be “lightweight concrete.” The latter material uses vermiculite or polystyrene beads instead of stone aggregate, and has significantly higher thermal resistance.

Figure 6 shows an installation awaiting concrete placement. The 1⁄2” PEX-AL-PEX tubing has been carefully fastened down in a predetermined patten using a special stapler. A layer of 6-mil polyethylene film provides a bond breaker between the bottom of the slab and the plywood subfloor.

[Figure 6] (Courtesy of Harvey Youker)

Screen Shot 2016-01-12 at 11.23.07 AM

Because the slab is thinner, it has somewhat poorer heat dispersion characteristics. This translates into a slightly higher water temperature requirement for a given rate of heat output. This difference is slight. A 1.5-inch concrete thin slab with 12-inch tube spacing and covered with a finish flooring resistance of 0.5oF•hr•ft2/Btu yields about 8% less heat output than a 4- inch-thick slab with the same tube spacing and finishing flooring. This can be easily compensated for by using 9-inch rather than 12-inch tube spacing.

The following guidelines are suggested for thin slabs supplied by renewable heat sources:

  •  Tube spacing for a thin slab application should not exceed 9 inches
  • Floors under thin-slabs should have minimum of R-19 underside insulation
  • Floor finishes should have a total R-value of 1.5 or less (lower is always better)

Heated Walls and Ceilings:

Walls and ceilings can also be turned into low temperature hydronic radiant panels. One construction that I’ve used on several projects is shown in Figure 7.

[Figure 7]Figure 7

When finished, this radiant wall is indistinguishable from a standard interior wall. Its low thermal mass lets it respond quickly to changing internal load conditions or zone setback schedules. This fast response is especially important in homes with low heat loss or significant internal heat gain.

The rate of heat emission from the panel shown in figure 7 is approximately 0.8 Btu/hr/ft2 for each degree Fahrenheit the average water temperature in the tubing exceeds room air temperature. Thus, if the wall operates with an average water temperature of 110oF in a room with 70oF air temperature, each square foot of wall releases about 0.8 x (110 – 70) = 32 Btu/hr/ ft2. This is good performance, and well within the water temperature spectrum that most renewable energy heat sources can supply.

If you plan to install this system on the inside of an exterior wall, make sure the R-value of that wall is 50% higher than that of non-heated exterior walls. That keeps the rate of heat loss to the outside about the same as for a non-heated wall. If you’re installing this on an inside partition, use a 3.5-inch fiberglass batt in the stud cavities behind the heated wall. Finally, radiant wall panels are best constructed to heights of 3 to 4 feet above the floor. These heights bias the radiant heat output into the occupied zone of rooms, and thus improve comfort.

Another possibility is a radiant ceiling using the same construction as the radiant wall. The only difference is that the materials are fastened to the ceiling framing rather than the studs. Figure 8 shows an infrared thermograph of such a ceiling as it warms up. The red areas on the left side indicated that the aluminum heat transfer plates are doing an excellent job of dissipating heat away from the tubing and across the adjacent ceiling surfaces Can you tell which way the water is flowing across the ceiling?

Figure 8


Like the radiant wall, this radiant ceiling has low thermal mass and can respond quickly to interior temperature changes. Heated ceilings also have the advantage of not being covered by rugs or furniture, and thus are likely to retain good performance over the life of the building.

The rate of heat emission from a ceiling panel constructed as shown in figure 7 is about 0.71 Btu/ hr/ft2 for each degree Fahrenheit the average water temperature exceeds room air temperature. Thus, if the ceiling operated with an average water temperature of 110oF in a room with 70oF air temperature, each square foot of ceiling would release about 0.71 x (110 – 70) = 28.4 Btu/hr/ft2. Although not as high as the radiant wall, this performance is still very acceptable for use with most renewable heat sources.

Panel Pleasantries:

Generously sized panel radiators can also provide good low temperature performance. Again, the suggested guideline is to size panels to deliver the maximum required heating output using a supply water temperature no higher than 120oF. An example of a panel radiator with integral thermostatic radiator valve (seen in the upper right corner of the panel) is shown in Figure 9.

[Figure 9]

Figure 9Manufacturers provide output ratings for their panel radiators using tables or graphs. Most list heat output for high water temperatures such as 180oF. Correction factors are provided to determine heat output at lower water temperatures. As an approximation, a panel radiator operating with an average water temperature of 110 oF in a room maintained at 68 oF, provides about 27 percent of the heat output it would yield at an average water temperature of 180 oF. Larger panels (longer, taller, and deeper) are available to increase surface area to compensate for lower operating temperatures.

If you want the latest in contemporary looks combined with excellent thermal performance, consider the “Low H20” panels from JAGA North America. One product from this line is shown in Figure 10.

[Figure 10]

Figure 10

A Low H2O panel has a large internal convective element consisting of multiple passes of copper tubing and aluminum fins. This element in housed in a simple powder-coated steel enclosure that channels air movement, and provides a low temperature radiant surface facing the room.

A unique feature of these panels is the rack of “microfans” seen at the top of the convective element. These fans operate on low voltage, and only require about 1.5 watts each when operating at full speed. Their purpose is to enhance convective heat transfer when the panel is operating at low water temperatures. They do this very well, boosting low temperature output about 250% compared to the same panel without fans.

Although some electrical power is required, it’s very small in comparison to standard fan convectors using AC-powered C-frame motors. The microfans are also very quiet, and can modulate their speed as needed based on the water temperature supplied to the panel. Each panel can also be equipped with a wireless thermostatic radiator valve to regulate water flow in response to room air temperature.

From Here to There:

Perhaps you’ve formed an opinion on what’s the “best” combination of renewable energy heat source and hydronic heat emitter. That’s fine, but keep in mind that none of these potential combinations will deliver as expected without a well planned hydronic distribution system.

Although there are several piping layouts that may serve your purpose, one stands out in my mind as the simplest, easiest to install, and literally most flexible approach. I refer to it as a “homerun” distribution system. An example of such a system using panel radiators for heat emitters is shown in Figure 11.

Figure 11

Homerun distribution systems start with a manifold station, the same kind as used for radiant panel heating. In figure 11, the manifold station is mounted in an accessible wall cavity. It could also be mounted horizontally under the floor provided it remains accessible.

Two lengths of 1⁄2” PEX or PEX-AL-PEX tubing provide the supply and return from the manifold station to each heat emitter. The flexibility of this tubing allows it to be routed through framing cavities much like an electrical cable. This is particularly helpful in retrofit situation, where the use of rigid tubing would otherwise require some “Sawsall® surgery” to building surfaces.

Figure 12 shows a homerun system in schematic form. A thermal storage tank has been added as the heat source. A variable speed pressure regulated circulator provides flow.

Figure 12

Variable speed pressure regulated circulators have been used in Europe for over a decade. They are now available in North America from companies including Grundfos, Wilo, and Xylem.

These circulator use microprocessor-controlled electronically commutated motors capable of operating over a wide range of speeds, and in different control modes depending on the application. For a homerun distribution system, the circulator is set for “constant differential pressure” mode. Its responsibility is to maintain a constant (installer set) differential pressure between its inlet and outlet ports. It does this by varying speed in response to changes in the “hydraulic resistance” of the distribution system

The motors in these “intelligent” circulators operate on approximately 50% of the electrical wattage required by standard hydronic circulators of equal capacity. This characteristic, in combination with speed control, delivers annual electrical energy savings of 60 to 80% relative to standard hydronic circulators. Without question, these circulators are quickly raising the performance bar in all types of hydronic systems. Their energy saving benefits makes them particularly attractive for renewable energy applications. Figure 13 shows three circulators of this type that are currently available in North America.

[Figure 13] Figure 13

The combination of a homerun distribution system, heat emitters equipped with non-electric thermostatic radiator valves, and a variable speed pressure regulated circulator is a marriage made in hydronics heaven.

The thermostatic radiator valves (TRV) shown on each panel radiator in figure 12 constantly monitor the room air temperature where the panel is located. If that temperature drops 1oF or more below the TRV’s temperature setting, the valve’s stem slowly begins opening to allow increased water flow through that panel. This causes a very slight drop in the hydraulic resistance of the distribution system, a change that’s quickly detected by the pressure regulated circulator. The circulator responds by increasing speed until the differential pressure it was previously operating at is restored. The yields a slight flow increase through the panel that needs it, and virtually no flow changes in the other panels. Think of this as “cruise control” for system flow.

The Big Picture:

Now that we’ve discussed several state-of-the-art hydronic components and design concepts, let’s put them together into a system that leverages their individual qualities. A schematic of that system is shown in Figure 14.

[Figure 14]

Figure 14

The main component in this system is a well insulated storage tank equipped with an integral modulating gas burner and internal condensing heat exchanger. The burner fires to keep the water at the top of the tank warm enough to provide domestic hot water (typically 120 to 130oF).

A drainback-protected solar subsystem is seen on the left side of the system. When the collectors are a few degrees warmer than the water near the bottom of the tank, the collector circulator runs to create flow through the collector array. When the collectors cool relative to the tank, this circulator turns off, and all water in the collectors and exposed piping flows back into the tank.

No antifreeze is required in this system, and no heat exchanger is needed between the collectors and the storage tank. These features reduce cost and increase collector efficiency. The same water that flows through the collectors also flows through the heating distribution system. The system is completely “closed” from the atmosphere, and protected against corrosion.

The captive air at the top of the tank is under slight positive pressure. This air space provides a drainback reservoir, and an integral expansion “tank” for the system. Assuming proper installation, most of the air initially occupying this space never leaves the system. The oxygen molecules in the initial air charge quickly react with any ferrous metal in the system to form a thin and inconsequential oxide film. What remains is mostly nitrogen, which is an inert gas, and doesn’t cause corrosion. Any air molecules that are dissolved in the water supplied to the distribution system are eventually gathered by the air separator downstream of the tank, and returned to the air space.

The water in the tank serves two purposes: First, it provides thermal storage for the solar collectors. Second, it provides thermal mass to buffer the highly zoned space heating distribution system. The latter function protects the burner against short operating cycles, which if present, lower efficiency and increase maintenance. Short cycle protection is very important in any hydronic systems with extensive zoning.

A flow switch detects whenever domestic hot water is being drawn at a flow rate of 0.4 gpm or higher. Under this condition, the switch turns on a small circulator that moves hot water from the top of the thermal storage tank through one side of a stainless steel brazed plate heat exchanger. Such heat exchangers have extremely fast response to temperature changes. Cold domestic water is instantaneously heated as it passes through the other side of this heat exchanger. The fact that minimal amounts of heated domestic water are “stored” by this system also lowers the risk of Legionella growth.

An anti-scald-rated thermostatic mixing valve protects against high domestic water delivery temperature when the tank is very hot. The latter condition is likely, especially at the end of a sunny warm day. For the fastest possible response, the piping between the thermal storage tank and heat exchanger should be short and fully insulated. Combination isolation / flushing valves should be installed on the domestic water inlet and outlet of this heat exchanger. They allow the heat exchanger to be isolated and flushed if necessary to remove scale.

A single variable speed pressure regulated circulator provides flow to the homerun distribution system for space heating. With good design, this circulator can supply the entire distribution system in a typical 2500 square foot house using no more than 40 watts of electrical power under maximum heating load.

Each panel radiator has an adjustable thermostatic radiator valve that monitors room temperature, and adjusts flow rate as needed to maintain that temperature. No thermostats, batteries, transformers, or programming, just simple, effective and reliable room-by-room temperature control.

The 3-way motorized mixing valve upstream of the manifold station protects the distribution system from what could be a very hot storage tank following a sunny spring or fall day. It also adjusts the water temperature supplied to the panels based on outdoor temperature. The latter function is called outdoor reset. It stabilizes room temperature for optimum comfort.

Use the Glue Wisely:

So, that’s a taste of what modern hydronics technology can offer those interested in heating homes using renewable energy. After reading this, I hope you agree that modern hydronics technology is the “glue” that holds most thermally based renewable energy systems together. It’s also a canvas upon which creative designers can develop unique, reliable, and highly efficient heating systems. Use it to its maximum potential.


© Copyright 2016, J. Siegenthaler, all other rights reserved.
No part of this article may be reproduced without written permission from the author.
All information presented is conceptual, and not meant to be used for the installation of any specific system.

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Person medium john siegenthaler About the author, John Siegenthaler – Principal, Appropriate Designs

John Siegenthaler, P.E., is a mechanical engineer and graduate of Rensselaer Polytechnic Institute, a licensed professional engineer, and Professor Emeritus of Engineering Technology at Mohawk Valley Community College. “Siggy” has over 32 years of experience in designing modern hydronic heating systems. He is a hall-of-fame member of the Radiant Professionals Alliance and a presenter at national and international conference on hydronic and radiant heating. John is principal of Appropriate Designs – a consulting engineering firm in Holland Patent, NY. The 3rd edition of his textbook – Modern Hydronic Heating – was released in January 2011. John currently writes about hydronic heating and solar thermal system design for several trade publications.

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