Thermal equilibrium can help you estimate the tradeoff between boiler efficiency and heat emitter cost.

Every hydronic heating system we design involves compromise. We’re constantly juggling options that effect performance, ease of installation, reliability and cost as we establish the system’s hardware configuration.

One of the biggest design compromises we must consider involves the relationship between the heat output characteristics of a hydronic distribution system and the water temperature supplied to that system.

Three decades ago, when fuel was cheap, the North American hydronics industry favored use of high supply water temperatures, which reduced the required surface area of heat emitters. The reasoning was simple: Why pay for 12 feet of fin-tube baseboard if eight feet could do the job using a higher water temperature? This is why you’ll find thermal output ratings for fin-tube baseboard that go up to at least 220°F. This made sense when the price of a barrel of crude oil was far from crossing the triple digit mark.

Figure 1.

Today the picture is very different and the trend is clear: The future of North American hydronics is reduced operating temperature. This is necessary to allow boilers to operate with sustained flue gas condensation, which boosts thermal efficiency from the mid-80 to mid-90% range. The days of cheap fuel and scalded water design are over. My suggestion: Never design any system for supply water temperatures over 200°F, and favor even lower temperatures whenever you can.

So what does this mean when you are selecting heat emitters? From the standpoint of improving thermal performance, it means bigger is better. Longer baseboards, larger panel radiators, and perhaps closer tube spacing on radiant panel circuits are all advisable when the goal is to reduce system operating temperature and boost thermal efficiency. This approach is further supported by the increased use of solar collectors and geothermal heat pumps. Both of these heat sources offer significantly higher thermal efficiency when operating at lower water temperatures.

Quantifying the Relationship

A fundamental concept when sizing a hydronic heat emitter is that heat output is approximately proportional to the difference between supply water temperature and room air temperature. This can be written mathematically as follows:
Formula 1

Figure 2.

Q output = heat output of heat emitter (Btu/hr)
c= a number dependent on the type and size of heat emitter (Btu/hr/°F)
Ts = water temperature supplied to heat emitter (°F)
Tr = room air temperature °F)

This relationship holds true for a single heat emitter, as well as a group of heat emitters operating as a distribution system.

For example, consider a building where all the heat emitters in the system release 100,000 Btu/hr into a 70°F space when supplied with water at 170°F. The value of the “c” in Formula 1 could be determined for this system as follows:

This c value means that this particular distribution system releases 1,000 Btu/hr into the building for each degree F the supply water temperature exceeds the room air temperature. Hence, if the supply water temperature was 130°F, and the space air temperature was 68°F, this system would provide the following heat output to the building:

Figure 3.

The term (Ts minus Tr) in Formula 1 is called the “driving Delta T.” It’s the temperature difference that drives heat from the water through the heat emitter and out into the space being heated. Anything that makes the driving Delta T larger increases the rate of heat transfer into the building and vice versa.

Formula 1 also can be represented by a graph. Figure 1 shows an example using the same numbers used in the previous example.

To draw this graph for a given distribution system, all you need is the heat output rate at one supply water temperature and the associated space temperature. Subtract the space temperature from the supply temperature to get the value of the driving Delta T, (Ts-Tr), then plot that point along with the associated heat output rate. This point must lie on a line that also passes through the point zero heat output at zero driving Delta T.

The slope of the line depends on the number and size of the heat emitters in the distribution system. The larger the surface area of the heat emitters, the steeper the slope of the graph. This concept is shown in Figure 2.

Steeper lines mean that a given rate of heat release is achieved at lower values of the driving Delta T. For a given room temperature, steeper lines favor lower supply water temperature. This, in turn, improves the efficiency of condensing boilers, geothermal heat pumps and solar collectors.

In the case of floor heating, steeper lines are achieved by closer tube spacing, as shown in Figure 3.

Adding the desired room temperature to the numbers along the bottom axis makes a useful variant of this graph, as illustrated in Figure 4. This graph shows heat delivery versus supply water temperature for the same system represented in Figure 2. Note that each number on the horizontal axis of Figure 4 is 70°F (the assumed desired room temperature) higher than the numbers along the bottom axis of Figure 1.

Figure 4.

Seeking Balance

Every hydronic system you’ll ever design or install “wants” to operate at a condition called thermal equilibrium. This occurs when the rate of heat release from the circulating water exactly equals the rate at which heat is added to the water by the heat source. The water temperature in the system automatically adjusts to make this condition occur.

If not for the intervention of temperature limiting controls, every hydronic system would eventually stabilize at a supply water temperature where thermal equilibrium exists. This temperature may or may not provide the proper heat input to the building. Likewise, it may or may not be conducive to safe and efficient operation or long system life. Simply stated: The system “doesn’t care” if it’s delivering the proper amount of heat to the rooms or if it’s operating safely. It only “cares” about achieving a balance between heat input and heat output.

You can use a distribution system heat output graph like that shown in Figure 4 to find the supply temperature at which thermal equilibrium occurs with a given heat source. First, locate the heat output rate of the heat source on the vertical axis. Next, draw a horizontal line to the right until it intersects the sloping line. Finally, draw a line straight down to the horizontal axis to read the water supply temperature at which the system wants to operate.

For example, if a boiler having a fixed heat output rate of 60,000 Btu/hr were coupled to the distribution system represented by Figure 4, that system would seek to operate at a supply water temperature of 130°F.

You can use the concept of thermal equilibrium to study the supply temperature required versus heat emitter size as you contemplate future systems. Once you know the temperature at which the system “wants to operate,” you can estimate the tradeoff between boiler efficiency and heat emitter cost.