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Go big to go low: Maximize the efficiency of your heat pumps, chillers, boilers and solar systems by getting the return temperatures down in heating and up in cooling

Copyright (c) 2012, Robert Bean, R.E.T., P.L.(Eng.), and content contributors

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Note: This page has interactive demonstrations activated with Wolfram CDF player - a free viewing software tool for CDF files. To take full advantage of the educational content download the Wolfram CDF player.

As discussed on previous pages, its not enough to own an energy efficient heating and cooling appliance, you have to get the return fluid temperatures right to get the efficiency out of the equipment. One way to do this is to increase the surface area of the heat terminal unit. Heat terminal unit or HTU represents the entire gamut of heating equipment from baseboards, to fan/coils to radiant floors, walls and ceilings. Keep this in mind, increasing the surface area of a HTU is a one time capital cost but the efficiency benefits last the life of the system.


Lets start with the effectiveness coefficient to see how all of this work...

Effectiveness coefficient, (Φ )

The effectiveness coefficient, (Φ ), represents a means of evaluating temperatures needed to condition people and spaces for which energy and exergy efficiency is intimately connected. In many ways the energy conservation and exergy efficiency of a nation can be compared against another based on its typical use of temperatures for its traditional HVAC systems (Table 1). The higher the effectiveness value the better attributes a system has for energy and exergy efficiency.


The effectiveness coefficient, (Φ ) is a simple calculation and it looks like this,

        Φ = (ts tr) / (ts tis)



        ts = fluid supply temperature

        tr = fluid return temperature

        tis = desired space temperature

Table 1. Effectiveness coefficient, (Φ ) for temperatures in various countries where tis = 20C (68F)

Other examples:

Hypothetical example of embedded pipes in a radiant heated high performance home
effectiveness = (80-70)/(80-68) = 0.83

Hypothetical example with heat transfer plates in a traditional to transitional home
effectiveness = (120-100)/(120-72) = 0.42

Hypothetical example without plates in traditional to transitional home
effectiveness = (150-130)/(150-72) = 0.26

Hypothetical example of typical baseboard or fan/coil system in a historical to traditional home
effectiveness = (180-160)/(180-72) = 0.19

Those that understand heat exchanger design will see the relationships between surface area, fluid temperatures, space temperatures and effectiveness. Not shown in the effectiveness coefficient is the combustion and compression efficiency which goes up with the higher effectiveness (>95%) or down with the lower effectiveness (<85%). Also there can be a shift from predominantly convective based heating (n power factors as high as 1.5) with lower effectiveness systems to radiant based heating (n power factors 1 to 1.1) with higher effectiveness (see Fig.1).

Space heating design capacity

Fig. 1 (above) Space heating design capacity based on the temperature differences for various power exponent (n) for various heat terminal units.

The thermal output for a heat terminal unit is another simple formula and can be expressed as,

        Q = U * A * ∆Tlmn

        Q = thermal power transferred, Btu/hr, (W)
        U = coefficient of heat transfer, Btu/hr/ft2/F (W/m2K) - determined by experiment or by calculation
        A = surface area of the heat transfer component, ft2, (m2)
        ∆Tlm = log mean temperature difference between the hot and the cold medium, F (K)
        n = power exponent (empirical values through testing)

The demonstration below calculates and plots the heat flow, (in watts/), through a heat exchanger's wall of a chosen thickness, (in mm), and thermal conductivity, (in watts/m C), with chosen surface heat transfer coefficients at either side of the wall, and (in watts/ C), and logarithmic mean temperature difference, Δ (in C), between them. Since the heat transfer coefficients can vary over a very large range, the and parameters can be specified as being high or low using a setter bar. The calculations are done using the equation , whose parameters can be modified by moving sliders. The red dot on the plot marks the heat flow per unit area for a Δ chosen by moving the top slider. The top graphic depicts the heat resistances as a schematic diagram (not to scale). Don't see the interactive graphic? Download the Wolfram CDF player.

Fig. 2 (above) Heat flow through a heat exchanger

Calculating the log mean temperature difference, LMTD (∆Tlm)

Fig. 3 (above) is an illustration of how the log mean temperature differences, LMTD (∆Tlm) is calculated for counter flow (left image) and co-current flow (right image). The individual temperatures (t) are established by design or assumption. The space temperature can be represented by the minimum entering (tA,1) and maximum discharging (tA,2) with the fluid supply temperature in heating represented by the minimum discharging (tB,2) and maximum entering(tB,1).

The demonstration below using the Wolfram CDF player illustrates the effects of various input parameters on parallel-flow and counter-flow heat exchangers. It shows the temperature distribution and calculates the total heat transfer. Don't see the interactive graphic? Don't see the interactive graphic? Download the Wolfram CDF player.

Fig. 4 (above) Operation of parallel-flow and counter-flow heat exchangers.

Oversize factor

Fig. 5 (above) required over sizing for cast iron radiators with n=1.3 as a result of a lower fluid temperature. For example if at design conditions when 100% output is required, the supply fluid temperature is 120F to maintain a 70F space temperature, then the cast iron radiator must be upsized by a factor of 4 since its output is approximately 25% of its performance at 215F supply temperature.

Oversize Factor (OF), the increase in size to restore the system to full heating capacity is written as;

       OF = [(T* – Ta)/(Tf Ta)]n


        T* = is the effective temperature for full heat output capacity of the original equipment size
        Tf = effective fluid temperature in F
        Ta= temperature of the air contacting the heat transfer surface of the equipment.

Example 1. Required radiator oversize for an effective temperature of 175F and air temperature of 70F
OF = (215F – 70F)/(175F – 70F)]1.3 ≈ 1.5

Example 2. Required radiator oversize for an effective temperature of 120F and air temperature of 70F
OF = (215F – 70F)/(120F – 70F)]1.3 ≈ 4

If one applies the same principle to baseboards (Fig.1, n= 1.4 curve) and convectors (Fig. 1, n=1.5 curve) it becomes evident that due to the higher reliance on convection these types of system will require even greater increase in size in comparisons to system more reliant on radiant.

Message: There will be a one time capital cost for the increased size of the heat terminal unit (bigger radiator, more baseboard, larger coil or more radiant tube etc.) but there will be a lifetime benefit for being able to operate the system at a lower temperature for the maximum efficiency.

This Wolfram CDF demonstration plots the radiated heat from a gray body having a given emissivity as a function of its temperature and that of its surroundings using the Stefan–Boltzmann law.

Fig. 6 (above) By clicking on the grey boxes marked with a "+" you can edit the operational regions. For radiators for space heating, change the Tmin = 0C and Tmax = 100C and Tradiator to 40C and Tambient=20C

Other considerations:

Radiant based systems (MRT / enclosure performance augmented if necessary with for example radiant floors) tend to have higher overall thermal efficacy than convective based systems (due to suppressed stratification and reduced radiant asymmetry) this generally has a positive influence on thermal comfort. Also the electrical power/thermal power ratio tends to go up with lower effectiveness systems due to the use of blowers rather than pumps.

Fig. 7 (above)  Based on various research projects funded by ASHVE (ASHRAE) and DTU, stratification and surface temperatures are representative of terrible, traditional and transitional housing types. Note however that as the building performance improves to a terrific model, the driving motive forces in buoyancy based on surface temperatures (MRT) are reduced and the stratification becomes less and in some cases insignificant.

The other consideration has to do with matching load temperatures with source temperatures (which is a study in exergy - yes…e-X-e-r-g-y). The temperatures in the higher effectiveness systems (i.e. those with plates) can more readily be matched to the temperatures available in renewable energy sources for higher exergy efficiencies.

Suffice to say every design decision in HVAC is not a trivial matter; debating for example whether one should use heat transfer plates in a radiant system has consequences that affects the lifetime operating costs of the system - in energy and IEQ analysis everything matters.

Message for consumers, builders and architects - it behoves you to work with a qualified design professional who using the above principles will be able to make sure you get the maximum work for your HVAC investment.


  1. Ishino, H., Research on Calculation Method of Thermal Design Load in Radiant Heating and Cooling Systems, Dept. of Architecture, Graduate School of Engineering Tokyo Metropolitan University, 1999

  2. Kilkis, B.I. 1998. Equipment Oversizing Issues with Hydronic Heating Systems. ASHRAE Journal 40(1):25-31.

  3. Peeters, L., Water-based Heating/cooling in Residential Buildings: Towards Optimal Heat Emission/absorption elements, Dissertation, University of Leuven Energy Institute, Applied Mechanics and Energy Conversion Section, 2009

  4. Exergy Assessment Guidebook for the Built Environment: Summary Report, edited by Herena Torio and Dietrich Schmidt. ECBCS Annex 49. Low Exergy Systems for High Performance Buildings and Communities

  5. Exergy Assessment Guidebook for the Built Environment: Guidebook, edited by Herena Torio and Dietrich Schmidt report. ECBCS Annex 49. Low Exergy Systems for High Performance Buildings and Communities.


Related pages
Programmable Thermostats Part I
Programmable Thermostats - Part II (includes boiler efficiency )
Radiant design guide

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