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 size
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.
Let's start with
the effectiveness coefficient to see how all of this works...
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 = (t_{s} – t_{r}) / (t_{s}
– t_{is})
where,
t_{s }
=_{ }fluid supply temperature
t_{r}
= fluid return temperature
t_{is }
=_{ }desired space temperature
Table 1.
Effectiveness coefficient, (Φ
) for temperatures in various countries where
tis
= 20°C
(68°F)
Other examples:
Hypothetical example of embedded pipes in a radiant
heated high performance
home
effectiveness = (8070)/(8068) = 0.83
Hypothetical example
with heat transfer plates in a traditional
to transitional home
effectiveness = (120100)/(12072) = 0.42
Hypothetical example
without plates in traditional to
transitional home
effectiveness = (150130)/(15072) = 0.26
Hypothetical example of
typical baseboard or fan/coil system in
a historical to traditional home
effectiveness = (180160)/(18072) = 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 *
∆T_{lm}^{n }
where;
Q = thermal power transferred,
Btu/hr, (W)
U = coefficient of heat transfer,
Btu/hr/ft^{2}/°F (W/m^{2}K)  determined by
experiment or by calculation
A
= surface area of the heat transfer
component, ft^{2}, (m^{2})
∆T_{lm}
= log mean temperature difference between the hot and the cold
medium, °F (K)
n = power exponent (empirical values
through testing)
Watch how the elements of a heat
exchanger work using the
Wolfram CDF player. Don't see the interactive graphic?
Download the
Wolfram CDF player.
Calculating the log mean temperature
difference, LMTD (∆T_{lm})
Fig. 3 (above) is an illustration of how the log mean
temperature differences, LMTD (∆T_{lm})
is calculated for counter flow (left image) and cocurrent flow
(right image). The individual temperatures (t)
are established by design or assumption. The space temperature
can be represented by the minimum entering (t_{A,1})
and maximum discharging (t_{A,}_{2})
with the fluid supply temperature in heating represented by
the minimum discharging (t_{B,}_{2})
and maximum entering(t_{B,}_{1}).
The demonstration below using the
Wolfram CDF player illustrates the effects of various input
parameters on parallelflow and counterflow heat exchangers. It
shows the temperature distribution and calculates the total heat
transfer. Don't see the interactive graphic?
Download the
Wolfram CDF player.
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 70°F 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* –
T_{a})/(T_{f}
– T_{a})]^{n}
where,
T* = is the
effective temperature for full heat output capacity of the
original equipment size
T_{f}
= effective fluid temperature in °F
T_{a}=
temperature of the air contacting the heat transfer surface of
the equipment.
Example 1. Required radiator oversize for an effective
temperature of 175°F and air temperature of 70°F
OF = (215°F – 70°F)/(175°F – 70°F)]^{1.3} ≈ 1.5
Example 2. Required radiator
oversize for an effective temperature of 120°F and air
temperature of 70°F
OF = (215°F – 70°F)/(120°F – 70°F)]^{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.
Don't see the interactive graphic?
Download the
Wolfram CDF player.
Fig. 6 (above)
StefanBoltzmann Law from the
Wolfram Demonstrations Project by Mark D. Normand. By
clicking on the grey boxes marked with a "+" you can edit
the operational regions. For radiators for space heating,
change the T_{min} = 0°C
and T_{max} = 100°C
and T_{radiator} to 40°C
and T_{ambient}=20°C
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…eXergy). 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. Resources:

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

Kilkis, B.I. 1998.
Equipment Oversizing
Issues with Hydronic Heating Systems. ASHRAE Journal
40(1):2531.

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

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

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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