TP-16: Heat Emitters | HEM Reference

Overview

Heat emitters transfer thermal energy from a wet heating circuit into the conditioned zone. TP-16 models three emitter types: radiators, underfloor heating (UFH), and fan coil units. Each type converts the enthalpy of circulating water into a combination of convective and radiative heat output that enters the zone heat balance.

The emitter model sits between the heat generator (a heat pump per TP-12: Heat Pumps or a boiler per TP-14: Boilers) and the zone demand calculation (TP-04: Space Heating Demand). It determines the flow and return temperatures seen by the heat generator, accounts for the thermal inertia of the emitter body, and calculates the actual heat delivered to the zone air node at each timestep.

Flow temperature control follows the Ecodesign Regulation classification system, supporting both fixed flow temperature operation and weather-compensated control curves.

Inputs

Parameter	Symbol	Unit	Description
Thermal mass of emitters	$K_{E}$	kWh/K	Total thermal capacity of the emitter body
Emitter power coefficient	$c$	kW/K $^{n}$	Coefficient from characteristic equation (BS EN 442 for radiators)
Emitter power exponent	$n$	-	Exponent from characteristic equation (BS EN 442 for radiators)
Convective fraction	$f_{co n v}$	-	Fraction of emitter output delivered by convection (0 to 1)
Design temperature difference	$Δ T_{d s g n}$	K	Design flow-minus-return temperature difference across emitters
Design flow temperature	$T_{f l o w, d s g n}$	°C	Maximum (design) flow temperature
Ecodesign control class	-	-	Control classification I to VIII
Minimum outdoor temperature	$T_{o u t, min}$	°C	Weather compensation curve lower outdoor limit
Maximum outdoor temperature	$T_{o u t, ma x}$	°C	Weather compensation curve upper outdoor limit
Minimum flow temperature	$T_{f l o w, min}$	°C	Weather compensation curve lower flow limit
Variable flow flag	-	-	Whether the heat source can modulate flow rate
Design flow rate	$\dot{V}_{d s g n}$	l/min	Fixed flow rate (constant-flow systems)
Minimum flow rate	$\dot{V}_{min}$	l/min	Lower bound for variable-flow systems
Maximum flow rate	$\dot{V}_{ma x}$	l/min	Upper bound for variable-flow systems
Bypass recirculation fraction	$f_{b y p a ss}$	-	Fraction of return water recirculated into flow (0 to 1)
System performance factor (UFH)	$K_{h}$	W/(m²·K)	Heat output per unit floor area per degree (BS EN 1264)
Equivalent specific thermal mass (UFH)	$κ_{U F H}$	kJ/(m²·K)	Thermal mass per unit floor area (BEAMA guidance)
Emitter floor area (UFH)	$A_{U F H}$	m²	Floor area served by underfloor heating
Number of fan coil units	$N_{f c}$	-	Count of fan coil units in the zone
Fan coil test data	-	-	Manufacturer performance data: power output at each fan speed versus temperature difference, and fan electrical power per speed

Calculation

Emitter Types

Radiators

Radiators are characterised by a power law derived from BS EN 442 test data. The coefficient $c$ and exponent $n$ are determined experimentally for a given radiator design. The thermal mass $K_{E}$ is a required input.

Underfloor Heating

For UFH, the exponent is fixed at $n = 1$ , consistent with BS EN 1264 and BS EN 11855 under normal operating conditions. The coefficient is derived from the system performance factor and floor area:

$c_{U F H} = \frac{K _{h} \cdot A _{U F H}}{1000}$

where the factor of 1000 converts from W to kW.

The thermal mass contribution from the UFH system is added to any radiator thermal mass:

$K_{E, U F H} = \frac{κ _{U F H} \cdot A _{U F H}}{3600}$

where the factor of 3600 converts from kJ/K to kWh/K. The total emitter floor area must not exceed the zone floor area.

Fan Coil Units

Fan coils use manufacturer test data rather than the power-law characteristic. Performance is defined by a matrix of power output values indexed by temperature difference and fan speed. At each timestep, the model interpolates the manufacturer data to determine the achievable output and associated fan electrical consumption. A fan coil must be the sole emitter type in a zone.

Emitter Characteristic Equation

For radiators and UFH, the instantaneous power output follows:

$Q_{e mi t} = \sum_{i} c_{i} \cdot max (0, T_{E} - T_{r m})^{n_{i}}$

Where:

$Q_{e mi t}$ is the total emitter power output (kW)
$c_{i}$ is the power coefficient of emitter $i$ (kW/K $^{n_{i}}$ )
$n_{i}$ is the power exponent of emitter $i$
$T_{E}$ is the mean emitter temperature (°C)
$T_{r m}$ is the zone air temperature (°C)

The mean emitter temperature is the average of the flow and return temperatures:

$T_{E} = \frac{T _{f l o w} + T _{r e t u r n}}{2}$

Flow and Return Temperature

Ecodesign Control Classes

The flow temperature is determined by the Ecodesign Regulation control classification. Eight classes are defined, falling into two groups.

Fixed flow temperature (classes I, IV, V, VIII):

$T_{f l o w} = T_{f l o w, d s g n}$

These classes use a fixed design flow temperature regardless of external conditions. They correspond to on/off room thermostats (class I), TPI room thermostats with on/off heaters (class IV), modulating room thermostats with modulating heaters (class V), and multi-room temperature control with modulating heaters (class VIII).

Weather-compensated flow temperature (classes II, III, VI, VII):

The flow temperature is linearly interpolated between the minimum and maximum flow temperatures based on the outdoor air temperature:

$T_{f l o w} = T_{f l o w, min} + (T_{o u t} - T_{o u t, ma x}) \cdot \frac{T _{f l o w, ma x} - T _{f l o w, min}}{T _{o u t, min} - T _{o u t, ma x}}$

Where:

$T_{o u t}$ is the current outdoor air temperature (°C), from TP-03: External Conditions
$T_{f l o w, ma x} = T_{f l o w, d s g n}$

The flow temperature is clamped:

If $T_{o u t} < T_{o u t, min}$ , then $T_{f l o w} = T_{f l o w, ma x}$
If $T_{o u t} > T_{o u t, ma x}$ , then $T_{f l o w} = T_{f l o w, min}$

These classes correspond to weather compensators with modulating heaters (class II), weather compensators with on/off heaters (class III), weather compensators with room sensor for modulating heaters (class VI), and weather compensators with room sensor for on/off heaters (class VII).

Initial Return Temperature

The initial estimate of the return temperature uses the 6/7ths rule:

$T_{r e t u r n} = \frac{6}{7} \cdot T_{f l o w}$

With an override: if $T_{f l o w} \geq 70$ °C, the return temperature is set to 60 °C.

Return Temperature Refinement

The initial return temperature is refined through an iterative procedure that balances the energy released by the emitters against the enthalpy drop across the heating circuit. The energy balance at convergence satisfies:

$\frac{Q _{e mi t}}{Δ t} = c_{p} \cdot ρ \cdot \dot{V} \cdot (T_{f l o w} - T_{r e t u r n})$

Where:

$c_{p}$ is the specific heat capacity of water (kJ/(kg·K))
$ρ$ is the density of water (kg/l)
$\dot{V}$ is the volumetric flow rate (l/s)
$Δ t$ is the timestep duration (h)

For variable-flow systems, when the flow rate corresponding to the design temperature difference falls within the permitted range ( $\dot{V}_{min} \leq \dot{V} \leq \dot{V}_{ma x}$ ), the return temperature is set directly:

$T_{r e t u r n} = T_{f l o w} - Δ T_{d s g n}$

When the flow rate falls outside this range, or for fixed-flow systems, an iterative solver finds the return temperature that satisfies the energy balance.

Bypass Recirculation

When a fraction of the return water is recirculated back into the flow pipe (bypass), the blended flow temperature entering the emitter is:

$T_{f l o w, b l e n d e d} = \frac{T _{f l o w} + f _{b y p a ss} \cdot T _{r e t u r n}}{1 + f _{b y p a ss}}$

The return temperature is then reduced by the difference between the blended and unblended flow temperatures, and the return temperature calculation is repeated using the blended flow temperature.

Emitter Thermal Dynamics

The emitter body has thermal mass $K_{E}$ that introduces a lag between the heat input from the circuit and the heat output to the zone. This is modelled as an ordinary differential equation (ODE).

Heat Balance

The energy balance on the emitter body is:

$K_{E} \cdot \frac{d T _{E}}{d t} = Q_{in p u t} - Q_{e mi t}$

Where:

$K_{E}$ is the emitter thermal mass (kWh/K)
$Q_{in p u t}$ is the power delivered by the heat source (kW)
$Q_{e mi t}$ is the power output to the zone (kW)

Substituting the characteristic equation and defining $Δ T = T_{E} - T_{r m}$ (assuming $T_{r m}$ is constant over the timestep):

$\frac{d ( Δ T )}{d t} = \frac{Q _{in p u t} - \sum _{i} c _{i} \cdot m a x ( 0 , Δ T ) ^{n_{i}}}{K _{E}}$

This ODE is solved numerically using an adaptive Runge-Kutta method (RK45, Dormand-Prince) over each timestep to obtain the emitter temperature trajectory.

Terminal Event Detection

When a maximum emitter temperature $T_{E, ma x}$ is specified (derived from the flow and return temperatures), the ODE solver detects the time at which $Δ T$ reaches $Δ T_{ma x} = T_{E, ma x} - T_{r m}$ . This is implemented as a terminal event: the solver monitors the function $g (Δ T) = Δ T - Δ T_{ma x}$ and halts integration when $g$ crosses zero.

Timestep Calculation Sequence

Each timestep proceeds through the following stages.

1. Target Temperature Determination

The required emitter temperature $T_{E, r e q}$ is the temperature at which the emitter output matches the zone heating demand. For a demand power $P_{d e man d}$ :

$P_{d e man d} = \sum_{i} c_{i} \cdot (T_{E, r e q} - T_{r m})^{n_{i}}$

This is solved numerically for $T_{E, r e q}$ using a root-finding algorithm, with an initial guess of $T_{r m} + 10$ .

The maximum achievable emitter temperature for the timestep is:

$T_{E, ma x} = \frac{T _{f l o w} + T _{r e t u r n}}{2}$

If a blended flow temperature applies, $T_{f l o w, b l e n d e d}$ replaces $T_{f l o w}$ in this expression.

2. Cooldown Phase

If the emitter temperature from the previous timestep ( $T_{E, p r e v}$ ) exceeds $T_{E, r e q}$ , the emitters first cool with no heat input. The cooldown time $t_{coo l}$ is determined by root-finding: the solver finds the time at which the total energy released during cooling equals the heating demand accumulated over that fraction of the timestep.

During cooldown, the emitter temperature ODE is solved with $Q_{in p u t} = 0$ :

$\frac{d ( Δ T )}{d t} = \frac{- \sum _{i} c _{i} \cdot m a x ( 0 , Δ T ) ^{n_{i}}}{K _{E}}$

The energy released during the cooldown period is:

$E_{coo l} = K_{E} \cdot (T_{E, p r e v} - T_{E, coo l})$

where $T_{E, coo l}$ is the emitter temperature at the end of the cooldown phase. The root-finding algorithm solves for the cooldown time $t_{coo l}$ such that:

$E_{coo l} = E_{d e man d} \cdot \frac{t _{coo l}}{Δ t}$

If $T_{E, p r e v} < T_{E, r e q}$ , no cooldown occurs and heating starts immediately ( $t_{coo l} = 0$ ).

3. Energy Required from Heat Source

During the heating phase (from $t_{coo l}$ to the end of the timestep), the energy required from the heat source combines two components:

$E_{r e q} = K_{E} \cdot (T_{E, r e q} - T_{E, coo l}) + E_{d e man d} \cdot (1 - \frac{t _{coo l}}{Δ t})$

Where:

The first term is the energy needed to warm the emitter body
The second term is the remaining zone demand after the cooldown period

This is capped by the maximum energy the heat source can deliver:

$E_{r e q, f ina l} = min (E_{r e q}, E_{r e q, ma x})$

The maximum energy limit $E_{r e q, ma x}$ accounts for two phases:

Warm-up/cool-down phase: The heat source runs at maximum output while the emitter temperature rises towards $T_{E, ma x}$ . The ODE solver determines whether (and when) $T_{E, ma x}$ is reached.
Steady-state phase: Once $T_{E, ma x}$ is reached, the heat source output matches the emitter output at that temperature for the remainder of the timestep.

$E_{r e q, ma x} = P_{ma x} \cdot t_{w a r m u p} + Q_{e mi t} (T_{E, ma x}) \cdot (Δ t - t_{coo l} - t_{w a r m u p})$

Where:

$P_{ma x}$ is the maximum power output of the heat source (kW)
$t_{w a r m u p}$ is the duration of the warm-up/cool-down phase (h)

4. Heat Source Demand

The calculated energy requirement $E_{r e q, f ina l}$ is passed to the heat source (heat pump or boiler) along with the target flow and return temperatures, and the heating start time within the timestep. The heat source returns the energy it can actually provide, $E_{p r o v i d e d}$ .

5. Emitter Output

The total energy released by the emitters to the zone over the timestep is:

$E_{r e l e a se d} = E_{p r o v i d e d} + K_{E} \cdot (T_{E, p r e v} - T_{E, e n d})$

Where:

$E_{p r o v i d e d}$ is the energy delivered by the heat source (kWh)
$T_{E, e n d}$ is the emitter temperature at the end of the timestep (°C)

The second term accounts for the change in stored energy within the emitter body. If the emitters cool during the timestep, this term is positive, contributing additional heat to the zone. The emitter temperature is clamped so it cannot fall below the room temperature.

Fan Coil Calculation

Fan coils follow a different procedure. They have negligible thermal mass, so there is no warm-up or cooldown phase.

For a given temperature difference $Δ T_{f c} = T_{E, ma x} - T_{r m}$ , the model interpolates the manufacturer data across all fan speeds to determine:

The maximum achievable output at the highest fan speed
The actual output, capped at the demanded power per unit

$Q_{f c, a c t u a l} = min (\frac{P _{d e man d}}{N _{f c}}, Q_{f c, ma x})$

The fan electrical power is interpolated from the manufacturer data based on the actual output. The fraction of the timestep during which the fan coil runs is:

$f_{r u n} = min (1, \frac{Q _{f c, a c t u a l}}{Q _{f c, min}})$

where $Q_{f c, min}$ is the minimum output (lowest fan speed). The fan electrical consumption for the timestep is:

$E_{f an} = \frac{P _{f an} \cdot N _{f c}}{1000} \cdot Δ t \cdot f_{r u n}$

where $P_{f an}$ is the fan power in W and the factor of 1000 converts to kW. The energy required from the heat source excludes the fan power contribution:

$E_{r e q, f c} = (Q_{f c, a c t u a l} - P_{f an, s in g l e}) \cdot N_{f c} \cdot Δ t$

where $P_{f an, s in g l e}$ is the fan power for a single unit. The total energy released to the zone is the sum of the heat source contribution and fan electrical input.

Convective Fraction

The split between convective and radiative output determines how emitter heat enters the zone heat balance. For a single emitter type, $f_{co n v}$ is a direct input. When multiple emitters are present (for example, radiators and UFH in the same zone), the effective convective fraction is a power-weighted average:

$f_{co n v, e f f} = \sum_{i} w_{i} \cdot f_{co n v, i}$

where the weight $w_{i}$ for each emitter is its share of the total output at design conditions:

$w_{i} = \frac{c _{i} \cdot ( T _{E} - T _{r m} ) ^{n_{i}}}{\sum _{j} c _{j} \cdot ( T _{E} - T _{r m} ) ^{n_{j}}}$

evaluated at an assumed room temperature of 20 °C and the mean of the design flow and return temperatures. If no emitter produces output at this temperature difference (for example, when the mean emitter temperature is at or below 20 °C), equal weights are applied.

Minimum Energy Output

When the heat source provides no energy, the emitters release stored thermal energy as they cool towards room temperature. The minimum energy output is:

$E_{min} = K_{E} \cdot (T_{E, p r e v} - T_{E, coo l e d})$

where $T_{E, coo l e d}$ is the emitter temperature at the end of the timestep after cooling with zero heat input, clamped to be no lower than $T_{r m}$ . For fan coils, the minimum energy output is zero (no thermal mass).

Outputs

Quantity	Symbol	Unit	Description
Energy released to zone	$E_{r e l e a se d}$	kWh	Total heat delivered to the zone in the timestep
Energy required from heat source	$E_{r e q}$	kWh	Demand placed on the heat generator
Flow temperature	$T_{f l o w}$	°C	Target flow temperature for the heat source
Return temperature	$T_{r e t u r n}$	°C	Calculated return temperature
Emitter temperature	$T_{E}$	°C	Mean emitter temperature at end of timestep
Fan energy	$E_{f an}$	kWh	Electrical energy consumed by fan coil fans
Convective fraction	$f_{co n v}$	-	Effective convective fraction for the zone heat balance

Assumptions

The emitter body is treated as a single lumped thermal mass. Internal temperature gradients within the emitter are not modelled.
The zone air temperature $T_{r m}$ is assumed constant over each timestep when solving the emitter ODE.
The initial emitter temperature at the start of the simulation is set to 20 °C.
For UFH, the power exponent is fixed at $n = 1$ (linear relationship between output and temperature difference), per BS EN 1264 and BS EN 11855.
The initial return temperature estimate uses the 6/7ths rule ( $T_{r e t u r n} = \frac{6}{7} T_{f l o w}$ ), with a hard cap of 60 °C when $T_{f l o w} \geq 70$ °C.
Fan coils have negligible thermal mass. No warm-up or cooldown dynamics are modelled for fan coil units.
A fan coil must be the sole emitter type in a zone. Mixed fan-coil-and-radiator configurations are not supported.
Water properties (density and specific heat capacity) are treated as constants, independent of temperature.
The bypass recirculation fraction is constant across all timesteps.

Cross-references

TP-03: External Conditions -- outdoor air temperature for weather compensation curves
TP-04: Space Heating Demand -- zone heating demand that drives the emitter calculation
TP-10: Pipework and Ductwork Losses -- distribution losses between heat source and emitters
TP-12: Heat Pumps -- heat pump as upstream heat source; flow/return temperatures feed into COP calculation
TP-14: Boilers -- boiler as upstream heat source; flow/return temperatures affect efficiency
TP-17: Controls -- heating schedules and setpoints that determine when emitters are active