Radiator

EN 442 radiator (Buildings RadiatorEN442_2): nEle water and metal elements in series

FastSmoothBuildings.Hydronics.Radiator, model (source)

Extends PartialConserving.

Purpose

Radiator after EN 442: nEle elements of water and metal in series, each giving heat to the room air (heatPortCon) and to the room surfaces (heatPortRad) by the power law of EN 442.

Equations

For element i at the water temperature T_i, with UA = UAEle, f = fraRad, n the exponent and δ = dT0:

Q_con,i = (1 − f) UA ΔT_con (ΔT_con² + δ²)^{(n − 1)/2},   ΔT_con = T_i − T_air,

Q_rad,i = f UA ΔT_rad (ΔT_rad² + δ²)^{(n − 1)/2},   ΔT_rad = T_i − T_surf,

(C/nEle) dT_i/dt = mTra c_p (T_i−1 − T_i) − Q_con,i − Q_rad,i,

with T₀ = TIn; the water leaves at the temperature of the last element, TOut = T_nEle. Far from ΔT = 0 the law is ΔT |ΔT|^{n − 1}; around it, it is linear, its slope δ^{n − 1} times the conductance, so the derivative stays finite where that of the exact power law does not. A radiator colder than the room takes heat from it.

The heat capacity C = ρ VWat c_p + 500 J/(kg K) mDry is shared evenly by the elements. UAEle is computed by radiatorConductance so that the radiator gives Q_flow_nominal at the nominal temperatures and at the nominal flow m_flow_nominal = |Q_flow_nominal / (c_p (T_a_nominal − T_b_nominal))|.

Set flows and pressure-driven flows

With set flows, what enters leaves. With pressure-driven flows, the outlets have the linear conductance m_flow_nominal/dp_nominal, shared evenly by the outlet connections.

Relation to Buildings

Buildings.Fluid.HeatExchangers.Radiators.RadiatorEN442_2, its pressure drop linearized.

Use

Connect heatPortCon to the air and heatPortRad to the radiant node of a zone, and a Valve in series, as in Examples.BoilerCircuit.

Parameters

Parameter	Type	Unit	Default	Description
dp_nominal	Real	Pa	2000	Pressure drop at the nominal flow, linearized (pressure-driven flows)
Q_flow_nominal	Real	W		Nominal heating power
T_a_nominal	Real	K		Water inlet temperature at nominal conditions
T_b_nominal	Real	K		Water outlet temperature at nominal conditions
TAir_nominal	Real	K	293.15	Air temperature at nominal conditions
TRad_nominal	Real	K	TAir_nominal	Radiative temperature at nominal conditions
n	Real		1.24	Exponent of the EN 442 power law
fraRad	Real		0.35	Radiant share of the heat output
nEle	Integer		5	Number of elements
VWat	Real	m3	5.8e-6*abs(Q_flow_nominal)	Water volume
mDry	Real	kg	0.0263*abs(Q_flow_nominal)	Dry mass lumped to the water
T_start	Real	K	293.15	Initial water temperature
dT0	Real	K	0.05	Regularisation of the power law around a zero temperature difference
UAEle	Real	W/K	radiatorConductance(Q_flow_nominal, T_a_nominal, T_b_nominal, TAir_nominal, TRad_nominal, fraRad, n, nEle)	Conductance of each element
C	Real	J/K	rhoWatVWatcpWat + 500*mDry	Heat capacity of the water and of the dry mass
m_flow_nominal	Real	kg/s	abs(Q_flow_nominal/cpWat/(T_a_nominal - T_b_nominal))	Nominal flow

Revisions

• October 2026: moved from trano's FastModel.Hydronics.