This is a model of a radiator that can be used as a dynamic or steady-state model. The required parameters are data that are typically available from manufacturers that follow the European Norm EN 442-2.
However, to allow for varying mass flow rates, the transferred heat is computed using a discretization along the water flow path, and heat is exchanged between each compartment and a uniform room air and radiation temperature. This discretization is different from the computation in EN 442-2, which may yield water outlet temperatures that are below the room temperature at low mass flow rates. Furthermore, rather than using only one room temperature, this model uses a room air and room radiation temperature.
The transferred heat is modeled as follows: Let N denote the number of elements used to discretize the radiator model. For each element i ∈ {1, … , N}, the convective and radiative heat transfer Q^{i}_{c} and Q^{i}_{r} from the radiator to the room is
Q^{i}_{c} = sign(T^{i}-T_{a})
(1-f_{r}) UA ⁄ N |T^{i}-T_{a}|^{n}
Q^{i}_{r} = sign(T^{i}-T_{r})
f_{r} UA ⁄ N |T^{i}-T_{r}|^{n}
where T^{i} is the water temperature of the element, T_{a} is the temperature of the room air, T_{r} is the radiative temperature, 0 < f_{r} < 1 is the fraction of radiant to total heat transfer, UA is the UA-value of the radiator, and n is an exponent for the heat transfer. The model computes the UA-value by numerically solving the above equations for given nominal heating power, nominal temperatures, fraction radiant to total heat transfer and exponent for heat transfer.
The parameter energyDynamics
(in the Assumptions tab),
determines whether the model computes the dynamic or the steady-state response.
For the transient response, heat storage is computed using a
finite volume approach for the
water and the metal mass, which are both assumed to be at the same
temperature.
The default parameters for the heat capacities are valid for a flat plate radiator without fins, with one plate of water carying fluid, and a height of 0.42 meters.
final massDynamics=energyDynamics
.homotopyInitialization
to a constant.preHea(final alpha=0)
as this allows to simplify the
system of equations.showDesignFlowDirection
in extends
statement.
This is for
#349.
vol.massDynamics
to
top level parameter massDynamics
instead of energyDynamics
.
fraRad
parameter and the complementary (1-fraRad)
in the equation used to calculate the nominal heating power of each element, QEle_flow_nominal[i]
.
mFactor
final, and changed computation of
density to use default medium states as are also used to compute the
specific heat capacity.
mFactor
and removed thermal capacity
which can lead to an index reduction.
Evaluate=true
.
mDry
, as this is incorrect syntax.
equation
section.
homotopy
operator.