BuildingSystems.Fluid.HeatExchangers.Radiators.RadiatorEN442_2

# .BuildingSystems.Fluid.HeatExchangers.Radiators.RadiatorEN442_2

Dynamic radiator for space heating

## Information

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 Qic and Qir from the radiator to the room is

Qic = sign(Ti-Ta) (1-fr) UA ⁄ N |Ti-Ta|n
Qir = sign(Ti-Tr) fr UA ⁄ N |Ti-Tr|n

where Ti is the water temperature of the element, Ta is the temperature of the room air, Tr is the radiative temperature, 0 < fr < 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.

## Revisions

- March 7, 2022, by Michael Wetter:
  Set `final massDynamics=energyDynamics`.
  This is for #1542.
- April 14, 2020, by Michael Wetter:
  Changed `homotopyInitialization` to a constant.
  This is for IBPSA, #1341.
- February 21, 2020, by Michael Wetter:
  Changed icon to display its operating state.
  This is for #1294.
- November 17, 2016, by Filip Jorissen:
  Added pressure drop equations and parameters.
  This is for #586.
- November 3, 2016, by Michael Wetter:
  Set `preHea(final alpha=0)` as this allows to simplify the system of equations.
  This is for #570.
- March 17, 2016, by Michael Wetter:
  Reformulated model to reduce the dimension of the nonlinear system of equations. This is for #435.
- November 19, 2015, by Michael Wetter:
  Removed assignment of parameter `showDesignFlowDirection` in `extends` statement. This is for #349.
- April 11, 2015, by Filip Jorissen:
  Propagated `vol.massDynamics` to top level parameter `massDynamics` instead of `energyDynamics`.
- November 25, 2014, by Carles Ribas Tugores:
  Interchange position of `fraRad` parameter and the complementary `(1-fraRad)` in the equation used to calculate the nominal heating power of each element, `QEle_flow_nominal[i]`.
- October 29, 2014, by Michael Wetter:
  Made assignment of `mFactor` final, and changed computation of density to use default medium states as are also used to compute the specific heat capacity.
- October 21, 2014, by Filip Jorissen:
  Added parameter `mFactor` and removed thermal capacity which can lead to an index reduction.
- May 29, 2014, by Michael Wetter:
  Removed undesirable annotation `Evaluate=true`.
- October 8, 2013 by Michael Wetter:
  Removed conditional statement in the declaration of the parameter `mDry`, as this is incorrect syntax.
- September 26, 2013 by Michael Wetter:
  Reformulated implementation to avoid mixing textual and graphical declarations in the `equation` section.
- April 4, 2011 by Michael Wetter:
  Changed the implementation to use BuildingSystems.Utilities.Math.Functions.regNonZeroPower. This allows formulating the model without any non-differentiable function inside the equation section.
- April 2, 2011 by Michael Wetter:
  Added `homotopy` operator.
- February 11, 2011 by Michael Wetter:
  Revised the initialization to ensure that at the nominal conditions, the amount of transferred heat is excatly the same as the specified nominal power. In the previous implementation, the UA-value was computed using a simplified expression for the temperature difference, leading to a slightly different amount of heat transfer.
- February 4, 2011 by Michael Wetter:
  Simplified implementation.
- January 30, 2009 by Michael Wetter:
  First implementation.

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