Annex60.ThermalZones.ReducedOrder.EquivalentAirTemperature.UsersGuide

# .Annex60.ThermalZones.ReducedOrder.EquivalentAirTemperature.UsersGuide

User's Guide

## Information

This package package contains models for calculating an equivalent air temperature. There are two common ways to consider solar radiation hitting exterior surfaces. One way is to consider the resulting heat load at the wall's capacity. The other way is to add correction terms to the outdoor air temperature. The models in the package Annex60.ThermalZones.ReducedOrder.EquivalentAirTemperature follow the second approach. This approach is, for example, described in the German Guideline VDI 6007 Part 1 (VDI, 2012). The influence of indoor temperatures via heat transfer through exterior walls is neglected. The exterior wall's outdoor surface is assumed to have the outdoor air temperature for calculation of radiative heat exchange with the ambient.

The fundamental equation is:

TEqAirExt = T AirAmb+ΔTEqLW+ΔT EqSW

The correction term for long-wave radiation is based on the black body sky temperature and dry bulb temperature.

ΔTEqLW = (TBlaSky-TDryBul) αRad/ (αRad+αExt).

The Guideline VDI 6007 Part 1 considers in addition an environmental radiative temperature (similar to the black-body sky temperature) and tilt angles for all orientations. As necessary inputs for the environmental radiative temperature are not defined in TMY weather data sets (radiation from the environment is missing), the influence of this temperature is not considered in the presented models. It is in any case a minor effect as black-body sky temperature and environmental radiative temperature hardly differ. Furthermore, the Guideline VDI 6007 Part 1 calculates the correction term for each orientation separately with individual radiative and convective coefficients of heat transfer. In the presented models, the user can define only one radiative and one convective coefficient of heat transfer. When using area-weighted coefficients, the impact is of minor importance for typical values.

If a sunblind is present, the current status (closed = 1 and open = 0) is considered by multiplying the long-wave correction terms for windows with the status variable minus one. The sunblind status is defined per orientation.

The correction term for short-wave radiation does not count for windows and is calculated with the help of the solar radiation for the specific orientations as

ΔTEqSW = HSol aExt/(αRad+αExt).

With the equations above, one equivalent air temperature per orientation and wall or window is calculated. These equivalent air temperatures are then aggregated weighting each entry with a weighting factor. In this part, constant temperatures of ground coupled elements or adjacent rooms can be considered. The sum of weighting factors per calculated equivalent air temperature must be one. If you consider two equivalent air temperatures, one for walls and one for windows, the sum of weighting factors should be one per category. In the given case, the weighting factors are calculated with the U-value and area of the concerned wall elements as

WeighFaci = Ui Ai/ΣUi Ai

More information about this topic can be found in Lauster et al . (2014).

#### References

VDI. German Association of Engineers Guideline VDI 6007-1 March 2012. Calculation of transient thermal response of rooms and buildings - modelling of rooms.

M. Lauster, P. Remmen, M. Fuchs, J. Teichmann, R. Streblow, D. Mueller. Modelling long-wave radiation heat exchange for thermal network building simulations at urban scale using Modelica. Proceedings of the 10th International Modelica Conference, p. 125-133, Lund, Sweden. Mar. 10-12, 2014. doi:10.3384/ECP14096125

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