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Design of an Automatic Control Algorithm for Energy-Efficient ...

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3 System description 19<br />

calculated by summing up the contributions <strong>of</strong> all the cabin parts [1]:<br />

����<br />

����<br />

�<br />

����� ���� �<br />

���<br />

�<br />

��������� ��<br />

� ��<br />

�<br />

��<br />

�<br />

���������� (3.3)<br />

While the thermal conductivity � <strong>an</strong>d the material thickness � <strong>an</strong>d area � are usually<br />

known <strong>an</strong>d const<strong>an</strong>t, the convection heat tr<strong>an</strong>sfer coefficients on the outside, ��������, <strong>an</strong>d<br />

inside the cabin, �������, depend on the air speed. Großm<strong>an</strong>n gives approximations <strong>for</strong><br />

these correlations: ������� � �� ���<br />

������, �������� � � ���<br />

���<br />

equation:<br />

The temperature <strong>of</strong> the air blown into the cabin c<strong>an</strong> be expressed with the following<br />

��� � � ����� ¡<br />

�<br />

�������� ¡ ������<br />

� ����� �������� ¡ ���� � ������� ¡ ���� (3.4)<br />

Combining equations 3.1, 3.2 <strong>an</strong>d 3.4, a differential equation <strong>for</strong> <strong>an</strong> estimation <strong>of</strong><br />

the me<strong>an</strong> cabin temperature c<strong>an</strong> be given.<br />

�� �<br />

�<br />

�������� ¡ ������ � � ���� ¡ ��� ¡<br />

�<br />

�������� ¡ ������ ¡ ����<br />

�����<br />

3.1.2 Water mass in the cabin air<br />

����� � ����<br />

¡ �����<br />

����<br />

����� � � �� � � �������<br />

� (3.5)<br />

Water in the cabin has two sources. One is the incoming (moist) air. The other are the<br />

passengers with their respiration, sweat as well as other humidity in the clothes <strong>an</strong>d shoes.<br />

Water leaves the car through the air outlet or is separated at the evaporator.<br />

A basic water equation is found at Großm<strong>an</strong>n [1]. It is however only applicable in<br />

a steady context <strong>an</strong>d does not implement a recirculated air percentage �������. There<strong>for</strong>e,<br />

it is modified in the following:<br />

�������<br />

�� � ������ ������� � ������� �������� (3.6)

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