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

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3 System description 24<br />

given based on Figure 3.2.<br />

����<br />

�� � � ������ � � ������� � � ����������� (3.14)<br />

����<br />

��<br />

�������<br />

��������<br />

Thermal energy ch<strong>an</strong>ge <strong>of</strong> the windscreen glass [�]<br />

Heat tr<strong>an</strong>sfer rate between the cabin <strong>an</strong>d the windscreen [�]<br />

Heat tr<strong>an</strong>sfer rate between the ambient air <strong>an</strong>d the windscreen [�]<br />

������������ Heat tr<strong>an</strong>sfer caused by other influences like rain or sun [�]<br />

����<br />

�� �<br />

����<br />

��<br />

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

��<br />

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

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

�<br />

¡<br />

������ ¡ ��� ¡ ��� ¡ ������<br />

�<br />

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

(3.15)<br />

� (3.16)<br />

The temperature <strong>of</strong> the air reaching the middle part <strong>of</strong> the windscreen is lower th<strong>an</strong><br />

at the outlet. This is due to the heat tr<strong>an</strong>sfer to the (here assumed) colder glass. This<br />

will be taken into account with a simple estimation using the already calculated me<strong>an</strong><br />

convection heat tr<strong>an</strong>sfer coefficient at the inner windscreen (equations 3.10 <strong>an</strong>d 3.13) <strong>for</strong><br />

half the windscreen.<br />

�������� � ���<br />

������ ¡ ���<br />

� ¡ ������ ¡ ��������<br />

¡ ���� ���� (3.17)<br />

There are two errors that are made in this equation. ������ is higher in the lower parts<br />

<strong>of</strong> the windscreen due to higher air speeds. On the other h<strong>an</strong>d, the air temperature<br />

difference ���� ���� driving the heat tr<strong>an</strong>sfer diminishes towards the middle. There<strong>for</strong>e,<br />

this estimation should not be used <strong>for</strong> precise calculations but c<strong>an</strong> be integrated into a<br />

controller due to its simplicity.<br />

Now, the windscreen temperature c<strong>an</strong> be written as a function <strong>of</strong> the ambient <strong>an</strong>d

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