Page 181 - Power Electronic Control in Electrical Systems

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Power electronic control in electrical systems 169

The energy flow per unit time by conduction is given by the following formula:
l
P conduction ˆ A (T 1 T 2 ) (5:1)
d
where
l is the thermal conductivity of the material in [W=m C]

T 1 , T 2 are the temperatures in [ C]

2
A is the surface area in [m ]
d is the length in [m]
The energy flow per unit time by convection is
P convection ˆ a A (T 1 T 2 ) (5:2)
where
W
2 ]
a is the convection coefficient [ m C
2
A is the surface area in [m ]
T 1 , T 2 are the temperatures in [ C]

Finally, the energy flow per unit time by radiation is
4
4
P radiation ˆ S E A (T T ) (5:3)
1 2
where
W
S is the Stefan±Boltzmann constant [5:67 10 8 m 2 K 4 ]
E is the emissivity of the material
2
A is the area in [m ]
T 1 , T 2 are the temperatures in [ K]

In all previously mentioned cases, the heat transfer is dependent upon the surface
area of the object. To increase the surface area, a heat sink is used to mount the
device. The heat generated in the device is transferred first from the semiconductor to
the heat sink and then to the ambient air if no other means are provided. In heat sinks
all modes of heat transfer exist, namely, conduction between the semiconductor, and
the heat sink, convection between the heat sink and the air, and radiation from the
heat sink and semiconductor to the air. The efficiency of the transfer mode also
depends upon the medium used for cooling when forced mechanisms are used. To
improve the heat transfer due to conduction, the contact pressure between the
semiconductor and the heat sink surface may be increased and conductive grease
or soft thermal padding may also be used.
However, in most cases of low power electronic equipment a fan is placed at the
bottom of the enclosure and slotted openings are provided to allow circulation of the
air. In converters of significant power level and when the power-to-weight-ratio is
very high, other means of forced cooling are used. For instance, oil similar to the one
used in transformers is used to remove the heat from the converter.
In many cases water forced through hollow pipes is used as a cooling means. The
heat-pipe coolers are composed of
. An aluminium base with elements clamped to conduct heat.
. Cooling plates composed of copper or aluminium with surfaces.
. Heat pipes that provide the thermal link between the aluminium base and the
plates.