Page 74 - Power Electronics Handbook

Heatsinks 67

the heatsink and P, is the rate of heat flow in watts. The thermal resistance
of the heatsink (&) is then given by equation (2.11).
kTadT
Pc = - (2.10)
d

=- d (2.11)
kT a
connctioll. Convection may be due to natural air flow or forced air flow.
Forced convection is further dependent on whether the air flow is laminar
or turbulent. At low air velocities the flow is laminar and this changes at
higher velocities to turbulent, the actual point of changeover being
dependent on the design of the heatsink.
The heat flow from the heatsink having a cross-sectional area of a, a
vertical length of I, and a temperature difference above the surrounding of
dT, is given empirically by equation (2.12).

(2.12)

where the constant k, has a value of about 1.37.
If the heatsink is now cooled by forced air, having a velocity of v,, then
the heat flow for laminar and turbulent air flow are given by equations
(2.13) and (2.14) respectively, where the constants have the approximate
values kfl = 3.9 and kft = 6.0.
Pn = kaadT (7) (2.13)
M

Pn = knadTF V.0.8
(2.14)
Rdhtion. The heat loss due to radiation is dependent on the emissivity of
the heatsink (E) and its temperature difference above the ambient. The
maximum value of emissivity is unity, that of a black body radiator. If TI
and T2 are the temperatures of the surface of the heatsink and that of the
surrounding air, then the heat loss in watts due to radiation*is given by
equation (2.15) where the constant k, is approximately equal to 5.7 X
lo-*.
P, = k,ae(T: - a) (2.15)
Thermal analysis using the equations given above can result in errors up
to 25% since many factors affect the actual heat-dissipation properties of
heatsinks. The errors arise due to:
(i) The mix of heat transfer modes and the difficulty of predicting the
actual heat transfer path. Heat radiating from adjacent bodies also
grossly affects the final result.
(ii) The variation in power dissipation between semiconductors of the
same type, even when these come from the same batch. Power