open field is self-consistently solving the 2- or 3-dimenisonal The effective heat transfer coefficient heff for the plate is
current distribution, i.e. power distribution, on non-straight heff=P/(A*'T)=q/'T. Substituting for 'T from Eq. (A-3) gives
broad traces together with the temperature field. the effective heat transfer coefficient as
heff=9 q0.14 . (A-4)
Acknowledgments
I gratefully acknowledge stimulating contributions from
the FED (German designer association) internet discussion
forum and Drs. Poschmann (FED) and Lehnberger (Andus
GmbH) for valuable hints.
References
1. Joule, J., Phil. Mag., Vol. 19, p.18, 1841.
2. Brooks, D., “Temperature Rise in PCB Traces”, pdf-file
in http://www.ultracad.com from the Proc. of the PCB
Design Conf., West, March pp. 23-27, 1998.
3. Jouppi, M. R., “Thermal Characterization of PCB
Conductors”, Electronics Circuits World Convention 9
Cologne, 2002.
4. Jouppi, M.R.: http://www.thermalman.com, 2003.
5. Flotherm 4.2 User Manual. Flomerics Ltd., 2003.
6. Adam, J., „Strombelastbarkeit von Leiterbahnen II.“,
PLUS, Vol. 4, No. 11, pp. 1817-1823, 2002.
Fig. A-1: Mean temperature rise above ambient for a
7. Lehnberger, C., Andus GmbH Berlin, priv. comm., 2003.
homogeneously heated plate in free convection and radiative
8. Guenin, B.M., “Convection and radiation heat loss from a
cooling calculated from standard Nu-Gr heat transfer
printed circuit board”, Electronics Cooling, Vol. 4, No. 3,
correlations (the various lines are for various board formats,
p. 33, 1998.
e.g. Euro, double Euro and some others).
9. Kraus, A.D., Bar-Cohen, A., Thermal analysis and
control of electronic equipment, Hemisphere Publ..
(Washington, 1983), pp. 345-346.
10. Ling, Y., “On current carrying capacities of PCB traces”,
Electronic Components and Technology Conference, pp.
1683-1693, 2002.
11. Adam, J., „IPC-2152: Neue Richtwerte für die
Strombelastbarkeit von Leiterzügen in Leiterplatten“,
Konferenzband 11. FED-Konferenz, pp. 11-33, 2003.
Appendix. Effective heat transfer coefficient for a plate
The total heat flux balance for a homogeneously heated
plate of area A is
thermal gain – convective loss - radiative loss = 0. (A-1)
With the input heat flux (thermal power) P and other standard
notations [9] we have to solve the implicit equation
( 4 4
P A Ÿh Ÿ Tplate T ) A ŸH VŸ Ÿ(T T ) 0 (A-2)
a plate a
for the plate temperature Tplate. We restrict ourselves to
laminar, free convection. For h(T)=NuH*Oair/H we are using
the Nusselt-Grashof correlation NuH=0.49GrH1/4 based on the
height H of the plate. For the emissivity we take H=0.9 and for
the ambient temperature Ta=35 degC. Because of the non-
linear terms, the temperature of the plate Tplate in ambient
temperature Ta has to be solved numerically (e.g. Newton-
Raphson method). Eq. (A-2) can be divided by A and solved
for plate temperature as function of specific heat load q:=P/A
[W/m²]. Fig. A-1 represents the numerical result for various
board heights showing an almost perfect power law and little
deviation from each other. A good numerical fit is represented
by
'T = 0.11 q0.86. (A-3)
Adam, New Correlations Between Electrical Current and … 20th IEEE SEMI-THERM Symposium
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