Obvious in retrospect but not always apparent effect

Given one larger X watt resistor or N smaller X/N Watt resistors, both
arrangements dissipating the same Watts,  - the N smaller resistors
are liable to operate at a significantly lower rise above ambience.

      If dissipating    say 5 Watts in a 10W resistors or 5 Watts in 5
x 2W resistors

              This can be useful.
___________________

Body temperature rise of air mounted 'ceramic" resistors has been
discussed on various occasions.

It may be that many other data sheets have body temperature rise data
or air cooling, but this is the first that I'd noted.

               http://www.yageo.com/documents/recent/Leaded-R_SQP-NSP_2011.=
pdf
                 <------------          *********   Data sheet

As these are similar in shape size and and surface finish to many of
the generic "white ceramic rectangular" power resistors the results
will be generically extensible with due care.

Of especial interest to me is  the graph that gives  temperature rise
above ambient as a percentage of rated wattage and body style.
Some results are interesting.
Several may be somewhat surprising at first glance but obvious enough
on consideration and are (probably mostly) due to the effects of the
"square-cube" law.
ie the volume of  a body increases proportional to the edge or radius
squared, but the volume increases proportional to radius cubed.
Accordingly the ratio of surface area per volume falls linearly with
increasing radius or edge.
So, IF a resistor's volume  is linearly related to its rated Wattage
(which may or may not be true but which probably tends to be true)
then the ability to cool for rated wattage decreases as rated wattage
increases as there is less surface area available per Watt .


Actual:

For a given Wattage a larger Wattage resistor will run cooler than a
lower Wattage one.
eg if 2W is dissipated a 2W resistor will be at 100C above ambient but
a 10 W resistor will rise 50C above ambient
ie bigger body cools better.

__________________

For a given % of their rate power a large resistor will be HOTTER.

eg at 50% rated power a 2W resistor dissipating 1 Watt (2/1) will rise
70C but a 10/5 will rise 130C.
Obvious after consideration cube-square law.

__________________

Corollary of the above.

For a given Wattage dissipated , if 1 x 10W or 2 x 5W or 5 x 2W
resistors are used, the small resistors will run at a lower
temperature.
eg
5W in a 10W =3D 135C
5W in 2 x 5W =3D 110 C
5W in 5 x 2W =3D 65 C



      Russell McMahon
      Applied Technology
      New Zealand.
--=20
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