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[Fwd: Re: PLEUROCOELOUS VERTEBRAE IN SAUROPODS]



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>         1: Does heat loss progress at a different rate than heat gain,
> ceteris paribus?  If so, is it possible to guesstimate a ballpark figure of
> the coefficient for a big sauropod?
>         2: Is rate of heat loss dependant on outside temperature?

Just a quick review of back-of-the-envelope thermodynamics. You can
think about thermal problems by their electrical equivalents.

Temperature -> Voltage
Thermal resistance -> electrical resistance
Power burned ie watts -> amps
"Thermal inertia" -> capacitance (use def. of "calorie" to get #'s)

So two thermal resistances (say a layer of skin over a layer of
subcutaneous fat) add together. Two parallel paths, say a dermal
path and an aspirated path, add as 1(1/R1+1/R2).

[I believe that's missing a solidus: resistance = 1/(1/R1+1/R2)
 -- MR ]

You can trivially model many useful thermal problems quite nicely
this way, incl 1 and 2 above. I don't have the time to be able to
do a complete job here for such a model(it would require graphics
too), but a basic dino model would include

a capacitor representing the body mass
a constant-current source representing metabolic heat
a resistor network representing various heat-dumping mechanisms
a fixed- or constant-voltage element(battery) representing the
        ambient external temperature

When you set these up they can be solved easily with 1st-year physics
Ohm's Law equations, and with a little calculus you get REAL NUMBERS
for thermal time constants.

The short answers are NO and YES. But really, the rate is dependent
on the DIFFERENCE between internal and ambient temperature.

Russ Andersson
Autonomous Effects
engineering lurker...

[ I think the above is reasonably good, but probably a bit too
  simplistic for anything but very rough calculations.  First off, all
  of the thermal conductivities (the reciprocals of the thermal
  resistances) are dependent upon temperature (though I suspect this
  is a small effect for physiologically reasonable temperatures).
  Bigger neglected effects are a) metabolic heat production isn't
  necessarily constant -- it will vary with activity levels, gut
  loading and probably temperature.  The ambient temperature isn't
  fixed.  Finally, no mention is made of the variable current source
  provided by solar (and to a much lesser extent indirect solar)
  radiation.  But it's a good start, and I'll allow such messages
  because I think people should have some understanding of the basic
  physics before they try to conclude anything about the not so basic
  biology. -- MR ]





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