🚀 go-pugleaf

In article <1e7bmaINNslq@network.ucsd.edu> mbk@lyapunov.ucsd.edu (Matt Kennel) writes:
>mroussel@alchemy.chem.utoronto.ca (Marc Roussel) writes:
>: >	dX/dt = a(Y-X)
>: >	dY/dt = bX-Y-XZ
>: >	dZ/dt = XY - cZ
>: >
>: >				where a = 10
>: >				      c = 8/3
>: >				      b = control parameter (try 28)
>: 
>:      These are indeed the Lorenz equations (as they are now known) but
>: these aren't the original weather simulation equations where Lorenz
>: noticed sensitive dependence on initial conditions.  Lorenz actually
>: started out with some specialized version of the Navier-Stokes equation
>: (a PDE) and noticed sensitive dependence in these equations under the conditions
>: of his weather simulation.  The Lorenz ODEs shown above are a truncation
>: of the Navier-Stokes equation for the special case of (I think)
>: Rayleigh-Benard convection under certain fairly restrictive conditions.
>
>There is a physical system for which the Lorenz equations are a
>"not incredibly bad" approximation (to use them for simple R-B convection is a 
>"well that's really pretty cheezy" approximation).
>
>It's called a thermosyphon, and it actually gets used for some engineering
>applications but I don't know how really.
>
>Think of a loop of pipe in an 'O' standing up vertically, like a bicycle
>wheel, with fluid in the interior.
>
>Now, keep the walls on the bottom half of the "O" hot, and the
>walls on the top half cold. Given enough of a temperature difference,
>you can start to get convective motion of the fluid as it tries to
>transport heat from hot to cold.
>
	Quite a lot of solar heating systems were/are set up that
way.  They are not as high performance as forced circulation, but
then, they don't have all the hardware, either.  The cooling systems
in some old engines were thermosyphon also.  And any process where you
are heating a vessel from the bottom could exhibit this behavior,
couldn't they?  (you'd have convection cells, rather than water
running in a pipe, though)

-- 

Brad Whitehurst    |   Aerospace Research Lab
rbw3q@Virginia.EDU |   We like it hot...and fast.