Pardon the wordy and repetitive prior post. geeze .. one might think I got
locked out of my car yesterday :-)
There was one point I forgot to make - which might make a good subject for
further study: the "geometry of the container being used" for freezing and
how the shape of that container might affect convection, and more
particularly the "momentum of convection" as it becomes cooler and the
active zone becomes diminished.
My premise is that "convection-inertia" will be maintained at a higher level
with a geometry that promotes a symmetrical and circular flow. Why?
A form of inertia applicable to convection currents might be rotational
inertia (moment of inertia), which refers to the fact that a rotating body
maintains a state of uniform rotational motion. The "body" in this case is
not rigid, but there is some similarity and analogy.
Assuming that conservation of angular momentum is applicable, then - the
geometry of the freezing container could come into play if it promotes or
hinders that factor. We might expect the Mpemba effect to be minimal with a
capillary tube, low with test tube, for instance - but maximized with
spherical pyrex (labware).
Rotational inertia depends on a spin object ("metaphorical" ) and therefore
its structurally integrity as a rigid body, would come into play - and any
geometry that diminished that hidden "structure", would thereby lower the
convection rate (of the hotter container).
From: Jones Beene
Yes, the "continuity" of an established convection rate, which Scott
mentions - is the only detail not specifically addressed (but it is implied)
in Horace Heffner's fine 10 yr old analysis which is still online at:
http://www.mtaonline.net/~hheffner/Mpemba.pdf
. and it is a key detail which is quantifiable by analyzing the convection
currents over time.
A key point of Horace's paper is that it takes as much heat transfer to drop
~80 deg. C as it does to then freeze 0 deg. C water.
The "heat transfer rate" then is the key to any anomaly - and this rate is
controlled by convection currents which themselves have momentum.
"Momentum" then, or inertia, and its continuity - may be the key to any
improved understanding. although it is implied in the prior analysis.
HH: "Convection currents can dramatically affect heat transfer rates, by
exposing large volumes of the liquid directly to the heat transfer boundary,
be that the container walls or the
ice itself. Slow moving molecules are culled out of the moving stream of
water at the
water-ice boundary. If the water does not move, then the relatively slower
mechanism of thermal conduction is all that remains to effect the freezing..
If the heat transfer rate at 0 deg. C is only doubled by the increased
convection, then water with an initial temperature of less than about 39.9
deg. C will freeze at about the same time as water initially at 0 deg. C.
*An almost 40 deg. advantage is given to the hotter water.*
If the convection momentum is greater than doubled, which it probably is -
then more than 40 degrees can be offset.
Jones
From: Wm. Scott Smith
I think that water that is warmer than its surrounding will experience
greater convection; this means that the water is set into a more vigorous
motion that is sustained even as the temperature difference passes that of
the more-still, originally colder water.
Scott
Remarkably consistent results. See:
http://arxiv.org/abs/1003.3185
A search for the Mpemba effect: When hot water freezes faster than cold
water
James D. Brownridge
(Submitted on 16 Mar 2010)
Abstract
An explanation for why hot water will sometime freeze more rapidly than cold
water is offered. Two specimens of water from the same source will often
have different spontaneous freezing temperatures; that is, the temperature
at which freezing begins. When both specimens supercool and the spontaneous
freezing temperature of the hot water is higher than that of the cold water,
then the hot water will usually freeze first, if all other conditions are
equal and remain so during cooling. The probability that the hot water will
freeze first if it has the higher spontaneous freezing temperature will be
larger for a larger difference in spontaneous freezing temperature. Heating
the water may lower, raise or not change the spontaneous freezing
temperature. The keys to observing hot water freezing before cold water are
supercooling the water and having a significant difference in the
spontaneous freezing temperature of the two water specimens. We observed hot
water freezing before cold water 28 times in 28 attempts under the
conditions described here.
- Jed
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