A completely filled curved cylinder on its side would be best, especially if the curvature was smaller on one side than the other.
A vertical tube shaped like a Force-Free Spiral (google this!) would probably be the very best, but very tricky to design and build. Scott From: jone...@pacbell.net To: vortex-l@eskimo.com Subject: RE: [Vo]:Scott on Mpemba effect Date: Sun, 11 Apr 2010 08:32:04 -0700 Pardon the wordy and repetitive prior post… geeze …. one might think I got locked out of my car yesterday J 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 The New Busy think 9 to 5 is a cute idea. Combine multiple calendars with Hotmail. Get busy. _________________________________________________________________ The New Busy is not the too busy. Combine all your e-mail accounts with Hotmail. http://www.windowslive.com/campaign/thenewbusy?tile=multiaccount&ocid=PID28326::T:WLMTAGL:ON:WL:en-US:WM_HMP:042010_4
