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From: morse@leadsv.UUCP (Terry Morse)
Newsgroups: net.physics
Subject: A thought experiment on freezing water
Message-ID: <455@leadsv.UUCP>
Date: Thu, 23-May-85 13:47:22 EDT
Article-I.D.: leadsv.455
Posted: Thu May 23 13:47:22 1985
Date-Received: Sun, 26-May-85 16:40:10 EDT
Distribution: na
Organization: LMSC, Sunnyvale CA
Lines: 38
Keywords: water,cooling,heat

There has been a discussion in net.cooks (of all places) of whether
or not it is possible to freeze hot water faster than cold water, all else
being equal.

There have been several explanations as to why it might happen.  Some
people have even done experiments.  I would like to pose this as a problem
and see if anybody has a solution.  I want to know under what conditions
hot water will freeze faster than cold.

The energy transport mechanisms to consider are:

1)	evaporative heat loss (and evaporative mass transfer)
2)	convective heat loss (consider h = constant to simplify)

The container should be thought of as a rectangular cube with the top
side exposed to the air (your basic ice cube tray).  As a start, think
of the following relationships:

mass loss = f ( T difference, surface area, humidity )
convective loss = f ( T difference alone (simplification) )

A simple form of the differential equation may be written in the form
outflow - inflow + change in storage = 0, or:

q(conv) + q(evap) + c d/dt( M Tw ) = 0
	q(conv) = convective heat loss rate = h (Tw - Ta)
	q(evap) = evaporative heat loss rate = ?
	M = mass of water
	c = specific heat of water (assume constant)
	Tw = temperature of water

Happy gedanken experimenting!!!
-- 

Terry Morse  (408)743-1487

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