Review of 'Mpemba Effect- the Effect of Time'

The Abstract promises a characteristic of time in an explanation of the Mpemba effect.  The author offers properties of time to include speed varied by strength of gravitational fields and energy density of space, providing convincing equations.  The Author’s linking paragraph from the Cosmic discussion of space and time to the Mpemba effect demonstration by Avinash Kumar and

John Bechhoefer in their experiment [9] as “the embodiment of this characteristic of time”.  Even a cursory glance at this paper would reveal the time as used by them has properties of direction, start and finish and the intervals in between were measured in milliseconds.

Time is not a property of energy, rather it is a popular parameter to study the rate of energy conversion.  A different rate of energy conversion could be the summer strength of sunlight in the Antarctic as Joules per square meter.  Or: “His falling speed was already fatally fast halfway down his fall”.  Here the parameter is percentage of fall height.

It is unclear what is the Author’s definition of time.  In his explanation of the Mpemba effect he states:

 “… if the energy density of the space in which the objects are located remains constant, then the time on the high temperature object will be faster than on the low temperature object.”

This appears to allude to a varying flow of time.  If it refers to elapsed time (i.e. shorter rather than faster) then the statement is using his conclusion as evidence to prove his conclusion.  The proverbial cart before the horse.

In the Author’s conclusion he refers to a time effect: “The Mpemba effect is the time effect produced when heat flows from objects into space”, supporting the idea of a time curve that is not linear.

The Cosmic discussion taking up most of his paper may well translate into a fascinating paper in its own right.  However, as evidence of the Mpemba effect, it fails.

Heat transfer from one body to another body occurs only via the following three basic thermal mechanisms in Earth time:

1. Convection

There are the distinct areas of convective currents.

• The surface area exposed to the cold air.
• The water circulating in response to cooling.
• The air circulating on the outside of the container.

1. Conduction

Heat must be conducted through the wall of the container and both the inside and outside film thicknesses which vary in thickness according to the velocity of circulation.

1. Radiation

Radiation loss can be expressed as follows:

q = ε σ (T_h⁴ - T_c⁴) A_h , in W/m² ,   where

T_h = hot body absolute temperature (K)

T_c = cold surroundings absolute temperature (K)

A_h = area of the hot object (m²)

ε   = 0.85 - 0.95 for Pyrex glass

     = 0.20 – 0.32 for steel
σ = 5.6703 10^-8 (W/m²K⁴) – (The Stefan-Boltzmann Constant)

The Mpemba effect is an artifact of all three mechanisms in varying degrees and not the result of an interstellar time warp.  In addition, there are studies which consider:

• Loss of water mass due to evaporation.
• Supercooling where water samples are below 0^O.
• Convective flows induced by heat gradients still present during cooling.
• Local nucleation of ice – freezing takes place early and locally on surface aberrations.
• Dissolved gasses affecting cold water sample but not hot samples.
• Hydrogen Molecules – Cluster of molecules disturbed by heating, needing time to regroup.
• Entropy of sample shown higher upon cooling from hot condition.
• 4th Phase of water, not solid nor liquid but in between, occurring at hydrophilic surfaces.
• Frost under beaker can be found under the cold sample but melted under the hot sample.
• Denial of the Mpenda effect altogether.

A complete and comprehensive mechanism of the phenomenon has eluded the scientific community and the paper under review does little to advance a universal causation.  Meanwhile, the 20,000 people who responded to the Royal Society of Chemistry competition have a renewed interest in science.