Influence of initial thermal convection momentum on the cooling rates

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Debajyoti karmakar
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TL;DR
A query exploring if high initial kinetic energy in hot water drives rapid convective circulation loops that optimize surface cooling rates and bypass the density stabilization threshold at 4°C to trigger faster overall freezing.
Hello everyone,
I am researching the thermodynamic variables involved in the Mpemba effect, specifically focusing on the fluid dynamics of natural convection loops.
A fluid starting at a significantly higher initial temperature will exhibit substantially higher initial kinetic energy and vigorous convective cycling compared to a fluid starting at room temperature.
I am trying to understand a scenario where the top layer of water in contact with a cold boundary experiences a rapid localized increase in density, causing it to drop and establish a highly active circulation loop. In a hotter fluid, this rapid shuffling of layers maximizes the surface boundary's exposure to the cold, maintaining a high cooling rate. Conversely, in a room-temperature fluid, the lower initial temperature differential results in sluggish convective circulation, slowing down the overall heat transfer to the surroundings.
My question regarding fluid mechanics is this: Can the fluid momentum generated by this initial, vigorous convective cycling carry enough kinetic energy to bypass or delay the stabilization that typically occurs when water reaches its maximum density peak at 4°C?
If anyone could point me toward existing textbook concepts, papers, or models that look at convective momentum vs. density changes during cooling, I would greatly appreciate it!
Thank you!
 
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Welcome to PF.

Debajyoti karmakar said:
TL;DR: A query exploring if high initial kinetic energy in hot water drives rapid convective circulation loops that optimize surface cooling rates and bypass the density stabilization threshold at 4°C to trigger faster overall freezing.

Can the fluid momentum generated by this initial, vigorous convective cycling carry enough kinetic energy to bypass or delay the stabilization that typically occurs when water reaches its maximum density peak at 4°C?
Almost anything is possible under some given set of conditions. You will need to use numerical modelling of situations where it might be possible. Maybe only a 2D model is required. The Mpemba effect is an observation, not a rule.
 
As I am 14years old I can create the 2D model but not the numerical modelling
 
Many applied mathematicians and skilled scientists would have trouble modelling the Mpemba effect. Here is a summary of the mathematical modelling and its complexity. There are plenty of references at the end of the paper.
https://www.nature.com/articles/s42005-025-02251-6.pdf

Without finite element numerical modelling, you might experiment with the system in your mind, possibly testing some practical extreme examples, and maybe calculating some of the radiative effects from the surfaces of the container.

I would begin by considering what shape container produces the best Mpemba effect. A large flat dish would be cooled by evaporation from the top surface. There would also be radiative cooling through the bottom of the dish, and from the upper surface. How might the air and the water flow as a result of the density variations?

A tall thin container would be cooled by conduction with the rising flow of warming air at the sides. That forms an efficient countercurrent heat exchanger. There will also be radiative cooling from the sides, through the air to the environment. How might the air and the water flow in that situation?
https://en.wikipedia.org/wiki/Countercurrent_exchange

Now consider those two processes together, for an average shape container. How would the flow of each reinforce or cancel the flow in the other. What shaped container best demonstrates the Mpemba effect?
 
Wait, if I find the strength of convection current then it can eventually help to find a new formula for my hypothesis
 
Thank you for your guidance and for sharing the research paper.
I'm currently trying to develop a basic mathematical model of my hypothesis, mainly focusing on how temperature differences affect water density and convection currents. I understand that the complete modelling is complex, but I'd like to learn step by step. Could you suggest which basic equations or concepts I should study first to develop my idea further?
 
Debajyoti karmakar said:
I'm currently trying to develop a basic mathematical model of my hypothesis...
Could you suggest which basic equations or concepts I should study first to develop my idea further?
Physics Forums is a great place if you need assistance in understanding current physics. But be aware that seeking help here to develop a new hypothesis is explicitly disallowed by the forum rules that you agreed to follow when you joined:
Speculative or Personal Theories:
Physics Forums is not intended as an alternative to the usual professional venues for discussion and review of new ideas, e.g. personal contacts, conferences, and peer review before publication. If you have a new theory or idea, this is not the place to look for feedback on it or to ask for help developing and publishing it.
 
Debajyoti karmakar said:
Could you suggest which basic equations or concepts I should study first to develop my idea further?
To model water, you will need to calculate the unusual relationship between the temperature and the properties of water. Write out those functions as code for use later in your model. Check the functions against tables of data and other authors equations. You can start here.
https://www.powderprocess.net/Tools_html/Data_Diagrams/Water_Properties_Correlations.html
 
The reason why continuous smooth functions are required, rather than a table of data, is because the model will trip up on, or oscillate about, the steps in a data table.
 
Thank you for your guidance, for helping me to improve my idea and this hypothesis
 
Also I forgot to add that the less dense the molecule is, the more it has space to maintain cooling rate between them
Therefore, density is indirectly proportional to the cooling rate
 
Debajyoti karmakar said:
Also I forgot to add that the less dense the molecule is, the more it has space to maintain cooling rate between them
Therefore, density is indirectly proportional to the cooling rate
I think it is more involved than that.

The link I gave in post #10 includes "liquid water thermal conductivity correlation to temperature", so that will take density into account.