Mpemba effect, Newton cooling law and heat transfer equation

TL;DR

This paper proposes a simple theoretical explanation for the Mpemba effect by linearizing the heat transfer equation, aligning well with experimental observations and using Newton's cooling law as an effective approximation.

Contribution

It introduces a novel linearization approach of the heat transfer equation to explain the Mpemba effect, connecting it with Newton's cooling law.

Findings

The solution aligns with experimental data.

Linearization effectively models the Mpemba effect.

Provides a simplified theoretical framework for heat transfer phenomena.

Abstract

In this work we suggest a simple theoretical solution of the Mpemba effect in full agreement with known experimental data. This solution follows simply as an especial approximation (linearization) of the usual heat (transfer) equation, precisely linearization of the second derivation of the space part of the temperature function (as it is well-known Newton cooling law can be considered as the effective approximation of the heat (transfer) equation for constant space part of the temperature function).