Mpemba Paradox Revisited -- Numerical Reinforcement

TL;DR

This paper revisits the Mpemba paradox by numerically solving a nonlinear Fourier heat conduction problem, revealing conditions under which the effect occurs, such as hydrogen bond memory effects and skin super-solidity, but not convection.

Contribution

It introduces a finite element numerical approach to analyze the Mpemba effect, identifying key physical factors influencing its occurrence in complex systems.

Findings

Hydrogen bonds exhibit memory effects influencing energy emission.

Skin super-solidity creates thermal diffusion gradients with an optimal ratio.

Convection alone does not produce the Mpemba effect.

Abstract

Inspired by responses to the work (arXiv:1310.6514), we solved the one-dimensional, nonlinear Fourier initial and boundary condition problem using the finite element method. Examination of all possible parameters reveals the following: 1. Hydrogen bond has memory effect to emit energy at a rate, or with a relaxation time, depending on initial energy storage. 2. Skin super-solidity creates gradients in thermal diffusion coefficient for heat conduction in liquid with the optimal skin-bulk ratio of 1.48. 3. Convection alone produces no such effect. 4. Mpemba effect happens only in the highly non-diabetic source-path-drain cycling system.