Mpemba Paradox Revisited -- Numerical Reinforcement

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.