When mathematics meets thermal science: The simpler is the better

Abstract

Mathematics is an important tool to dealing with a complex problem, but it might be too abstract and elusive to be directly applied by engineers. This paper shows mathematics should be simple but effective for thermodynamic problems, the simpler is the better. The two-scale fractal is used as an example to show the importance of application of mathematics to practical problems, and a fast-slow law is suggested to deal with many discontinuous problems by fractal calculus.

Flame-retardant and crease-proofing finishing of cotton fabrics via in-situ copolymerization of ethylene phytic acid and itaconic acid, part I: Fabrication process

“…The thermal properties are basically consistent with PA and the carbon residue content was about 70%, which thereby effectively inhibits or slows down the combustion degree. This study provides a method for flame-retardant and wrinkle resistant finishing of fabrics, which can be mathematically treated [16][17][18]. The theoretical analysis will be carried out in Part 2 of this series of publications, where a mathematical model will be established.…”

Fractal variational principle for an optimal control problem

“…As claimed by Ji-Huan He, a single scale is often unbelieving, and sometimes a wrong result might be obtained. 21,22 When we see a blackboard, it is smooth when we evaluate it with our eyes; however, it is unsmooth on a micro-scale. If we want to study the effect of surface morphology on a chalk's friction property, two-scale fractal theory 21,22 has to be considered.…”

Taylor series solution for the non-linear Emden-Fowler equations

“…Without them, progress in science and technology is impossible. The differential models for engineering applications should be simple; the simpler, the better [1]. A simple mathematical treatment has revealed the mechanism of a long-lost technology called Fangzhu, an ancient technology to collect water from the air [2].…”