Microfluidic multiscale model of transport phenomena for engineering and interdisciplinary education applied to elements of a stirling engine

Abstract

Microfluidic model based on elementary mathematical tools and basic corpuscular physics is applied to flow configurations simulating the Stirling engine. Universality and mathematical simplicity of the model is main objective of its development. This to facilitate its application not only in micro and standard macro, single- and multiphase flows in engineering but in biology, medicine and interdisciplinary sciences as well. As dynamics of disperse systems it promotes the common physical background of multiple, apparently unrelated phenomena. Main feature of the method - compared with standard methods - is departure from differential notation where possible to ensure suitability for analysis of discontinuous systems. Physical quantities are determined directly at required scale by choice of reference volumes/surfaces and use of the mean value theorem (MVT) of integral calculus where required. Thus the method is applicable to discrete particles and avoids higher order requirements of Navier-Stokes solutions. Besides saving one integration step it generally facilitates the analysis considerably. Newton’s second law is used explicitly as single equation of motion. Together with conservation laws it is applied to non-relativistic motion of particle systems in range from individual particles, atoms, molecules or even electrons, over to macroscopic particle sets in solid or flowing systems of traditional mechanics, up to celestial bodies of classical astro-physics. The basically microfluidic model was used to derive all definitions and equations of standard continuum fluid mechanics and multiphase flows. Compared with standard methods the here used model has the singular ability to describe consistently all phenomena related to one of most inspiring technical devices: to Stirling engine.