Differential Equations of Thermodynamics

Abstract

Every mathematical formulation has an underlying physical principle, and every physical principle may have a mathematical formulation. We cannot solve mathematical problems more often than not because we fail to recognize the physical principles behind a mathematical modeling. Recently, two laws of nature (thermodynamics) have been discovered: One is the “Constructal Law” by Adrian Bejan (1996), and the other is the “Law of Motive Force” by Achintya Kumar Pramanick (2014). These two laws have greatly enabled physical solutions of a large variety of practical problems of interest. By virtue of the “Constructal Law,” the problems of fluid mechanics, heat transfer, and thermodynamics can be brought under the single umbrella that is none other than thermodynamic optimization. On the other hand, the “Law of Motive Force” facilitates the understanding of true physical nature of problems and consequently the formulation of corresponding governing equations. This is at any rate by the opinion of the author; a plethora of problems of physical reality can be solved by the applications of Reynolds transport theorem, momentum theorem, first and second laws of thermodynamics, Gouy-Stodola theorem, Patankar-Spalding-type partial differential equations, continuity equation, Navier-Stokes equation, energy conservation equation, and k – ε turbulence model, employing elementary mathematics alone.