New functional relationships in analytical thermal physics for locally none-equilibrium heat transfer processes


Аuthors

Kartashov E. M.1, 2*, Krylov S. S.2

1. MIREA — Russian Technological University (Lomonosov Institute of Fine Chemical Technologies), 78, Vernadsky prospect, Moscow, 119454, Russia
2. Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

*e-mail: professor.kartashov@qmail.com

Abstract

The article is devoted to the development of a new mathematical apparatus for the study of locally nonequilibrium heat transfer and other areas of science and technology. In particular, a series of operational (according to Laplace) non-standard images, the originals of which are not in known reference books on operational calculus, are considered. It is shown that analytical solutions of the corresponding mathematical models using the found originals have a wave character, which is expressed by the presence of the Heaviside step function in the solutions. The latter means that at any moment of time there is a region of physical disturbance before the point of rupture and an undisturbed region after the point of rupture. The considered images are included in the operational solutions of mathematical models in many areas of applied mathematics, physics, thermomechanics, electrical engineering, thermophysics when studying the thermal reaction of solids based on the generalized phenomenology of Maxwell – Cattaneo – Lykov – Vernott, taking into account the finite speed of heat propagation. The main problem that arises when finding the originals of complex operational images is the identification of the Heaviside step function in the original, which does not formally follow from the rules of operational calculus. At the same time, the studied generalized models of analytical thermophysics are necessary to study the thermal response of relatively new consolidated structure-sensitive polymer materials in structures subject to high-intensity external influences. The originals obtained in the article can be used in the general methodology for constructing and applying various mathematical models in a wide range of external influences on modern structural materials.

Keywords:

hyperbolic models of locally nonequilibrium heat transfer, surgical images, heaviside function, originals

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