Analytical solutions to complex heat transfer problems


Аuthors

Kartashov E. M.1*, Krylov S. S.2, Nenakhov E. V.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: kartashov@mitht.ru
**e-mail: newnew94@mail.ru

Abstract

The article is devoted to the development of a rather rare method of splitting the Fourier-Hankel integral transform when finding an exact analytical solution to a generalized third boundary value problem with a time-varying heat transfer coefficient and a time-varying ambient temperature (dT / dn)|г = h(t)[Tг - Tc(t)], t>0. Such cases in analytical thermal physics are related to complex heat transfer. The generalization consists in the fact that the original problem is considered simultaneously in three coordinate systems: Cartesian (a half-space bounded by a flat surface), cylindrical (a space bounded from within by a cylindrical cavity), and spherical (a space bounded from within by a spherical cavity). A generalized integral transform developed for these purposes simultaneously in three coordinate systems and a method of splitting it are used as applied to the problem of complex heat transfer. As an illustration, a special case in Cartesian coordinates is considered and a rapid growth of the Picard process is established.

Based on the developed special mathematical apparatus, an exact analytical solution is obtained for the generalized third boundary value problem of thermal conductivity with time-varying heat transfer coefficient and ambient temperature simultaneously in three coordinate systems. The obtained results constitute the scientific novelty of the work and are new in analytical thermal physics.

Keywords:

generalized integral transform, splitting method, analytical solution of a heat problem, non-stationary heat exchange problem, complex heat exchange

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