Modification of the generalized Tikhonov - Samarsky heat potentials in the analytical theory of nonstationary heat transfer for non-cylindrical regions

Аuthors

Kartashov E. M.^{1, 2*}, Krylov S. S.^3**

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
3. ,

*e-mail: professor.kartashov@qmail.com
**e-mail: krylov@mai.ru

Abstract

A modification of the method of generalized thermal potentials is developed as applied to the boundary value problems solution of nonstationary heat conduction in a domain with a boundary uniformly moving in time. The classical approach to finding the unknown potential density from the boundary condition of the problem involves solving the corresponding Volterra integral equation of the second kind for partially bounded domains or a system of equations for finite domains. The modified approach consists in preliminary finding the operational form of the potential and identifying the operational density of the potential to be found. Due to this approach, analytical solutions to the heat conduction problems are of the simplest functional form, convenient for numerical experiments. The authors considered a series of specific illustrative problems of non-stationary heat conduction of a practical nature, and described a new effect of the thermally insulated moving boundary impact on the thermal response of a non-cylindrical region. An assumption is made on the transition of the kinetic energy of a moving thermally insulated boundary into the thermal energy of the region.

Keywords:

generalized thermal potentials, noncylindrical regions, analytical solutions

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