Method for splitting integral transformation in problems of complex heat transfer
https://doi.org/10.32362/2500-316X-2025-13-6-104-115
EDN: NGHUVB
Abstract
Objectives. This paper presents the development of a rather rare method for splitting the integral Fourier–Hankel transform when finding an exact analytical solution to the generalized third boundary value problem of complex heat transfer, where both the heat transfer coefficient and ambient temperature vary in time. The generalization lies in the simultaneous consideration of the problem in three different coordinate systems: Cartesian (a half-space bounded by a flat surface), cylindrical (a space bounded by a cylindrical cavity from the inside), and spherical (a space bounded by a spherical cavity from the inside). The aim was to develop a method for splitting the integral transformation as applied to finding an exact analytical solution to a generalized model problem of non-stationary thermal conductivity of complex heat exchange with an arbitrary dependence of the heat exchange coefficient and ambient temperature on time.
Methods. The generalized integral transformation developed for these purposes is used simultaneously in three coordinate systems, and the method for its splitting is applied to the problem of complex heat transfer.
Results. Initially, a special mathematical apparatus constituting a generalized integral Fourier–Hankel transform for three coordinate systems simultaneously was developed. For comparison, in the literature, such a transformation is formulated, as a rule, separately for each coordinate system. The availability of this mathematical apparatus made it possible to develop a method for its splitting and to obtain an exact analytical solution to the third boundary value problem for nonstationary thermal conductivity in complex heat transfer, simultaneously for all three coordinate systems. To illustrate this, a specific case in Cartesian coordinates was considered and a rapid growth of the Picard process was established.
Conclusions. Based on the developed special mathematical apparatus, an exact analytical solution to the generalized third boundary value problem of heat conductivity with time-varying heat transfer coefficient and ambient temperature, simultaneously in three coordinate systems, was obtained. These results constitute the scientific novelty of the work and represent a significant contribution to analytical thermal physics.
About the Author
E. M. Kartashov
MIREA – Russian Technological University
Russian Federation
Competing Interests:
Russian Federation
Eduard M. Kartashov, Dr. Sci. (Phys.-Math.), Honored Scientist of the Russian Federation, Honorary Worker of Higher Professional Education of the Russian Federation, Honorary Worker of Science and Technology of the Russian Federation, Honorary Professor of the Lomonosov Moscow State University of Fine Chemical Technology, Laureate of the Golden Medal of the Academy of Sciences of Belarus in Thermophysics, Professor, Department of Higher and Applied Mathematics, M.V. Lomonosov Institute of Fine Chemical Technologies
78, Vernadskogo pr., Moscow, 119454
Scopus Author ID 7004134344
ResearcherID Q-9572-2016
Competing Interests:
The author declares no conflicts of interest.
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For citations:
Kartashov E.M. Method for splitting integral transformation in problems of complex heat transfer. Russian Technological Journal. 2025;13(6):104-115. https://doi.org/10.32362/2500-316X-2025-13-6-104-115. EDN: NGHUVB
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