Abstract
Practically important problems of non-stationary heat conduction for hyperbolic transport models are considered. An analytical approach based on contour integration of operational solutions of hyperbolic models is developed. This leads to new integral relationships convenient for numerical experiments. The equivalence of new functional constructions and known analytical solutions of this class of problems is shown. On the basis of the obtained relations, the wave character of the nonstationary thermal conductivity is described taking into account the finite velocity of heat propagation. The jumps at the front of the heat wave are calculated. The proposed approach gives effective results when studying the thermal reaction to heating or cooling regions bounded from within by a flat surface, either a cylindrical cavity or a spherical surface.
Highlights
Important problems of non-stationary heat conduction for hyperbolic transport models are considered
An analytical approach based on contour integration of operational solutions of hyperbolic models is developed
This leads to new integral relationships convenient for numerical experiments
Summary
Important problems of non-stationary heat conduction for hyperbolic transport models are considered. ANALYTICAL SOLUTIONS OF HYPERBOLIC MODELS OF NON-STATIONARY HEAT CONDUCTION Moscow Technological University (M.V. Lomonosov Institute of Fine Chemical Technologies), Moscow 119571, Russia @ Corresponding author e-mail: kartashov@mitht.ru An analytical approach based on contour integration of operational solutions of hyperbolic models is developed.
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